http://www.physicsbook.gatech.edu/api.php?action=feedcontributions&feedformat=atom&user=Jshah46 2026-05-06T00:14:07Z User contributions MediaWiki 1.42.7 http://www.physicsbook.gatech.edu/index.php?title=Polarization_of_a_conductor&diff=23111 2016-04-18T03:16:23Z

<p>Jshah46: /* Mobile Electron Sea */</p> <hr /> <div><br /> ==The Main Idea==<br /> <br /> Based on the definition of a conductor, it is easily assumed that stronger conductors can have charged particles moving more freely within it and in larger distances. There are two main situations where this can be observed. The first is in ionic solutions:<br /> <br /> ===Ionic Solutions===<br /> <br /> Ionic solutions, such as KCl or NaCl or NaI (solutions in which the ions dissociate), have individual ions of the dissociated particles. For example, a solution of NaI will have Na+, I-, and because it is an aqueous solution, some H+ and OH- as well. When an electric field is applied to this solution, the particles (as you'd imagine) move in the direction of the force applied by the electric field. However, the interesting concept here is that the charged particles move in a direction and accumulate, therefore creating a charge gradient, '''which in turn creates its own electric field!''' This can be shown in Figure 1, taken from the textbook. While ions are constantly moving, this is an accurate snapshot of what would be expected in the event of applied field/force. Furthermore, while ions move around the solution at all times (it is a conductor after all), there is a measurable excess of ions on the edges that generates the field. <br /> <br /> '''The net electric field is the superposition of the applied field and the field generated by the charge gradient and excess ion concentrations on the edges.'''<br /> <br /> [[File:Shah1.jpg]]<br /> <br /> Figure taken from Matter and Interactions 4th Edition<br /> <br /> ====A Mathematical Model: Drift Speed====<br /> <br /> In the phenomenon described above, when the external field is applied on an ionic solution, the Na+ and I- ions will move and bounce around a good bit, but due to collisions, they do not maintain a specific speed or trajectory. This is in spite of whether or not the force experienced is constant. In order to keep the ions moving at constant speed, also known as the drift speed, a constant electric field must be applied. This is modeled mathematically using the following equation: <br /> <br /> '''v = u*Enet''' <br /> <br /> where v is the drift speed, u is the mobility of the charge ((m/s)/(N/C)), and Enet is the net electric field applied to the ionic solution. The proportionality constant, u, is determined for the ions based on the solution and will be usually given or easy to derive in all practical problem sets using this concept. This is a linear relationship overall, meaning that in the event of no electric field, the ions will stop moving. <br /> <br /> ====Polarization Process in Ionic Solution====<br /> <br /> While polarization is a rapid process once initiated, it is not an on-off binary process. The instant that an electric field is applied, the drift speed is nonzero and the particles start tending towards the direction of the electric field. As ions pile up on the sides of the solution, the electric field inside becomes weaker and the system approaches an equilibrium at a microscopic level. At this equilibrium, drift speed is 0 and there is no NET MOTION of mobile charges in solution<br /> <br /> ===Charge Motion in Metals===<br /> <br /> The second example to look at for conductors is in metals.<br /> <br /> ====Mobile Electron Sea====<br /> <br /> Metals are an interesting idea structurally. Atoms of a metal are arranged in a rigid, ordered structure, sometimes known as a lattice structure (similar to crystal). Due to this, there is a interesting pattern of behavior. The inner electrons of each of these ordered atoms are attracted to the positively charged nucleus. Some of the outer electrons engage in solid atom interactions (ball and spring model), but other outer electrons participate in a pool of electrons that is allowed to move freely across the solid, in an &quot;electron sea&quot;. While they can move across the solid, they are very hard to extract and there are obviously some limitations to its direction of movement (different from liquid ionic solutions), but the mobile electron sea makes metals great conductor candidates (and thus are used in so many practical applications, including wires, microchips, cars, etc.) <br /> <br /> There is a caveat to this, however. You may ask, well won't the electrons repel each other and this not really allow for movement? Yes, but due to the presence of the positive cores, this interaction is neutralized. There is, therefore, no net interaction between the electrons inside a metal. Thus, the sea electrons move freely independent of electron field, positive cores, and appear not to interact with each other. The model of electron motion is defined by the Drude model, the steps of which are shown here:<br /> <br /> 1) When an electric field is applied in a metal, the electrons get excited and accelerate.<br /> <br /> 2) The electrons lose their energy when they collide with the lattices of the positive atomic cores<br /> <br /> 3) After the collision, the electrons again get accelerated and the entire process repeats itself. <br /> <br /> [[File:Shah2.JPG]]<br /> <br /> Figure taken from Matter and Interactions 4th Edition<br /> <br /> The average speed, then is defined by v, the drift speed, as mentioned earlier. For metals this equation is:<br /> <br /> '''v = (e*Enet*deltaT)/(m)'''<br /> <br /> where v is the drift speed, e is the charge of the electron, Enet is the net applied electric field, deltaT is the average time between collisions, and m is the mass of the electron. The average time between collisions is used because the time between each collision is uncontrollable and inconsistent. This equation is derived from the momentum equation where p = F*deltaT and F = Enet*e.<br /> <br /> This YouTube video does an excellent job of explaining the concept in further detail:<br /> <br /> https://www.youtube.com/watch?v=HKgOpmX-OFI<br /> <br /> ==Examples==<br /> <br /> ===Simple===<br /> <br /> The mobility of electrons in copper is 4.5E-3 (m/s)/(N/C). How much net electric field would be needed in order to give the electrons in copper a drift speed of 1.5E-3 m/s?<br /> <br /> ====Solution====<br /> <br /> This is a simple problem using the formula given for drift speed <br /> <br /> '''v = u*Enet''' <br /> <br /> Thus, Enet = v/u = 1.5E-3/4.5E-3 = 0.333 N/C. <br /> <br /> This also makes sense from a units perspective, as our solution is in N/C, the speed is m/s, and the mobility is given in (m/s)/(N/C). <br /> <br /> ===Middling===<br /> <br /> In a simple metal lattice structure, an electric field of 10 N/C is applied and 15 collisions are observed. The time between collisions increases after each collision, starting with 1 second, from collision 1 to collision 2. After 15 collisions, what is the drift speed of an electron in this metal lattice structure? <br /> <br /> ====Solution====<br /> <br /> This is a slightly more complex problem that requires a bit of analytical thinking and application of a formula. The formula:<br /> <br /> '''v = (e*Enet*deltaT)/(m)'''<br /> <br /> All of the quantities are known. e = 1.6E-19 C, Enet = 10 N/C, m = 9.1E-31<br /> <br /> However, deltaT is not immediately discernible. The question asks for the drift speed after 15 collisions. It might be some people's thought to just use the time between the 14th and 15th collision as the deltaT in the equation. DeltaT refers to the AVERAGE time between collisions. In this case, the deltaT would therefore be 7.5 seconds. <br /> <br /> Plugging these numbers in, you get: 1.3E13 m/s. This is extremely fast. As you can see, this speaks to how quickly electrons move through substances and how quickly polarization occurs, both in metals and in ionic solutions. <br /> <br /> ===Difficult===<br /> <br /> Summarize the difference between conductors and insulators in the following 4 categories:<br /> <br /> Mobile Charges<br /> Polarization<br /> Equilibrium<br /> Excess Charge<br /> <br /> ====Solution====<br /> <br /> 1) Conductors have mobile charges while insulators do not<br /> <br /> 2) Sea or mass of mobile electrons move when electric field is applied to a conductor. When an electric field is applied to an insulator, INDIVIDUAL atoms polarize. <br /> <br /> 3) Net electric field is 0 in a conductor at equilibrium whereas there is a nonzero electric field in an insulator at equilibrium. <br /> <br /> 4) Excess charge spreads over the surface of a conductor but clumps in patches in an insulator. <br /> <br /> (Adapted from textbook)<br /> <br /> ==Real World Application==<br /> <br /> While this isn't exactly related to conductors (the exact opposite, actually), this is a very important concept in polarization. As mentioned earlier, when a conductor is polarized, electron seas move rapidly and cause polarization. When an insulator has an applied electric field, the individual atoms or molecules become polarized. An interesting aspect of this is the concept of dielectric. A dielectric is a material or substance that is usually an insulator, but when an electric field is applied, the electrons shift slightly from their usual equilibrium creating a positive and negative space and thus, polarization. Usually, a dielectric is a material with EXTREMELY HIGH polarizability, which is extremely useful in the real world. The concept was developed by William Wheewell during a discussion with Michael Faraday. Diaelectrics are commonly used in developing capacitors.<br /> <br /> == See also ==<br /> <br /> ===External links===<br /> YouTube Video: [https://www.youtube.com/watch?v=HKgOpmX-OFI]<br /> <br /> IEEE Report: [http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=6507323]<br /> <br /> ==References==<br /> <br /> Matter and Interactions 4th Edition by Chabay and Sherwood<br /> <br /> [[Category:Textbook]]</div>

Jshah46 http://www.physicsbook.gatech.edu/index.php?title=Polarization_of_a_conductor&diff=23110 2016-04-18T03:16:10Z

<p>Jshah46: /* Ionic Solutions */</p> <hr /> <div><br /> ==The Main Idea==<br /> <br /> Based on the definition of a conductor, it is easily assumed that stronger conductors can have charged particles moving more freely within it and in larger distances. There are two main situations where this can be observed. The first is in ionic solutions:<br /> <br /> ===Ionic Solutions===<br /> <br /> Ionic solutions, such as KCl or NaCl or NaI (solutions in which the ions dissociate), have individual ions of the dissociated particles. For example, a solution of NaI will have Na+, I-, and because it is an aqueous solution, some H+ and OH- as well. When an electric field is applied to this solution, the particles (as you'd imagine) move in the direction of the force applied by the electric field. However, the interesting concept here is that the charged particles move in a direction and accumulate, therefore creating a charge gradient, '''which in turn creates its own electric field!''' This can be shown in Figure 1, taken from the textbook. While ions are constantly moving, this is an accurate snapshot of what would be expected in the event of applied field/force. Furthermore, while ions move around the solution at all times (it is a conductor after all), there is a measurable excess of ions on the edges that generates the field. <br /> <br /> '''The net electric field is the superposition of the applied field and the field generated by the charge gradient and excess ion concentrations on the edges.'''<br /> <br /> [[File:Shah1.jpg]]<br /> <br /> Figure taken from Matter and Interactions 4th Edition<br /> <br /> ====A Mathematical Model: Drift Speed====<br /> <br /> In the phenomenon described above, when the external field is applied on an ionic solution, the Na+ and I- ions will move and bounce around a good bit, but due to collisions, they do not maintain a specific speed or trajectory. This is in spite of whether or not the force experienced is constant. In order to keep the ions moving at constant speed, also known as the drift speed, a constant electric field must be applied. This is modeled mathematically using the following equation: <br /> <br /> '''v = u*Enet''' <br /> <br /> where v is the drift speed, u is the mobility of the charge ((m/s)/(N/C)), and Enet is the net electric field applied to the ionic solution. The proportionality constant, u, is determined for the ions based on the solution and will be usually given or easy to derive in all practical problem sets using this concept. This is a linear relationship overall, meaning that in the event of no electric field, the ions will stop moving. <br /> <br /> ====Polarization Process in Ionic Solution====<br /> <br /> While polarization is a rapid process once initiated, it is not an on-off binary process. The instant that an electric field is applied, the drift speed is nonzero and the particles start tending towards the direction of the electric field. As ions pile up on the sides of the solution, the electric field inside becomes weaker and the system approaches an equilibrium at a microscopic level. At this equilibrium, drift speed is 0 and there is no NET MOTION of mobile charges in solution<br /> <br /> ===Charge Motion in Metals===<br /> <br /> The second example to look at for conductors is in metals.<br /> <br /> ====Mobile Electron Sea====<br /> <br /> Metals are an interesting idea structurally. Atoms of a metal are arranged in a rigid, ordered structure, sometimes known as a lattice structure (similar to crystal). Due to this, there is a interesting pattern of behavior. The inner electrons of each of these ordered atoms are attracted to the positively charged nucleus. Some of the outer electrons engage in solid atom interactions (ball and spring model), but other outer electrons participate in a pool of electrons that is allowed to move freely across the solid, in an &quot;electron sea&quot;. While they can move across the solid, they are very hard to extract and there are obviously some limitations to its direction of movement (different from liquid ionic solutions), but the mobile electron sea makes metals great conductor candidates (and thus are used in so many practical applications, including wires, microchips, cars, etc.) <br /> <br /> There is a caveat to this, however. You may ask, well won't the electrons repel each other and this not really allow for movement? Yes, but due to the presence of the positive cores, this interaction is neutralized. There is, therefore, no net interaction between the electrons inside a metal. Thus, the sea electrons move freely independent of electron field, positive cores, and appear not to interact with each other. The model of electron motion is defined by the Drude model, the steps of which are shown here:<br /> <br /> 1) When an electric field is applied in a metal, the electrons get excited and accelerate.<br /> <br /> 2) The electrons lose their energy when they collide with the lattices of the positive atomic cores<br /> <br /> 3) After the collision, the electrons again get accelerated and the entire process repeats itself. <br /> <br /> [[File:Shah2.JPG]]<br /> <br /> The average speed, then is defined by v, the drift speed, as mentioned earlier. For metals this equation is:<br /> <br /> '''v = (e*Enet*deltaT)/(m)'''<br /> <br /> where v is the drift speed, e is the charge of the electron, Enet is the net applied electric field, deltaT is the average time between collisions, and m is the mass of the electron. The average time between collisions is used because the time between each collision is uncontrollable and inconsistent. This equation is derived from the momentum equation where p = F*deltaT and F = Enet*e.<br /> <br /> This YouTube video does an excellent job of explaining the concept in further detail:<br /> <br /> https://www.youtube.com/watch?v=HKgOpmX-OFI<br /> <br /> ==Examples==<br /> <br /> ===Simple===<br /> <br /> The mobility of electrons in copper is 4.5E-3 (m/s)/(N/C). How much net electric field would be needed in order to give the electrons in copper a drift speed of 1.5E-3 m/s?<br /> <br /> ====Solution====<br /> <br /> This is a simple problem using the formula given for drift speed <br /> <br /> '''v = u*Enet''' <br /> <br /> Thus, Enet = v/u = 1.5E-3/4.5E-3 = 0.333 N/C. <br /> <br /> This also makes sense from a units perspective, as our solution is in N/C, the speed is m/s, and the mobility is given in (m/s)/(N/C). <br /> <br /> ===Middling===<br /> <br /> In a simple metal lattice structure, an electric field of 10 N/C is applied and 15 collisions are observed. The time between collisions increases after each collision, starting with 1 second, from collision 1 to collision 2. After 15 collisions, what is the drift speed of an electron in this metal lattice structure? <br /> <br /> ====Solution====<br /> <br /> This is a slightly more complex problem that requires a bit of analytical thinking and application of a formula. The formula:<br /> <br /> '''v = (e*Enet*deltaT)/(m)'''<br /> <br /> All of the quantities are known. e = 1.6E-19 C, Enet = 10 N/C, m = 9.1E-31<br /> <br /> However, deltaT is not immediately discernible. The question asks for the drift speed after 15 collisions. It might be some people's thought to just use the time between the 14th and 15th collision as the deltaT in the equation. DeltaT refers to the AVERAGE time between collisions. In this case, the deltaT would therefore be 7.5 seconds. <br /> <br /> Plugging these numbers in, you get: 1.3E13 m/s. This is extremely fast. As you can see, this speaks to how quickly electrons move through substances and how quickly polarization occurs, both in metals and in ionic solutions. <br /> <br /> ===Difficult===<br /> <br /> Summarize the difference between conductors and insulators in the following 4 categories:<br /> <br /> Mobile Charges<br /> Polarization<br /> Equilibrium<br /> Excess Charge<br /> <br /> ====Solution====<br /> <br /> 1) Conductors have mobile charges while insulators do not<br /> <br /> 2) Sea or mass of mobile electrons move when electric field is applied to a conductor. When an electric field is applied to an insulator, INDIVIDUAL atoms polarize. <br /> <br /> 3) Net electric field is 0 in a conductor at equilibrium whereas there is a nonzero electric field in an insulator at equilibrium. <br /> <br /> 4) Excess charge spreads over the surface of a conductor but clumps in patches in an insulator. <br /> <br /> (Adapted from textbook)<br /> <br /> ==Real World Application==<br /> <br /> While this isn't exactly related to conductors (the exact opposite, actually), this is a very important concept in polarization. As mentioned earlier, when a conductor is polarized, electron seas move rapidly and cause polarization. When an insulator has an applied electric field, the individual atoms or molecules become polarized. An interesting aspect of this is the concept of dielectric. A dielectric is a material or substance that is usually an insulator, but when an electric field is applied, the electrons shift slightly from their usual equilibrium creating a positive and negative space and thus, polarization. Usually, a dielectric is a material with EXTREMELY HIGH polarizability, which is extremely useful in the real world. The concept was developed by William Wheewell during a discussion with Michael Faraday. Diaelectrics are commonly used in developing capacitors.<br /> <br /> == See also ==<br /> <br /> ===External links===<br /> YouTube Video: [https://www.youtube.com/watch?v=HKgOpmX-OFI]<br /> <br /> IEEE Report: [http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=6507323]<br /> <br /> ==References==<br /> <br /> Matter and Interactions 4th Edition by Chabay and Sherwood<br /> <br /> [[Category:Textbook]]</div>

Jshah46 http://www.physicsbook.gatech.edu/index.php?title=Polarization_of_a_conductor&diff=23102 2016-04-18T03:14:33Z

<p>Jshah46: /* References */</p> <hr /> <div><br /> ==The Main Idea==<br /> <br /> Based on the definition of a conductor, it is easily assumed that stronger conductors can have charged particles moving more freely within it and in larger distances. There are two main situations where this can be observed. The first is in ionic solutions:<br /> <br /> ===Ionic Solutions===<br /> <br /> Ionic solutions, such as KCl or NaCl or NaI (solutions in which the ions dissociate), have individual ions of the dissociated particles. For example, a solution of NaI will have Na+, I-, and because it is an aqueous solution, some H+ and OH- as well. When an electric field is applied to this solution, the particles (as you'd imagine) move in the direction of the force applied by the electric field. However, the interesting concept here is that the charged particles move in a direction and accumulate, therefore creating a charge gradient, '''which in turn creates its own electric field!''' This can be shown in Figure 1, taken from the textbook. While ions are constantly moving, this is an accurate snapshot of what would be expected in the event of applied field/force. Furthermore, while ions move around the solution at all times (it is a conductor after all), there is a measurable excess of ions on the edges that generates the field. <br /> <br /> '''The net electric field is the superposition of the applied field and the field generated by the charge gradient and excess ion concentrations on the edges.'''<br /> <br /> [[File:Shah1.jpg]]<br /> <br /> ====A Mathematical Model: Drift Speed====<br /> <br /> In the phenomenon described above, when the external field is applied on an ionic solution, the Na+ and I- ions will move and bounce around a good bit, but due to collisions, they do not maintain a specific speed or trajectory. This is in spite of whether or not the force experienced is constant. In order to keep the ions moving at constant speed, also known as the drift speed, a constant electric field must be applied. This is modeled mathematically using the following equation: <br /> <br /> '''v = u*Enet''' <br /> <br /> where v is the drift speed, u is the mobility of the charge ((m/s)/(N/C)), and Enet is the net electric field applied to the ionic solution. The proportionality constant, u, is determined for the ions based on the solution and will be usually given or easy to derive in all practical problem sets using this concept. This is a linear relationship overall, meaning that in the event of no electric field, the ions will stop moving. <br /> <br /> ====Polarization Process in Ionic Solution====<br /> <br /> While polarization is a rapid process once initiated, it is not an on-off binary process. The instant that an electric field is applied, the drift speed is nonzero and the particles start tending towards the direction of the electric field. As ions pile up on the sides of the solution, the electric field inside becomes weaker and the system approaches an equilibrium at a microscopic level. At this equilibrium, drift speed is 0 and there is no NET MOTION of mobile charges in solution<br /> <br /> ===Charge Motion in Metals===<br /> <br /> The second example to look at for conductors is in metals.<br /> <br /> ====Mobile Electron Sea====<br /> <br /> Metals are an interesting idea structurally. Atoms of a metal are arranged in a rigid, ordered structure, sometimes known as a lattice structure (similar to crystal). Due to this, there is a interesting pattern of behavior. The inner electrons of each of these ordered atoms are attracted to the positively charged nucleus. Some of the outer electrons engage in solid atom interactions (ball and spring model), but other outer electrons participate in a pool of electrons that is allowed to move freely across the solid, in an &quot;electron sea&quot;. While they can move across the solid, they are very hard to extract and there are obviously some limitations to its direction of movement (different from liquid ionic solutions), but the mobile electron sea makes metals great conductor candidates (and thus are used in so many practical applications, including wires, microchips, cars, etc.) <br /> <br /> There is a caveat to this, however. You may ask, well won't the electrons repel each other and this not really allow for movement? Yes, but due to the presence of the positive cores, this interaction is neutralized. There is, therefore, no net interaction between the electrons inside a metal. Thus, the sea electrons move freely independent of electron field, positive cores, and appear not to interact with each other. The model of electron motion is defined by the Drude model, the steps of which are shown here:<br /> <br /> 1) When an electric field is applied in a metal, the electrons get excited and accelerate.<br /> <br /> 2) The electrons lose their energy when they collide with the lattices of the positive atomic cores<br /> <br /> 3) After the collision, the electrons again get accelerated and the entire process repeats itself. <br /> <br /> [[File:Shah2.JPG]]<br /> <br /> The average speed, then is defined by v, the drift speed, as mentioned earlier. For metals this equation is:<br /> <br /> '''v = (e*Enet*deltaT)/(m)'''<br /> <br /> where v is the drift speed, e is the charge of the electron, Enet is the net applied electric field, deltaT is the average time between collisions, and m is the mass of the electron. The average time between collisions is used because the time between each collision is uncontrollable and inconsistent. This equation is derived from the momentum equation where p = F*deltaT and F = Enet*e.<br /> <br /> This YouTube video does an excellent job of explaining the concept in further detail:<br /> <br /> https://www.youtube.com/watch?v=HKgOpmX-OFI<br /> <br /> ==Examples==<br /> <br /> ===Simple===<br /> <br /> The mobility of electrons in copper is 4.5E-3 (m/s)/(N/C). How much net electric field would be needed in order to give the electrons in copper a drift speed of 1.5E-3 m/s?<br /> <br /> ====Solution====<br /> <br /> This is a simple problem using the formula given for drift speed <br /> <br /> '''v = u*Enet''' <br /> <br /> Thus, Enet = v/u = 1.5E-3/4.5E-3 = 0.333 N/C. <br /> <br /> This also makes sense from a units perspective, as our solution is in N/C, the speed is m/s, and the mobility is given in (m/s)/(N/C). <br /> <br /> ===Middling===<br /> <br /> In a simple metal lattice structure, an electric field of 10 N/C is applied and 15 collisions are observed. The time between collisions increases after each collision, starting with 1 second, from collision 1 to collision 2. After 15 collisions, what is the drift speed of an electron in this metal lattice structure? <br /> <br /> ====Solution====<br /> <br /> This is a slightly more complex problem that requires a bit of analytical thinking and application of a formula. The formula:<br /> <br /> '''v = (e*Enet*deltaT)/(m)'''<br /> <br /> All of the quantities are known. e = 1.6E-19 C, Enet = 10 N/C, m = 9.1E-31<br /> <br /> However, deltaT is not immediately discernible. The question asks for the drift speed after 15 collisions. It might be some people's thought to just use the time between the 14th and 15th collision as the deltaT in the equation. DeltaT refers to the AVERAGE time between collisions. In this case, the deltaT would therefore be 7.5 seconds. <br /> <br /> Plugging these numbers in, you get: 1.3E13 m/s. This is extremely fast. As you can see, this speaks to how quickly electrons move through substances and how quickly polarization occurs, both in metals and in ionic solutions. <br /> <br /> ===Difficult===<br /> <br /> Summarize the difference between conductors and insulators in the following 4 categories:<br /> <br /> Mobile Charges<br /> Polarization<br /> Equilibrium<br /> Excess Charge<br /> <br /> ====Solution====<br /> <br /> 1) Conductors have mobile charges while insulators do not<br /> <br /> 2) Sea or mass of mobile electrons move when electric field is applied to a conductor. When an electric field is applied to an insulator, INDIVIDUAL atoms polarize. <br /> <br /> 3) Net electric field is 0 in a conductor at equilibrium whereas there is a nonzero electric field in an insulator at equilibrium. <br /> <br /> 4) Excess charge spreads over the surface of a conductor but clumps in patches in an insulator. <br /> <br /> (Adapted from textbook)<br /> <br /> ==Real World Application==<br /> <br /> While this isn't exactly related to conductors (the exact opposite, actually), this is a very important concept in polarization. As mentioned earlier, when a conductor is polarized, electron seas move rapidly and cause polarization. When an insulator has an applied electric field, the individual atoms or molecules become polarized. An interesting aspect of this is the concept of dielectric. A dielectric is a material or substance that is usually an insulator, but when an electric field is applied, the electrons shift slightly from their usual equilibrium creating a positive and negative space and thus, polarization. Usually, a dielectric is a material with EXTREMELY HIGH polarizability, which is extremely useful in the real world. The concept was developed by William Wheewell during a discussion with Michael Faraday. Diaelectrics are commonly used in developing capacitors.<br /> <br /> == See also ==<br /> <br /> ===External links===<br /> YouTube Video: [https://www.youtube.com/watch?v=HKgOpmX-OFI]<br /> <br /> IEEE Report: [http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=6507323]<br /> <br /> ==References==<br /> <br /> Matter and Interactions 4th Edition by Chabay and Sherwood<br /> <br /> [[Category:Textbook]]</div>

Jshah46 http://www.physicsbook.gatech.edu/index.php?title=Polarization_of_a_conductor&diff=23099 2016-04-18T03:13:18Z

<p>Jshah46: /* See also */</p> <hr /> <div><br /> ==The Main Idea==<br /> <br /> Based on the definition of a conductor, it is easily assumed that stronger conductors can have charged particles moving more freely within it and in larger distances. There are two main situations where this can be observed. The first is in ionic solutions:<br /> <br /> ===Ionic Solutions===<br /> <br /> Ionic solutions, such as KCl or NaCl or NaI (solutions in which the ions dissociate), have individual ions of the dissociated particles. For example, a solution of NaI will have Na+, I-, and because it is an aqueous solution, some H+ and OH- as well. When an electric field is applied to this solution, the particles (as you'd imagine) move in the direction of the force applied by the electric field. However, the interesting concept here is that the charged particles move in a direction and accumulate, therefore creating a charge gradient, '''which in turn creates its own electric field!''' This can be shown in Figure 1, taken from the textbook. While ions are constantly moving, this is an accurate snapshot of what would be expected in the event of applied field/force. Furthermore, while ions move around the solution at all times (it is a conductor after all), there is a measurable excess of ions on the edges that generates the field. <br /> <br /> '''The net electric field is the superposition of the applied field and the field generated by the charge gradient and excess ion concentrations on the edges.'''<br /> <br /> [[File:Shah1.jpg]]<br /> <br /> ====A Mathematical Model: Drift Speed====<br /> <br /> In the phenomenon described above, when the external field is applied on an ionic solution, the Na+ and I- ions will move and bounce around a good bit, but due to collisions, they do not maintain a specific speed or trajectory. This is in spite of whether or not the force experienced is constant. In order to keep the ions moving at constant speed, also known as the drift speed, a constant electric field must be applied. This is modeled mathematically using the following equation: <br /> <br /> '''v = u*Enet''' <br /> <br /> where v is the drift speed, u is the mobility of the charge ((m/s)/(N/C)), and Enet is the net electric field applied to the ionic solution. The proportionality constant, u, is determined for the ions based on the solution and will be usually given or easy to derive in all practical problem sets using this concept. This is a linear relationship overall, meaning that in the event of no electric field, the ions will stop moving. <br /> <br /> ====Polarization Process in Ionic Solution====<br /> <br /> While polarization is a rapid process once initiated, it is not an on-off binary process. The instant that an electric field is applied, the drift speed is nonzero and the particles start tending towards the direction of the electric field. As ions pile up on the sides of the solution, the electric field inside becomes weaker and the system approaches an equilibrium at a microscopic level. At this equilibrium, drift speed is 0 and there is no NET MOTION of mobile charges in solution<br /> <br /> ===Charge Motion in Metals===<br /> <br /> The second example to look at for conductors is in metals.<br /> <br /> ====Mobile Electron Sea====<br /> <br /> Metals are an interesting idea structurally. Atoms of a metal are arranged in a rigid, ordered structure, sometimes known as a lattice structure (similar to crystal). Due to this, there is a interesting pattern of behavior. The inner electrons of each of these ordered atoms are attracted to the positively charged nucleus. Some of the outer electrons engage in solid atom interactions (ball and spring model), but other outer electrons participate in a pool of electrons that is allowed to move freely across the solid, in an &quot;electron sea&quot;. While they can move across the solid, they are very hard to extract and there are obviously some limitations to its direction of movement (different from liquid ionic solutions), but the mobile electron sea makes metals great conductor candidates (and thus are used in so many practical applications, including wires, microchips, cars, etc.) <br /> <br /> There is a caveat to this, however. You may ask, well won't the electrons repel each other and this not really allow for movement? Yes, but due to the presence of the positive cores, this interaction is neutralized. There is, therefore, no net interaction between the electrons inside a metal. Thus, the sea electrons move freely independent of electron field, positive cores, and appear not to interact with each other. The model of electron motion is defined by the Drude model, the steps of which are shown here:<br /> <br /> 1) When an electric field is applied in a metal, the electrons get excited and accelerate.<br /> <br /> 2) The electrons lose their energy when they collide with the lattices of the positive atomic cores<br /> <br /> 3) After the collision, the electrons again get accelerated and the entire process repeats itself. <br /> <br /> [[File:Shah2.JPG]]<br /> <br /> The average speed, then is defined by v, the drift speed, as mentioned earlier. For metals this equation is:<br /> <br /> '''v = (e*Enet*deltaT)/(m)'''<br /> <br /> where v is the drift speed, e is the charge of the electron, Enet is the net applied electric field, deltaT is the average time between collisions, and m is the mass of the electron. The average time between collisions is used because the time between each collision is uncontrollable and inconsistent. This equation is derived from the momentum equation where p = F*deltaT and F = Enet*e.<br /> <br /> This YouTube video does an excellent job of explaining the concept in further detail:<br /> <br /> https://www.youtube.com/watch?v=HKgOpmX-OFI<br /> <br /> ==Examples==<br /> <br /> ===Simple===<br /> <br /> The mobility of electrons in copper is 4.5E-3 (m/s)/(N/C). How much net electric field would be needed in order to give the electrons in copper a drift speed of 1.5E-3 m/s?<br /> <br /> ====Solution====<br /> <br /> This is a simple problem using the formula given for drift speed <br /> <br /> '''v = u*Enet''' <br /> <br /> Thus, Enet = v/u = 1.5E-3/4.5E-3 = 0.333 N/C. <br /> <br /> This also makes sense from a units perspective, as our solution is in N/C, the speed is m/s, and the mobility is given in (m/s)/(N/C). <br /> <br /> ===Middling===<br /> <br /> In a simple metal lattice structure, an electric field of 10 N/C is applied and 15 collisions are observed. The time between collisions increases after each collision, starting with 1 second, from collision 1 to collision 2. After 15 collisions, what is the drift speed of an electron in this metal lattice structure? <br /> <br /> ====Solution====<br /> <br /> This is a slightly more complex problem that requires a bit of analytical thinking and application of a formula. The formula:<br /> <br /> '''v = (e*Enet*deltaT)/(m)'''<br /> <br /> All of the quantities are known. e = 1.6E-19 C, Enet = 10 N/C, m = 9.1E-31<br /> <br /> However, deltaT is not immediately discernible. The question asks for the drift speed after 15 collisions. It might be some people's thought to just use the time between the 14th and 15th collision as the deltaT in the equation. DeltaT refers to the AVERAGE time between collisions. In this case, the deltaT would therefore be 7.5 seconds. <br /> <br /> Plugging these numbers in, you get: 1.3E13 m/s. This is extremely fast. As you can see, this speaks to how quickly electrons move through substances and how quickly polarization occurs, both in metals and in ionic solutions. <br /> <br /> ===Difficult===<br /> <br /> Summarize the difference between conductors and insulators in the following 4 categories:<br /> <br /> Mobile Charges<br /> Polarization<br /> Equilibrium<br /> Excess Charge<br /> <br /> ====Solution====<br /> <br /> 1) Conductors have mobile charges while insulators do not<br /> <br /> 2) Sea or mass of mobile electrons move when electric field is applied to a conductor. When an electric field is applied to an insulator, INDIVIDUAL atoms polarize. <br /> <br /> 3) Net electric field is 0 in a conductor at equilibrium whereas there is a nonzero electric field in an insulator at equilibrium. <br /> <br /> 4) Excess charge spreads over the surface of a conductor but clumps in patches in an insulator. <br /> <br /> (Adapted from textbook)<br /> <br /> ==Real World Application==<br /> <br /> While this isn't exactly related to conductors (the exact opposite, actually), this is a very important concept in polarization. As mentioned earlier, when a conductor is polarized, electron seas move rapidly and cause polarization. When an insulator has an applied electric field, the individual atoms or molecules become polarized. An interesting aspect of this is the concept of dielectric. A dielectric is a material or substance that is usually an insulator, but when an electric field is applied, the electrons shift slightly from their usual equilibrium creating a positive and negative space and thus, polarization. Usually, a dielectric is a material with EXTREMELY HIGH polarizability, which is extremely useful in the real world. The concept was developed by William Wheewell during a discussion with Michael Faraday. Diaelectrics are commonly used in developing capacitors.<br /> <br /> == See also ==<br /> <br /> ===External links===<br /> YouTube Video: [https://www.youtube.com/watch?v=HKgOpmX-OFI]<br /> <br /> IEEE Report: [http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=6507323]<br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Jshah46 http://www.physicsbook.gatech.edu/index.php?title=Polarization_of_a_conductor&diff=23091 2016-04-18T03:11:19Z

<p>Jshah46: /* History */</p> <hr /> <div><br /> ==The Main Idea==<br /> <br /> Based on the definition of a conductor, it is easily assumed that stronger conductors can have charged particles moving more freely within it and in larger distances. There are two main situations where this can be observed. The first is in ionic solutions:<br /> <br /> ===Ionic Solutions===<br /> <br /> Ionic solutions, such as KCl or NaCl or NaI (solutions in which the ions dissociate), have individual ions of the dissociated particles. For example, a solution of NaI will have Na+, I-, and because it is an aqueous solution, some H+ and OH- as well. When an electric field is applied to this solution, the particles (as you'd imagine) move in the direction of the force applied by the electric field. However, the interesting concept here is that the charged particles move in a direction and accumulate, therefore creating a charge gradient, '''which in turn creates its own electric field!''' This can be shown in Figure 1, taken from the textbook. While ions are constantly moving, this is an accurate snapshot of what would be expected in the event of applied field/force. Furthermore, while ions move around the solution at all times (it is a conductor after all), there is a measurable excess of ions on the edges that generates the field. <br /> <br /> '''The net electric field is the superposition of the applied field and the field generated by the charge gradient and excess ion concentrations on the edges.'''<br /> <br /> [[File:Shah1.jpg]]<br /> <br /> ====A Mathematical Model: Drift Speed====<br /> <br /> In the phenomenon described above, when the external field is applied on an ionic solution, the Na+ and I- ions will move and bounce around a good bit, but due to collisions, they do not maintain a specific speed or trajectory. This is in spite of whether or not the force experienced is constant. In order to keep the ions moving at constant speed, also known as the drift speed, a constant electric field must be applied. This is modeled mathematically using the following equation: <br /> <br /> '''v = u*Enet''' <br /> <br /> where v is the drift speed, u is the mobility of the charge ((m/s)/(N/C)), and Enet is the net electric field applied to the ionic solution. The proportionality constant, u, is determined for the ions based on the solution and will be usually given or easy to derive in all practical problem sets using this concept. This is a linear relationship overall, meaning that in the event of no electric field, the ions will stop moving. <br /> <br /> ====Polarization Process in Ionic Solution====<br /> <br /> While polarization is a rapid process once initiated, it is not an on-off binary process. The instant that an electric field is applied, the drift speed is nonzero and the particles start tending towards the direction of the electric field. As ions pile up on the sides of the solution, the electric field inside becomes weaker and the system approaches an equilibrium at a microscopic level. At this equilibrium, drift speed is 0 and there is no NET MOTION of mobile charges in solution<br /> <br /> ===Charge Motion in Metals===<br /> <br /> The second example to look at for conductors is in metals.<br /> <br /> ====Mobile Electron Sea====<br /> <br /> Metals are an interesting idea structurally. Atoms of a metal are arranged in a rigid, ordered structure, sometimes known as a lattice structure (similar to crystal). Due to this, there is a interesting pattern of behavior. The inner electrons of each of these ordered atoms are attracted to the positively charged nucleus. Some of the outer electrons engage in solid atom interactions (ball and spring model), but other outer electrons participate in a pool of electrons that is allowed to move freely across the solid, in an &quot;electron sea&quot;. While they can move across the solid, they are very hard to extract and there are obviously some limitations to its direction of movement (different from liquid ionic solutions), but the mobile electron sea makes metals great conductor candidates (and thus are used in so many practical applications, including wires, microchips, cars, etc.) <br /> <br /> There is a caveat to this, however. You may ask, well won't the electrons repel each other and this not really allow for movement? Yes, but due to the presence of the positive cores, this interaction is neutralized. There is, therefore, no net interaction between the electrons inside a metal. Thus, the sea electrons move freely independent of electron field, positive cores, and appear not to interact with each other. The model of electron motion is defined by the Drude model, the steps of which are shown here:<br /> <br /> 1) When an electric field is applied in a metal, the electrons get excited and accelerate.<br /> <br /> 2) The electrons lose their energy when they collide with the lattices of the positive atomic cores<br /> <br /> 3) After the collision, the electrons again get accelerated and the entire process repeats itself. <br /> <br /> [[File:Shah2.JPG]]<br /> <br /> The average speed, then is defined by v, the drift speed, as mentioned earlier. For metals this equation is:<br /> <br /> '''v = (e*Enet*deltaT)/(m)'''<br /> <br /> where v is the drift speed, e is the charge of the electron, Enet is the net applied electric field, deltaT is the average time between collisions, and m is the mass of the electron. The average time between collisions is used because the time between each collision is uncontrollable and inconsistent. This equation is derived from the momentum equation where p = F*deltaT and F = Enet*e.<br /> <br /> This YouTube video does an excellent job of explaining the concept in further detail:<br /> <br /> https://www.youtube.com/watch?v=HKgOpmX-OFI<br /> <br /> ==Examples==<br /> <br /> ===Simple===<br /> <br /> The mobility of electrons in copper is 4.5E-3 (m/s)/(N/C). How much net electric field would be needed in order to give the electrons in copper a drift speed of 1.5E-3 m/s?<br /> <br /> ====Solution====<br /> <br /> This is a simple problem using the formula given for drift speed <br /> <br /> '''v = u*Enet''' <br /> <br /> Thus, Enet = v/u = 1.5E-3/4.5E-3 = 0.333 N/C. <br /> <br /> This also makes sense from a units perspective, as our solution is in N/C, the speed is m/s, and the mobility is given in (m/s)/(N/C). <br /> <br /> ===Middling===<br /> <br /> In a simple metal lattice structure, an electric field of 10 N/C is applied and 15 collisions are observed. The time between collisions increases after each collision, starting with 1 second, from collision 1 to collision 2. After 15 collisions, what is the drift speed of an electron in this metal lattice structure? <br /> <br /> ====Solution====<br /> <br /> This is a slightly more complex problem that requires a bit of analytical thinking and application of a formula. The formula:<br /> <br /> '''v = (e*Enet*deltaT)/(m)'''<br /> <br /> All of the quantities are known. e = 1.6E-19 C, Enet = 10 N/C, m = 9.1E-31<br /> <br /> However, deltaT is not immediately discernible. The question asks for the drift speed after 15 collisions. It might be some people's thought to just use the time between the 14th and 15th collision as the deltaT in the equation. DeltaT refers to the AVERAGE time between collisions. In this case, the deltaT would therefore be 7.5 seconds. <br /> <br /> Plugging these numbers in, you get: 1.3E13 m/s. This is extremely fast. As you can see, this speaks to how quickly electrons move through substances and how quickly polarization occurs, both in metals and in ionic solutions. <br /> <br /> ===Difficult===<br /> <br /> Summarize the difference between conductors and insulators in the following 4 categories:<br /> <br /> Mobile Charges<br /> Polarization<br /> Equilibrium<br /> Excess Charge<br /> <br /> ====Solution====<br /> <br /> 1) Conductors have mobile charges while insulators do not<br /> <br /> 2) Sea or mass of mobile electrons move when electric field is applied to a conductor. When an electric field is applied to an insulator, INDIVIDUAL atoms polarize. <br /> <br /> 3) Net electric field is 0 in a conductor at equilibrium whereas there is a nonzero electric field in an insulator at equilibrium. <br /> <br /> 4) Excess charge spreads over the surface of a conductor but clumps in patches in an insulator. <br /> <br /> (Adapted from textbook)<br /> <br /> ==Real World Application==<br /> <br /> While this isn't exactly related to conductors (the exact opposite, actually), this is a very important concept in polarization. As mentioned earlier, when a conductor is polarized, electron seas move rapidly and cause polarization. When an insulator has an applied electric field, the individual atoms or molecules become polarized. An interesting aspect of this is the concept of dielectric. A dielectric is a material or substance that is usually an insulator, but when an electric field is applied, the electrons shift slightly from their usual equilibrium creating a positive and negative space and thus, polarization. Usually, a dielectric is a material with EXTREMELY HIGH polarizability, which is extremely useful in the real world. The concept was developed by William Wheewell during a discussion with Michael Faraday. Diaelectrics are commonly used in developing capacitors.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> [http://www.scientificamerican.com/article/bring-science-home-reaction-time/]<br /> <br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Jshah46 http://www.physicsbook.gatech.edu/index.php?title=Polarization_of_a_conductor&diff=23088 2016-04-18T03:10:38Z

<p>Jshah46: </p> <hr /> <div><br /> ==The Main Idea==<br /> <br /> Based on the definition of a conductor, it is easily assumed that stronger conductors can have charged particles moving more freely within it and in larger distances. There are two main situations where this can be observed. The first is in ionic solutions:<br /> <br /> ===Ionic Solutions===<br /> <br /> Ionic solutions, such as KCl or NaCl or NaI (solutions in which the ions dissociate), have individual ions of the dissociated particles. For example, a solution of NaI will have Na+, I-, and because it is an aqueous solution, some H+ and OH- as well. When an electric field is applied to this solution, the particles (as you'd imagine) move in the direction of the force applied by the electric field. However, the interesting concept here is that the charged particles move in a direction and accumulate, therefore creating a charge gradient, '''which in turn creates its own electric field!''' This can be shown in Figure 1, taken from the textbook. While ions are constantly moving, this is an accurate snapshot of what would be expected in the event of applied field/force. Furthermore, while ions move around the solution at all times (it is a conductor after all), there is a measurable excess of ions on the edges that generates the field. <br /> <br /> '''The net electric field is the superposition of the applied field and the field generated by the charge gradient and excess ion concentrations on the edges.'''<br /> <br /> [[File:Shah1.jpg]]<br /> <br /> ====A Mathematical Model: Drift Speed====<br /> <br /> In the phenomenon described above, when the external field is applied on an ionic solution, the Na+ and I- ions will move and bounce around a good bit, but due to collisions, they do not maintain a specific speed or trajectory. This is in spite of whether or not the force experienced is constant. In order to keep the ions moving at constant speed, also known as the drift speed, a constant electric field must be applied. This is modeled mathematically using the following equation: <br /> <br /> '''v = u*Enet''' <br /> <br /> where v is the drift speed, u is the mobility of the charge ((m/s)/(N/C)), and Enet is the net electric field applied to the ionic solution. The proportionality constant, u, is determined for the ions based on the solution and will be usually given or easy to derive in all practical problem sets using this concept. This is a linear relationship overall, meaning that in the event of no electric field, the ions will stop moving. <br /> <br /> ====Polarization Process in Ionic Solution====<br /> <br /> While polarization is a rapid process once initiated, it is not an on-off binary process. The instant that an electric field is applied, the drift speed is nonzero and the particles start tending towards the direction of the electric field. As ions pile up on the sides of the solution, the electric field inside becomes weaker and the system approaches an equilibrium at a microscopic level. At this equilibrium, drift speed is 0 and there is no NET MOTION of mobile charges in solution<br /> <br /> ===Charge Motion in Metals===<br /> <br /> The second example to look at for conductors is in metals.<br /> <br /> ====Mobile Electron Sea====<br /> <br /> Metals are an interesting idea structurally. Atoms of a metal are arranged in a rigid, ordered structure, sometimes known as a lattice structure (similar to crystal). Due to this, there is a interesting pattern of behavior. The inner electrons of each of these ordered atoms are attracted to the positively charged nucleus. Some of the outer electrons engage in solid atom interactions (ball and spring model), but other outer electrons participate in a pool of electrons that is allowed to move freely across the solid, in an &quot;electron sea&quot;. While they can move across the solid, they are very hard to extract and there are obviously some limitations to its direction of movement (different from liquid ionic solutions), but the mobile electron sea makes metals great conductor candidates (and thus are used in so many practical applications, including wires, microchips, cars, etc.) <br /> <br /> There is a caveat to this, however. You may ask, well won't the electrons repel each other and this not really allow for movement? Yes, but due to the presence of the positive cores, this interaction is neutralized. There is, therefore, no net interaction between the electrons inside a metal. Thus, the sea electrons move freely independent of electron field, positive cores, and appear not to interact with each other. The model of electron motion is defined by the Drude model, the steps of which are shown here:<br /> <br /> 1) When an electric field is applied in a metal, the electrons get excited and accelerate.<br /> <br /> 2) The electrons lose their energy when they collide with the lattices of the positive atomic cores<br /> <br /> 3) After the collision, the electrons again get accelerated and the entire process repeats itself. <br /> <br /> [[File:Shah2.JPG]]<br /> <br /> The average speed, then is defined by v, the drift speed, as mentioned earlier. For metals this equation is:<br /> <br /> '''v = (e*Enet*deltaT)/(m)'''<br /> <br /> where v is the drift speed, e is the charge of the electron, Enet is the net applied electric field, deltaT is the average time between collisions, and m is the mass of the electron. The average time between collisions is used because the time between each collision is uncontrollable and inconsistent. This equation is derived from the momentum equation where p = F*deltaT and F = Enet*e.<br /> <br /> This YouTube video does an excellent job of explaining the concept in further detail:<br /> <br /> https://www.youtube.com/watch?v=HKgOpmX-OFI<br /> <br /> ==Examples==<br /> <br /> ===Simple===<br /> <br /> The mobility of electrons in copper is 4.5E-3 (m/s)/(N/C). How much net electric field would be needed in order to give the electrons in copper a drift speed of 1.5E-3 m/s?<br /> <br /> ====Solution====<br /> <br /> This is a simple problem using the formula given for drift speed <br /> <br /> '''v = u*Enet''' <br /> <br /> Thus, Enet = v/u = 1.5E-3/4.5E-3 = 0.333 N/C. <br /> <br /> This also makes sense from a units perspective, as our solution is in N/C, the speed is m/s, and the mobility is given in (m/s)/(N/C). <br /> <br /> ===Middling===<br /> <br /> In a simple metal lattice structure, an electric field of 10 N/C is applied and 15 collisions are observed. The time between collisions increases after each collision, starting with 1 second, from collision 1 to collision 2. After 15 collisions, what is the drift speed of an electron in this metal lattice structure? <br /> <br /> ====Solution====<br /> <br /> This is a slightly more complex problem that requires a bit of analytical thinking and application of a formula. The formula:<br /> <br /> '''v = (e*Enet*deltaT)/(m)'''<br /> <br /> All of the quantities are known. e = 1.6E-19 C, Enet = 10 N/C, m = 9.1E-31<br /> <br /> However, deltaT is not immediately discernible. The question asks for the drift speed after 15 collisions. It might be some people's thought to just use the time between the 14th and 15th collision as the deltaT in the equation. DeltaT refers to the AVERAGE time between collisions. In this case, the deltaT would therefore be 7.5 seconds. <br /> <br /> Plugging these numbers in, you get: 1.3E13 m/s. This is extremely fast. As you can see, this speaks to how quickly electrons move through substances and how quickly polarization occurs, both in metals and in ionic solutions. <br /> <br /> ===Difficult===<br /> <br /> Summarize the difference between conductors and insulators in the following 4 categories:<br /> <br /> Mobile Charges<br /> Polarization<br /> Equilibrium<br /> Excess Charge<br /> <br /> ====Solution====<br /> <br /> 1) Conductors have mobile charges while insulators do not<br /> <br /> 2) Sea or mass of mobile electrons move when electric field is applied to a conductor. When an electric field is applied to an insulator, INDIVIDUAL atoms polarize. <br /> <br /> 3) Net electric field is 0 in a conductor at equilibrium whereas there is a nonzero electric field in an insulator at equilibrium. <br /> <br /> 4) Excess charge spreads over the surface of a conductor but clumps in patches in an insulator. <br /> <br /> (Adapted from textbook)<br /> <br /> ==Real World Application==<br /> <br /> While this isn't exactly related to conductors (the exact opposite, actually), this is a very important concept in polarization. As mentioned earlier, when a conductor is polarized, electron seas move rapidly and cause polarization. When an insulator has an applied electric field, the individual atoms or molecules become polarized. An interesting aspect of this is the concept of dielectric. A dielectric is a material or substance that is usually an insulator, but when an electric field is applied, the electrons shift slightly from their usual equilibrium creating a positive and negative space and thus, polarization. Usually, a dielectric is a material with EXTREMELY HIGH polarizability, which is extremely useful in the real world. The concept was developed by William Wheewell during a discussion with Michael Faraday. Diaelectrics are commonly used in developing capacitors.<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> [http://www.scientificamerican.com/article/bring-science-home-reaction-time/]<br /> <br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Jshah46 http://www.physicsbook.gatech.edu/index.php?title=Polarization_of_a_conductor&diff=23084 2016-04-18T03:09:14Z

<p>Jshah46: </p> <hr /> <div><br /> ==The Main Idea==<br /> <br /> Based on the definition of a conductor, it is easily assumed that stronger conductors can have charged particles moving more freely within it and in larger distances. There are two main situations where this can be observed. The first is in ionic solutions:<br /> <br /> ===Ionic Solutions===<br /> <br /> Ionic solutions, such as KCl or NaCl or NaI (solutions in which the ions dissociate), have individual ions of the dissociated particles. For example, a solution of NaI will have Na+, I-, and because it is an aqueous solution, some H+ and OH- as well. When an electric field is applied to this solution, the particles (as you'd imagine) move in the direction of the force applied by the electric field. However, the interesting concept here is that the charged particles move in a direction and accumulate, therefore creating a charge gradient, '''which in turn creates its own electric field!''' This can be shown in Figure 1, taken from the textbook. While ions are constantly moving, this is an accurate snapshot of what would be expected in the event of applied field/force. Furthermore, while ions move around the solution at all times (it is a conductor after all), there is a measurable excess of ions on the edges that generates the field. <br /> <br /> '''The net electric field is the superposition of the applied field and the field generated by the charge gradient and excess ion concentrations on the edges.'''<br /> <br /> [[File:Shah1.jpg]]<br /> <br /> ====A Mathematical Model: Drift Speed====<br /> <br /> In the phenomenon described above, when the external field is applied on an ionic solution, the Na+ and I- ions will move and bounce around a good bit, but due to collisions, they do not maintain a specific speed or trajectory. This is in spite of whether or not the force experienced is constant. In order to keep the ions moving at constant speed, also known as the drift speed, a constant electric field must be applied. This is modeled mathematically using the following equation: <br /> <br /> '''v = u*Enet''' <br /> <br /> where v is the drift speed, u is the mobility of the charge ((m/s)/(N/C)), and Enet is the net electric field applied to the ionic solution. The proportionality constant, u, is determined for the ions based on the solution and will be usually given or easy to derive in all practical problem sets using this concept. This is a linear relationship overall, meaning that in the event of no electric field, the ions will stop moving. <br /> <br /> ====Polarization Process in Ionic Solution====<br /> <br /> While polarization is a rapid process once initiated, it is not an on-off binary process. The instant that an electric field is applied, the drift speed is nonzero and the particles start tending towards the direction of the electric field. As ions pile up on the sides of the solution, the electric field inside becomes weaker and the system approaches an equilibrium at a microscopic level. At this equilibrium, drift speed is 0 and there is no NET MOTION of mobile charges in solution<br /> <br /> ===Charge Motion in Metals===<br /> <br /> The second example to look at for conductors is in metals.<br /> <br /> ====Mobile Electron Sea====<br /> <br /> Metals are an interesting idea structurally. Atoms of a metal are arranged in a rigid, ordered structure, sometimes known as a lattice structure (similar to crystal). Due to this, there is a interesting pattern of behavior. The inner electrons of each of these ordered atoms are attracted to the positively charged nucleus. Some of the outer electrons engage in solid atom interactions (ball and spring model), but other outer electrons participate in a pool of electrons that is allowed to move freely across the solid, in an &quot;electron sea&quot;. While they can move across the solid, they are very hard to extract and there are obviously some limitations to its direction of movement (different from liquid ionic solutions), but the mobile electron sea makes metals great conductor candidates (and thus are used in so many practical applications, including wires, microchips, cars, etc.) <br /> <br /> There is a caveat to this, however. You may ask, well won't the electrons repel each other and this not really allow for movement? Yes, but due to the presence of the positive cores, this interaction is neutralized. There is, therefore, no net interaction between the electrons inside a metal. Thus, the sea electrons move freely independent of electron field, positive cores, and appear not to interact with each other. The model of electron motion is defined by the Drude model, the steps of which are shown here:<br /> <br /> 1) When an electric field is applied in a metal, the electrons get excited and accelerate.<br /> <br /> 2) The electrons lose their energy when they collide with the lattices of the positive atomic cores<br /> <br /> 3) After the collision, the electrons again get accelerated and the entire process repeats itself. <br /> <br /> [[File:Shah2.jpg]]<br /> <br /> The average speed, then is defined by v, the drift speed, as mentioned earlier. For metals this equation is:<br /> <br /> '''v = (e*Enet*deltaT)/(m)'''<br /> <br /> where v is the drift speed, e is the charge of the electron, Enet is the net applied electric field, deltaT is the average time between collisions, and m is the mass of the electron. The average time between collisions is used because the time between each collision is uncontrollable and inconsistent. This equation is derived from the momentum equation where p = F*deltaT and F = Enet*e.<br /> <br /> This YouTube video does an excellent job of explaining the concept in further detail:<br /> <br /> https://www.youtube.com/watch?v=HKgOpmX-OFI<br /> <br /> ==Examples==<br /> <br /> ===Simple===<br /> <br /> The mobility of electrons in copper is 4.5E-3 (m/s)/(N/C). How much net electric field would be needed in order to give the electrons in copper a drift speed of 1.5E-3 m/s?<br /> <br /> ====Solution====<br /> <br /> This is a simple problem using the formula given for drift speed <br /> <br /> '''v = u*Enet''' <br /> <br /> Thus, Enet = v/u = 1.5E-3/4.5E-3 = 0.333 N/C. <br /> <br /> This also makes sense from a units perspective, as our solution is in N/C, the speed is m/s, and the mobility is given in (m/s)/(N/C). <br /> <br /> ===Middling===<br /> <br /> In a simple metal lattice structure, an electric field of 10 N/C is applied and 15 collisions are observed. The time between collisions increases after each collision, starting with 1 second, from collision 1 to collision 2. After 15 collisions, what is the drift speed of an electron in this metal lattice structure? <br /> <br /> ====Solution====<br /> <br /> This is a slightly more complex problem that requires a bit of analytical thinking and application of a formula. The formula:<br /> <br /> '''v = (e*Enet*deltaT)/(m)'''<br /> <br /> All of the quantities are known. e = 1.6E-19 C, Enet = 10 N/C, m = 9.1E-31<br /> <br /> However, deltaT is not immediately discernible. The question asks for the drift speed after 15 collisions. It might be some people's thought to just use the time between the 14th and 15th collision as the deltaT in the equation. DeltaT refers to the AVERAGE time between collisions. In this case, the deltaT would therefore be 7.5 seconds. <br /> <br /> Plugging these numbers in, you get: 1.3E13 m/s. This is extremely fast. As you can see, this speaks to how quickly electrons move through substances and how quickly polarization occurs, both in metals and in ionic solutions. <br /> <br /> ===Difficult===<br /> <br /> Summarize the difference between conductors and insulators in the following 4 categories:<br /> <br /> Mobile Charges<br /> Polarization<br /> Equilibrium<br /> Excess Charge<br /> <br /> ====Solution====<br /> <br /> 1) Conductors have mobile charges while insulators do not<br /> <br /> 2) Sea or mass of mobile electrons move when electric field is applied to a conductor. When an electric field is applied to an insulator, INDIVIDUAL atoms polarize. <br /> <br /> 3) Net electric field is 0 in a conductor at equilibrium whereas there is a nonzero electric field in an insulator at equilibrium. <br /> <br /> 4) Excess charge spreads over the surface of a conductor but clumps in patches in an insulator. <br /> <br /> (Adapted from textbook)<br /> <br /> ==Real World Application==<br /> <br /> While this isn't exactly related to conductors (the exact opposite, actually), this is a very important concept in polarization. As mentioned earlier, when a conductor is polarized, electron seas move rapidly and cause polarization. When an insulator has an applied electric field, the individual atoms or molecules become polarized. An interesting aspect of this is the concept of dielectric. A dielectric is a material or substance that is usually an insulator, but when an electric field is applied, the electrons shift slightly from their usual equilibrium creating a positive and negative space and thus, polarization. Usually, a dielectric is a material with EXTREMELY HIGH polarizability, which is extremely useful in the real world. The concept was developed by William Wheewell during a discussion with Michael Faraday. Diaelectrics are commonly used in developing capacitors.<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> [http://www.scientificamerican.com/article/bring-science-home-reaction-time/]<br /> <br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Jshah46 http://www.physicsbook.gatech.edu/index.php?title=File:Shah2.JPG&diff=23083 2016-04-18T03:08:42Z

<p>Jshah46: Drude Model Chart</p> <hr /> <div>Drude Model Chart</div>

Jshah46 http://www.physicsbook.gatech.edu/index.php?title=Polarization_of_a_conductor&diff=23080 2016-04-18T03:05:59Z

<p>Jshah46: </p> <hr /> <div><br /> ==The Main Idea==<br /> <br /> Based on the definition of a conductor, it is easily assumed that stronger conductors can have charged particles moving more freely within it and in larger distances. There are two main situations where this can be observed. The first is in ionic solutions:<br /> <br /> ===Ionic Solutions===<br /> <br /> Ionic solutions, such as KCl or NaCl or NaI (solutions in which the ions dissociate), have individual ions of the dissociated particles. For example, a solution of NaI will have Na+, I-, and because it is an aqueous solution, some H+ and OH- as well. When an electric field is applied to this solution, the particles (as you'd imagine) move in the direction of the force applied by the electric field. However, the interesting concept here is that the charged particles move in a direction and accumulate, therefore creating a charge gradient, '''which in turn creates its own electric field!''' This can be shown in Figure 1, taken from the textbook. While ions are constantly moving, this is an accurate snapshot of what would be expected in the event of applied field/force. Furthermore, while ions move around the solution at all times (it is a conductor after all), there is a measurable excess of ions on the edges that generates the field. <br /> <br /> '''The net electric field is the superposition of the applied field and the field generated by the charge gradient and excess ion concentrations on the edges.'''<br /> <br /> [[File:Shah1.jpg]]<br /> <br /> ====A Mathematical Model: Drift Speed====<br /> <br /> In the phenomenon described above, when the external field is applied on an ionic solution, the Na+ and I- ions will move and bounce around a good bit, but due to collisions, they do not maintain a specific speed or trajectory. This is in spite of whether or not the force experienced is constant. In order to keep the ions moving at constant speed, also known as the drift speed, a constant electric field must be applied. This is modeled mathematically using the following equation: <br /> <br /> '''v = u*Enet''' <br /> <br /> where v is the drift speed, u is the mobility of the charge ((m/s)/(N/C)), and Enet is the net electric field applied to the ionic solution. The proportionality constant, u, is determined for the ions based on the solution and will be usually given or easy to derive in all practical problem sets using this concept. This is a linear relationship overall, meaning that in the event of no electric field, the ions will stop moving. <br /> <br /> ====Polarization Process in Ionic Solution====<br /> <br /> While polarization is a rapid process once initiated, it is not an on-off binary process. The instant that an electric field is applied, the drift speed is nonzero and the particles start tending towards the direction of the electric field. As ions pile up on the sides of the solution, the electric field inside becomes weaker and the system approaches an equilibrium at a microscopic level. At this equilibrium, drift speed is 0 and there is no NET MOTION of mobile charges in solution<br /> <br /> ===Charge Motion in Metals===<br /> <br /> The second example to look at for conductors is in metals.<br /> <br /> ====Mobile Electron Sea====<br /> <br /> Metals are an interesting idea structurally. Atoms of a metal are arranged in a rigid, ordered structure, sometimes known as a lattice structure (similar to crystal). Due to this, there is a interesting pattern of behavior. The inner electrons of each of these ordered atoms are attracted to the positively charged nucleus. Some of the outer electrons engage in solid atom interactions (ball and spring model), but other outer electrons participate in a pool of electrons that is allowed to move freely across the solid, in an &quot;electron sea&quot;. While they can move across the solid, they are very hard to extract and there are obviously some limitations to its direction of movement (different from liquid ionic solutions), but the mobile electron sea makes metals great conductor candidates (and thus are used in so many practical applications, including wires, microchips, cars, etc.) <br /> <br /> There is a caveat to this, however. You may ask, well won't the electrons repel each other and this not really allow for movement? Yes, but due to the presence of the positive cores, this interaction is neutralized. There is, therefore, no net interaction between the electrons inside a metal. Thus, the sea electrons move freely independent of electron field, positive cores, and appear not to interact with each other. The model of electron motion is defined by the Drude model, the steps of which are shown here:<br /> <br /> 1) When an electric field is applied in a metal, the electrons get excited and accelerate.<br /> <br /> 2) The electrons lose their energy when they collide with the lattices of the positive atomic cores<br /> <br /> 3) After the collision, the electrons again get accelerated and the entire process repeats itself. <br /> <br /> The average speed, then is defined by v, the drift speed, as mentioned earlier. For metals this equation is:<br /> <br /> '''v = (e*Enet*deltaT)/(m)'''<br /> <br /> where v is the drift speed, e is the charge of the electron, Enet is the net applied electric field, deltaT is the average time between collisions, and m is the mass of the electron. The average time between collisions is used because the time between each collision is uncontrollable and inconsistent. This equation is derived from the momentum equation where p = F*deltaT and F = Enet*e.<br /> <br /> This YouTube video does an excellent job of explaining the concept in further detail:<br /> <br /> https://www.youtube.com/watch?v=HKgOpmX-OFI<br /> <br /> ==Examples==<br /> <br /> ===Simple===<br /> <br /> The mobility of electrons in copper is 4.5E-3 (m/s)/(N/C). How much net electric field would be needed in order to give the electrons in copper a drift speed of 1.5E-3 m/s?<br /> <br /> ====Solution====<br /> <br /> This is a simple problem using the formula given for drift speed <br /> <br /> '''v = u*Enet''' <br /> <br /> Thus, Enet = v/u = 1.5E-3/4.5E-3 = 0.333 N/C. <br /> <br /> This also makes sense from a units perspective, as our solution is in N/C, the speed is m/s, and the mobility is given in (m/s)/(N/C). <br /> <br /> ===Middling===<br /> <br /> In a simple metal lattice structure, an electric field of 10 N/C is applied and 15 collisions are observed. The time between collisions increases after each collision, starting with 1 second, from collision 1 to collision 2. After 15 collisions, what is the drift speed of an electron in this metal lattice structure? <br /> <br /> ====Solution====<br /> <br /> This is a slightly more complex problem that requires a bit of analytical thinking and application of a formula. The formula:<br /> <br /> '''v = (e*Enet*deltaT)/(m)'''<br /> <br /> All of the quantities are known. e = 1.6E-19 C, Enet = 10 N/C, m = 9.1E-31<br /> <br /> However, deltaT is not immediately discernible. The question asks for the drift speed after 15 collisions. It might be some people's thought to just use the time between the 14th and 15th collision as the deltaT in the equation. DeltaT refers to the AVERAGE time between collisions. In this case, the deltaT would therefore be 7.5 seconds. <br /> <br /> Plugging these numbers in, you get: 1.3E13 m/s. This is extremely fast. As you can see, this speaks to how quickly electrons move through substances and how quickly polarization occurs, both in metals and in ionic solutions. <br /> <br /> ===Difficult===<br /> <br /> Summarize the difference between conductors and insulators in the following 4 categories:<br /> <br /> Mobile Charges<br /> Polarization<br /> Equilibrium<br /> Excess Charge<br /> <br /> ====Solution====<br /> <br /> 1) Conductors have mobile charges while insulators do not<br /> <br /> 2) Sea or mass of mobile electrons move when electric field is applied to a conductor. When an electric field is applied to an insulator, INDIVIDUAL atoms polarize. <br /> <br /> 3) Net electric field is 0 in a conductor at equilibrium whereas there is a nonzero electric field in an insulator at equilibrium. <br /> <br /> 4) Excess charge spreads over the surface of a conductor but clumps in patches in an insulator. <br /> <br /> (Adapted from textbook)<br /> <br /> ==Real World Application==<br /> <br /> While this isn't exactly related to conductors (the exact opposite, actually), this is a very important concept in polarization. As mentioned earlier, when a conductor is polarized, electron seas move rapidly and cause polarization. When an insulator has an applied electric field, the individual atoms or molecules become polarized. An interesting aspect of this is the concept of dielectric. A dielectric is a material or substance that is usually an insulator, but when an electric field is applied, the electrons shift slightly from their usual equilibrium creating a positive and negative space and thus, polarization. Usually, a dielectric is a material with EXTREMELY HIGH polarizability, which is extremely useful in the real world. The concept was developed by William Wheewell during a discussion with Michael Faraday. Diaelectrics are commonly used in developing capacitors.<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> [http://www.scientificamerican.com/article/bring-science-home-reaction-time/]<br /> <br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Jshah46 http://www.physicsbook.gatech.edu/index.php?title=File:Shah1.jpg&diff=23078 2016-04-18T03:04:44Z

<p>Jshah46: Polarization of Ionic Solution</p> <hr /> <div>Polarization of Ionic Solution</div>

Jshah46 http://www.physicsbook.gatech.edu/index.php?title=Polarization_of_a_conductor&diff=23074 2016-04-18T03:03:32Z

<p>Jshah46: </p> <hr /> <div><br /> ==The Main Idea==<br /> <br /> Based on the definition of a conductor, it is easily assumed that stronger conductors can have charged particles moving more freely within it and in larger distances. There are two main situations where this can be observed. The first is in ionic solutions:<br /> <br /> ===Ionic Solutions===<br /> <br /> Ionic solutions, such as KCl or NaCl or NaI (solutions in which the ions dissociate), have individual ions of the dissociated particles. For example, a solution of NaI will have Na+, I-, and because it is an aqueous solution, some H+ and OH- as well. When an electric field is applied to this solution, the particles (as you'd imagine) move in the direction of the force applied by the electric field. However, the interesting concept here is that the charged particles move in a direction and accumulate, therefore creating a charge gradient, '''which in turn creates its own electric field!''' This can be shown in Figure 1, taken from the textbook. While ions are constantly moving, this is an accurate snapshot of what would be expected in the event of applied field/force. Furthermore, while ions move around the solution at all times (it is a conductor after all), there is a measurable excess of ions on the edges that generates the field. <br /> <br /> '''The net electric field is the superposition of the applied field and the field generated by the charge gradient and excess ion concentrations on the edges.'''<br /> <br /> [[1_Shah_PhysWiki.jpg]]<br /> <br /> ====A Mathematical Model: Drift Speed====<br /> <br /> In the phenomenon described above, when the external field is applied on an ionic solution, the Na+ and I- ions will move and bounce around a good bit, but due to collisions, they do not maintain a specific speed or trajectory. This is in spite of whether or not the force experienced is constant. In order to keep the ions moving at constant speed, also known as the drift speed, a constant electric field must be applied. This is modeled mathematically using the following equation: <br /> <br /> '''v = u*Enet''' <br /> <br /> where v is the drift speed, u is the mobility of the charge ((m/s)/(N/C)), and Enet is the net electric field applied to the ionic solution. The proportionality constant, u, is determined for the ions based on the solution and will be usually given or easy to derive in all practical problem sets using this concept. This is a linear relationship overall, meaning that in the event of no electric field, the ions will stop moving. <br /> <br /> ====Polarization Process in Ionic Solution====<br /> <br /> While polarization is a rapid process once initiated, it is not an on-off binary process. The instant that an electric field is applied, the drift speed is nonzero and the particles start tending towards the direction of the electric field. As ions pile up on the sides of the solution, the electric field inside becomes weaker and the system approaches an equilibrium at a microscopic level. At this equilibrium, drift speed is 0 and there is no NET MOTION of mobile charges in solution<br /> <br /> ===Charge Motion in Metals===<br /> <br /> The second example to look at for conductors is in metals.<br /> <br /> ====Mobile Electron Sea====<br /> <br /> Metals are an interesting idea structurally. Atoms of a metal are arranged in a rigid, ordered structure, sometimes known as a lattice structure (similar to crystal). Due to this, there is a interesting pattern of behavior. The inner electrons of each of these ordered atoms are attracted to the positively charged nucleus. Some of the outer electrons engage in solid atom interactions (ball and spring model), but other outer electrons participate in a pool of electrons that is allowed to move freely across the solid, in an &quot;electron sea&quot;. While they can move across the solid, they are very hard to extract and there are obviously some limitations to its direction of movement (different from liquid ionic solutions), but the mobile electron sea makes metals great conductor candidates (and thus are used in so many practical applications, including wires, microchips, cars, etc.) <br /> <br /> There is a caveat to this, however. You may ask, well won't the electrons repel each other and this not really allow for movement? Yes, but due to the presence of the positive cores, this interaction is neutralized. There is, therefore, no net interaction between the electrons inside a metal. Thus, the sea electrons move freely independent of electron field, positive cores, and appear not to interact with each other. The model of electron motion is defined by the Drude model, the steps of which are shown here:<br /> <br /> 1) When an electric field is applied in a metal, the electrons get excited and accelerate.<br /> <br /> 2) The electrons lose their energy when they collide with the lattices of the positive atomic cores<br /> <br /> 3) After the collision, the electrons again get accelerated and the entire process repeats itself. <br /> <br /> The average speed, then is defined by v, the drift speed, as mentioned earlier. For metals this equation is:<br /> <br /> '''v = (e*Enet*deltaT)/(m)'''<br /> <br /> where v is the drift speed, e is the charge of the electron, Enet is the net applied electric field, deltaT is the average time between collisions, and m is the mass of the electron. The average time between collisions is used because the time between each collision is uncontrollable and inconsistent. This equation is derived from the momentum equation where p = F*deltaT and F = Enet*e.<br /> <br /> This YouTube video does an excellent job of explaining the concept in further detail:<br /> <br /> https://www.youtube.com/watch?v=HKgOpmX-OFI<br /> <br /> ==Examples==<br /> <br /> ===Simple===<br /> <br /> The mobility of electrons in copper is 4.5E-3 (m/s)/(N/C). How much net electric field would be needed in order to give the electrons in copper a drift speed of 1.5E-3 m/s?<br /> <br /> ====Solution====<br /> <br /> This is a simple problem using the formula given for drift speed <br /> <br /> '''v = u*Enet''' <br /> <br /> Thus, Enet = v/u = 1.5E-3/4.5E-3 = 0.333 N/C. <br /> <br /> This also makes sense from a units perspective, as our solution is in N/C, the speed is m/s, and the mobility is given in (m/s)/(N/C). <br /> <br /> ===Middling===<br /> <br /> In a simple metal lattice structure, an electric field of 10 N/C is applied and 15 collisions are observed. The time between collisions increases after each collision, starting with 1 second, from collision 1 to collision 2. After 15 collisions, what is the drift speed of an electron in this metal lattice structure? <br /> <br /> ====Solution====<br /> <br /> This is a slightly more complex problem that requires a bit of analytical thinking and application of a formula. The formula:<br /> <br /> '''v = (e*Enet*deltaT)/(m)'''<br /> <br /> All of the quantities are known. e = 1.6E-19 C, Enet = 10 N/C, m = 9.1E-31<br /> <br /> However, deltaT is not immediately discernible. The question asks for the drift speed after 15 collisions. It might be some people's thought to just use the time between the 14th and 15th collision as the deltaT in the equation. DeltaT refers to the AVERAGE time between collisions. In this case, the deltaT would therefore be 7.5 seconds. <br /> <br /> Plugging these numbers in, you get: 1.3E13 m/s. This is extremely fast. As you can see, this speaks to how quickly electrons move through substances and how quickly polarization occurs, both in metals and in ionic solutions. <br /> <br /> ===Difficult===<br /> <br /> Summarize the difference between conductors and insulators in the following 4 categories:<br /> <br /> Mobile Charges<br /> Polarization<br /> Equilibrium<br /> Excess Charge<br /> <br /> ====Solution====<br /> <br /> 1) Conductors have mobile charges while insulators do not<br /> <br /> 2) Sea or mass of mobile electrons move when electric field is applied to a conductor. When an electric field is applied to an insulator, INDIVIDUAL atoms polarize. <br /> <br /> 3) Net electric field is 0 in a conductor at equilibrium whereas there is a nonzero electric field in an insulator at equilibrium. <br /> <br /> 4) Excess charge spreads over the surface of a conductor but clumps in patches in an insulator. <br /> <br /> (Adapted from textbook)<br /> <br /> ==Real World Application==<br /> <br /> While this isn't exactly related to conductors (the exact opposite, actually), this is a very important concept in polarization. As mentioned earlier, when a conductor is polarized, electron seas move rapidly and cause polarization. When an insulator has an applied electric field, the individual atoms or molecules become polarized. An interesting aspect of this is the concept of dielectric. A dielectric is a material or substance that is usually an insulator, but when an electric field is applied, the electrons shift slightly from their usual equilibrium creating a positive and negative space and thus, polarization. Usually, a dielectric is a material with EXTREMELY HIGH polarizability, which is extremely useful in the real world. The concept was developed by William Wheewell during a discussion with Michael Faraday. Diaelectrics are commonly used in developing capacitors.<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> [http://www.scientificamerican.com/article/bring-science-home-reaction-time/]<br /> <br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Jshah46 http://www.physicsbook.gatech.edu/index.php?title=File:1_Shah_PhysWiki.JPG&diff=23073 2016-04-18T03:02:45Z

<p>Jshah46: Polarization of Ionic Solution</p> <hr /> <div>Polarization of Ionic Solution</div>

Jshah46 http://www.physicsbook.gatech.edu/index.php?title=Polarization_of_a_conductor&diff=23071 2016-04-18T03:00:13Z

<p>Jshah46: </p> <hr /> <div><br /> ==The Main Idea==<br /> <br /> Based on the definition of a conductor, it is easily assumed that stronger conductors can have charged particles moving more freely within it and in larger distances. There are two main situations where this can be observed. The first is in ionic solutions:<br /> <br /> ===Ionic Solutions===<br /> <br /> Ionic solutions, such as KCl or NaCl or NaI (solutions in which the ions dissociate), have individual ions of the dissociated particles. For example, a solution of NaI will have Na+, I-, and because it is an aqueous solution, some H+ and OH- as well. When an electric field is applied to this solution, the particles (as you'd imagine) move in the direction of the force applied by the electric field. However, the interesting concept here is that the charged particles move in a direction and accumulate, therefore creating a charge gradient, '''which in turn creates its own electric field!''' This can be shown in Figure 1, taken from the textbook. While ions are constantly moving, this is an accurate snapshot of what would be expected in the event of applied field/force. Furthermore, while ions move around the solution at all times (it is a conductor after all), there is a measurable excess of ions on the edges that generates the field. <br /> <br /> '''The net electric field is the superposition of the applied field and the field generated by the charge gradient and excess ion concentrations on the edges.'''<br /> <br /> [[File:Example.jpg]]<br /> <br /> ====A Mathematical Model: Drift Speed====<br /> <br /> In the phenomenon described above, when the external field is applied on an ionic solution, the Na+ and I- ions will move and bounce around a good bit, but due to collisions, they do not maintain a specific speed or trajectory. This is in spite of whether or not the force experienced is constant. In order to keep the ions moving at constant speed, also known as the drift speed, a constant electric field must be applied. This is modeled mathematically using the following equation: <br /> <br /> '''v = u*Enet''' <br /> <br /> where v is the drift speed, u is the mobility of the charge ((m/s)/(N/C)), and Enet is the net electric field applied to the ionic solution. The proportionality constant, u, is determined for the ions based on the solution and will be usually given or easy to derive in all practical problem sets using this concept. This is a linear relationship overall, meaning that in the event of no electric field, the ions will stop moving. <br /> <br /> ====Polarization Process in Ionic Solution====<br /> <br /> While polarization is a rapid process once initiated, it is not an on-off binary process. The instant that an electric field is applied, the drift speed is nonzero and the particles start tending towards the direction of the electric field. As ions pile up on the sides of the solution, the electric field inside becomes weaker and the system approaches an equilibrium at a microscopic level. At this equilibrium, drift speed is 0 and there is no NET MOTION of mobile charges in solution<br /> <br /> ===Charge Motion in Metals===<br /> <br /> The second example to look at for conductors is in metals.<br /> <br /> ====Mobile Electron Sea====<br /> <br /> Metals are an interesting idea structurally. Atoms of a metal are arranged in a rigid, ordered structure, sometimes known as a lattice structure (similar to crystal). Due to this, there is a interesting pattern of behavior. The inner electrons of each of these ordered atoms are attracted to the positively charged nucleus. Some of the outer electrons engage in solid atom interactions (ball and spring model), but other outer electrons participate in a pool of electrons that is allowed to move freely across the solid, in an &quot;electron sea&quot;. While they can move across the solid, they are very hard to extract and there are obviously some limitations to its direction of movement (different from liquid ionic solutions), but the mobile electron sea makes metals great conductor candidates (and thus are used in so many practical applications, including wires, microchips, cars, etc.) <br /> <br /> There is a caveat to this, however. You may ask, well won't the electrons repel each other and this not really allow for movement? Yes, but due to the presence of the positive cores, this interaction is neutralized. There is, therefore, no net interaction between the electrons inside a metal. Thus, the sea electrons move freely independent of electron field, positive cores, and appear not to interact with each other. The model of electron motion is defined by the Drude model, the steps of which are shown here:<br /> <br /> 1) When an electric field is applied in a metal, the electrons get excited and accelerate.<br /> <br /> 2) The electrons lose their energy when they collide with the lattices of the positive atomic cores<br /> <br /> 3) After the collision, the electrons again get accelerated and the entire process repeats itself. <br /> <br /> The average speed, then is defined by v, the drift speed, as mentioned earlier. For metals this equation is:<br /> <br /> '''v = (e*Enet*deltaT)/(m)'''<br /> <br /> where v is the drift speed, e is the charge of the electron, Enet is the net applied electric field, deltaT is the average time between collisions, and m is the mass of the electron. The average time between collisions is used because the time between each collision is uncontrollable and inconsistent. This equation is derived from the momentum equation where p = F*deltaT and F = Enet*e.<br /> <br /> This YouTube video does an excellent job of explaining the concept in further detail:<br /> <br /> https://www.youtube.com/watch?v=HKgOpmX-OFI<br /> <br /> ==Examples==<br /> <br /> ===Simple===<br /> <br /> The mobility of electrons in copper is 4.5E-3 (m/s)/(N/C). How much net electric field would be needed in order to give the electrons in copper a drift speed of 1.5E-3 m/s?<br /> <br /> ====Solution====<br /> <br /> This is a simple problem using the formula given for drift speed <br /> <br /> '''v = u*Enet''' <br /> <br /> Thus, Enet = v/u = 1.5E-3/4.5E-3 = 0.333 N/C. <br /> <br /> This also makes sense from a units perspective, as our solution is in N/C, the speed is m/s, and the mobility is given in (m/s)/(N/C). <br /> <br /> ===Middling===<br /> <br /> In a simple metal lattice structure, an electric field of 10 N/C is applied and 15 collisions are observed. The time between collisions increases after each collision, starting with 1 second, from collision 1 to collision 2. After 15 collisions, what is the drift speed of an electron in this metal lattice structure? <br /> <br /> ====Solution====<br /> <br /> This is a slightly more complex problem that requires a bit of analytical thinking and application of a formula. The formula:<br /> <br /> '''v = (e*Enet*deltaT)/(m)'''<br /> <br /> All of the quantities are known. e = 1.6E-19 C, Enet = 10 N/C, m = 9.1E-31<br /> <br /> However, deltaT is not immediately discernible. The question asks for the drift speed after 15 collisions. It might be some people's thought to just use the time between the 14th and 15th collision as the deltaT in the equation. DeltaT refers to the AVERAGE time between collisions. In this case, the deltaT would therefore be 7.5 seconds. <br /> <br /> Plugging these numbers in, you get: 1.3E13 m/s. This is extremely fast. As you can see, this speaks to how quickly electrons move through substances and how quickly polarization occurs, both in metals and in ionic solutions. <br /> <br /> ===Difficult===<br /> <br /> Summarize the difference between conductors and insulators in the following 4 categories:<br /> <br /> Mobile Charges<br /> Polarization<br /> Equilibrium<br /> Excess Charge<br /> <br /> ====Solution====<br /> <br /> 1) Conductors have mobile charges while insulators do not<br /> <br /> 2) Sea or mass of mobile electrons move when electric field is applied to a conductor. When an electric field is applied to an insulator, INDIVIDUAL atoms polarize. <br /> <br /> 3) Net electric field is 0 in a conductor at equilibrium whereas there is a nonzero electric field in an insulator at equilibrium. <br /> <br /> 4) Excess charge spreads over the surface of a conductor but clumps in patches in an insulator. <br /> <br /> (Adapted from textbook)<br /> <br /> ==Real World Application==<br /> <br /> While this isn't exactly related to conductors (the exact opposite, actually), this is a very important concept in polarization. As mentioned earlier, when a conductor is polarized, electron seas move rapidly and cause polarization. When an insulator has an applied electric field, the individual atoms or molecules become polarized. An interesting aspect of this is the concept of dielectric. A dielectric is a material or substance that is usually an insulator, but when an electric field is applied, the electrons shift slightly from their usual equilibrium creating a positive and negative space and thus, polarization. Usually, a dielectric is a material with EXTREMELY HIGH polarizability, which is extremely useful in the real world. The concept was developed by William Wheewell during a discussion with Michael Faraday. Diaelectrics are commonly used in developing capacitors.<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> [http://www.scientificamerican.com/article/bring-science-home-reaction-time/]<br /> <br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Jshah46 http://www.physicsbook.gatech.edu/index.php?title=Polarization_of_a_conductor&diff=23070 2016-04-18T02:57:03Z

<p>Jshah46: /* Connectedness */</p> <hr /> <div>'''THIS HAS BEEN CLAIMED BY JAY SHAH<br /> '''<br /> Short Description of Topic<br /> <br /> ==The Main Idea==<br /> <br /> Based on the definition of a conductor, it is easily assumed that stronger conductors can have charged particles moving more freely within it and in larger distances. There are two main situations where this can be observed. The first is in ionic solutions:<br /> <br /> ===Ionic Solutions===<br /> <br /> Ionic solutions, such as KCl or NaCl or NaI (solutions in which the ions dissociate), have individual ions of the dissociated particles. For example, a solution of NaI will have Na+, I-, and because it is an aqueous solution, some H+ and OH- as well. When an electric field is applied to this solution, the particles (as you'd imagine) move in the direction of the force applied by the electric field. However, the interesting concept here is that the charged particles move in a direction and accumulate, therefore creating a charge gradient, '''which in turn creates its own electric field!''' This can be shown in Figure 1, taken from the textbook. While ions are constantly moving, this is an accurate snapshot of what would be expected in the event of applied field/force. Furthermore, while ions move around the solution at all times (it is a conductor after all), there is a measurable excess of ions on the edges that generates the field. <br /> <br /> '''The net electric field is the superposition of the applied field and the field generated by the charge gradient and excess ion concentrations on the edges.'''<br /> <br /> ====A Mathematical Model: Drift Speed====<br /> <br /> In the phenomenon described above, when the external field is applied on an ionic solution, the Na+ and I- ions will move and bounce around a good bit, but due to collisions, they do not maintain a specific speed or trajectory. This is in spite of whether or not the force experienced is constant. In order to keep the ions moving at constant speed, also known as the drift speed, a constant electric field must be applied. This is modeled mathematically using the following equation: <br /> <br /> '''v = u*Enet''' <br /> <br /> where v is the drift speed, u is the mobility of the charge ((m/s)/(N/C)), and Enet is the net electric field applied to the ionic solution. The proportionality constant, u, is determined for the ions based on the solution and will be usually given or easy to derive in all practical problem sets using this concept. This is a linear relationship overall, meaning that in the event of no electric field, the ions will stop moving. <br /> <br /> ====Polarization Process in Ionic Solution====<br /> <br /> While polarization is a rapid process once initiated, it is not an on-off binary process. The instant that an electric field is applied, the drift speed is nonzero and the particles start tending towards the direction of the electric field. As ions pile up on the sides of the solution, the electric field inside becomes weaker and the system approaches an equilibrium at a microscopic level. At this equilibrium, drift speed is 0 and there is no NET MOTION of mobile charges in solution<br /> <br /> ===Charge Motion in Metals===<br /> <br /> The second example to look at for conductors is in metals.<br /> <br /> ====Mobile Electron Sea====<br /> <br /> Metals are an interesting idea structurally. Atoms of a metal are arranged in a rigid, ordered structure, sometimes known as a lattice structure (similar to crystal). Due to this, there is a interesting pattern of behavior. The inner electrons of each of these ordered atoms are attracted to the positively charged nucleus. Some of the outer electrons engage in solid atom interactions (ball and spring model), but other outer electrons participate in a pool of electrons that is allowed to move freely across the solid, in an &quot;electron sea&quot;. While they can move across the solid, they are very hard to extract and there are obviously some limitations to its direction of movement (different from liquid ionic solutions), but the mobile electron sea makes metals great conductor candidates (and thus are used in so many practical applications, including wires, microchips, cars, etc.) <br /> <br /> There is a caveat to this, however. You may ask, well won't the electrons repel each other and this not really allow for movement? Yes, but due to the presence of the positive cores, this interaction is neutralized. There is, therefore, no net interaction between the electrons inside a metal. Thus, the sea electrons move freely independent of electron field, positive cores, and appear not to interact with each other. The model of electron motion is defined by the Drude model, the steps of which are shown here:<br /> <br /> 1) When an electric field is applied in a metal, the electrons get excited and accelerate.<br /> <br /> 2) The electrons lose their energy when they collide with the lattices of the positive atomic cores<br /> <br /> 3) After the collision, the electrons again get accelerated and the entire process repeats itself. <br /> <br /> The average speed, then is defined by v, the drift speed, as mentioned earlier. For metals this equation is:<br /> <br /> '''v = (e*Enet*deltaT)/(m)'''<br /> <br /> where v is the drift speed, e is the charge of the electron, Enet is the net applied electric field, deltaT is the average time between collisions, and m is the mass of the electron. The average time between collisions is used because the time between each collision is uncontrollable and inconsistent. This equation is derived from the momentum equation where p = F*deltaT and F = Enet*e.<br /> <br /> This YouTube video does an excellent job of explaining the concept in further detail:<br /> <br /> https://www.youtube.com/watch?v=HKgOpmX-OFI<br /> <br /> ==Examples==<br /> <br /> ===Simple===<br /> <br /> The mobility of electrons in copper is 4.5E-3 (m/s)/(N/C). How much net electric field would be needed in order to give the electrons in copper a drift speed of 1.5E-3 m/s?<br /> <br /> ====Solution====<br /> <br /> This is a simple problem using the formula given for drift speed <br /> <br /> '''v = u*Enet''' <br /> <br /> Thus, Enet = v/u = 1.5E-3/4.5E-3 = 0.333 N/C. <br /> <br /> This also makes sense from a units perspective, as our solution is in N/C, the speed is m/s, and the mobility is given in (m/s)/(N/C). <br /> <br /> ===Middling===<br /> <br /> In a simple metal lattice structure, an electric field of 10 N/C is applied and 15 collisions are observed. The time between collisions increases after each collision, starting with 1 second, from collision 1 to collision 2. After 15 collisions, what is the drift speed of an electron in this metal lattice structure? <br /> <br /> ====Solution====<br /> <br /> This is a slightly more complex problem that requires a bit of analytical thinking and application of a formula. The formula:<br /> <br /> '''v = (e*Enet*deltaT)/(m)'''<br /> <br /> All of the quantities are known. e = 1.6E-19 C, Enet = 10 N/C, m = 9.1E-31<br /> <br /> However, deltaT is not immediately discernible. The question asks for the drift speed after 15 collisions. It might be some people's thought to just use the time between the 14th and 15th collision as the deltaT in the equation. DeltaT refers to the AVERAGE time between collisions. In this case, the deltaT would therefore be 7.5 seconds. <br /> <br /> Plugging these numbers in, you get: 1.3E13 m/s. This is extremely fast. As you can see, this speaks to how quickly electrons move through substances and how quickly polarization occurs, both in metals and in ionic solutions. <br /> <br /> ===Difficult===<br /> <br /> Summarize the difference between conductors and insulators in the following 4 categories:<br /> <br /> Mobile Charges<br /> Polarization<br /> Equilibrium<br /> Excess Charge<br /> <br /> ====Solution====<br /> <br /> 1) Conductors have mobile charges while insulators do not<br /> <br /> 2) Sea or mass of mobile electrons move when electric field is applied to a conductor. When an electric field is applied to an insulator, INDIVIDUAL atoms polarize. <br /> <br /> 3) Net electric field is 0 in a conductor at equilibrium whereas there is a nonzero electric field in an insulator at equilibrium. <br /> <br /> 4) Excess charge spreads over the surface of a conductor but clumps in patches in an insulator. <br /> <br /> (Adapted from textbook)<br /> <br /> ==Real World Application==<br /> <br /> While this isn't exactly related to conductors (the exact opposite, actually), this is a very important concept in polarization. As mentioned earlier, when a conductor is polarized, electron seas move rapidly and cause polarization. When an insulator has an applied electric field, the individual atoms or molecules become polarized. An interesting aspect of this is the concept of dielectric. A dielectric is a material or substance that is usually an insulator, but when an electric field is applied, the electrons shift slightly from their usual equilibrium creating a positive and negative space and thus, polarization. Usually, a dielectric is a material with EXTREMELY HIGH polarizability, which is extremely useful in the real world. The concept was developed by William Wheewell during a discussion with Michael Faraday. Diaelectrics are commonly used in developing capacitors.<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> [http://www.scientificamerican.com/article/bring-science-home-reaction-time/]<br /> <br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Jshah46 http://www.physicsbook.gatech.edu/index.php?title=Polarization_of_a_conductor&diff=23052 2016-04-18T02:48:19Z

<p>Jshah46: </p> <hr /> <div>'''THIS HAS BEEN CLAIMED BY JAY SHAH<br /> '''<br /> Short Description of Topic<br /> <br /> ==The Main Idea==<br /> <br /> Based on the definition of a conductor, it is easily assumed that stronger conductors can have charged particles moving more freely within it and in larger distances. There are two main situations where this can be observed. The first is in ionic solutions:<br /> <br /> ===Ionic Solutions===<br /> <br /> Ionic solutions, such as KCl or NaCl or NaI (solutions in which the ions dissociate), have individual ions of the dissociated particles. For example, a solution of NaI will have Na+, I-, and because it is an aqueous solution, some H+ and OH- as well. When an electric field is applied to this solution, the particles (as you'd imagine) move in the direction of the force applied by the electric field. However, the interesting concept here is that the charged particles move in a direction and accumulate, therefore creating a charge gradient, '''which in turn creates its own electric field!''' This can be shown in Figure 1, taken from the textbook. While ions are constantly moving, this is an accurate snapshot of what would be expected in the event of applied field/force. Furthermore, while ions move around the solution at all times (it is a conductor after all), there is a measurable excess of ions on the edges that generates the field. <br /> <br /> '''The net electric field is the superposition of the applied field and the field generated by the charge gradient and excess ion concentrations on the edges.'''<br /> <br /> ====A Mathematical Model: Drift Speed====<br /> <br /> In the phenomenon described above, when the external field is applied on an ionic solution, the Na+ and I- ions will move and bounce around a good bit, but due to collisions, they do not maintain a specific speed or trajectory. This is in spite of whether or not the force experienced is constant. In order to keep the ions moving at constant speed, also known as the drift speed, a constant electric field must be applied. This is modeled mathematically using the following equation: <br /> <br /> '''v = u*Enet''' <br /> <br /> where v is the drift speed, u is the mobility of the charge ((m/s)/(N/C)), and Enet is the net electric field applied to the ionic solution. The proportionality constant, u, is determined for the ions based on the solution and will be usually given or easy to derive in all practical problem sets using this concept. This is a linear relationship overall, meaning that in the event of no electric field, the ions will stop moving. <br /> <br /> ====Polarization Process in Ionic Solution====<br /> <br /> While polarization is a rapid process once initiated, it is not an on-off binary process. The instant that an electric field is applied, the drift speed is nonzero and the particles start tending towards the direction of the electric field. As ions pile up on the sides of the solution, the electric field inside becomes weaker and the system approaches an equilibrium at a microscopic level. At this equilibrium, drift speed is 0 and there is no NET MOTION of mobile charges in solution<br /> <br /> ===Charge Motion in Metals===<br /> <br /> The second example to look at for conductors is in metals.<br /> <br /> ====Mobile Electron Sea====<br /> <br /> Metals are an interesting idea structurally. Atoms of a metal are arranged in a rigid, ordered structure, sometimes known as a lattice structure (similar to crystal). Due to this, there is a interesting pattern of behavior. The inner electrons of each of these ordered atoms are attracted to the positively charged nucleus. Some of the outer electrons engage in solid atom interactions (ball and spring model), but other outer electrons participate in a pool of electrons that is allowed to move freely across the solid, in an &quot;electron sea&quot;. While they can move across the solid, they are very hard to extract and there are obviously some limitations to its direction of movement (different from liquid ionic solutions), but the mobile electron sea makes metals great conductor candidates (and thus are used in so many practical applications, including wires, microchips, cars, etc.) <br /> <br /> There is a caveat to this, however. You may ask, well won't the electrons repel each other and this not really allow for movement? Yes, but due to the presence of the positive cores, this interaction is neutralized. There is, therefore, no net interaction between the electrons inside a metal. Thus, the sea electrons move freely independent of electron field, positive cores, and appear not to interact with each other. The model of electron motion is defined by the Drude model, the steps of which are shown here:<br /> <br /> 1) When an electric field is applied in a metal, the electrons get excited and accelerate.<br /> <br /> 2) The electrons lose their energy when they collide with the lattices of the positive atomic cores<br /> <br /> 3) After the collision, the electrons again get accelerated and the entire process repeats itself. <br /> <br /> The average speed, then is defined by v, the drift speed, as mentioned earlier. For metals this equation is:<br /> <br /> '''v = (e*Enet*deltaT)/(m)'''<br /> <br /> where v is the drift speed, e is the charge of the electron, Enet is the net applied electric field, deltaT is the average time between collisions, and m is the mass of the electron. The average time between collisions is used because the time between each collision is uncontrollable and inconsistent. This equation is derived from the momentum equation where p = F*deltaT and F = Enet*e.<br /> <br /> This YouTube video does an excellent job of explaining the concept in further detail:<br /> <br /> https://www.youtube.com/watch?v=HKgOpmX-OFI<br /> <br /> ==Examples==<br /> <br /> ===Simple===<br /> <br /> The mobility of electrons in copper is 4.5E-3 (m/s)/(N/C). How much net electric field would be needed in order to give the electrons in copper a drift speed of 1.5E-3 m/s?<br /> <br /> ====Solution====<br /> <br /> This is a simple problem using the formula given for drift speed <br /> <br /> '''v = u*Enet''' <br /> <br /> Thus, Enet = v/u = 1.5E-3/4.5E-3 = 0.333 N/C. <br /> <br /> This also makes sense from a units perspective, as our solution is in N/C, the speed is m/s, and the mobility is given in (m/s)/(N/C). <br /> <br /> ===Middling===<br /> <br /> In a simple metal lattice structure, an electric field of 10 N/C is applied and 15 collisions are observed. The time between collisions increases after each collision, starting with 1 second, from collision 1 to collision 2. After 15 collisions, what is the drift speed of an electron in this metal lattice structure? <br /> <br /> ====Solution====<br /> <br /> This is a slightly more complex problem that requires a bit of analytical thinking and application of a formula. The formula:<br /> <br /> '''v = (e*Enet*deltaT)/(m)'''<br /> <br /> All of the quantities are known. e = 1.6E-19 C, Enet = 10 N/C, m = 9.1E-31<br /> <br /> However, deltaT is not immediately discernible. The question asks for the drift speed after 15 collisions. It might be some people's thought to just use the time between the 14th and 15th collision as the deltaT in the equation. DeltaT refers to the AVERAGE time between collisions. In this case, the deltaT would therefore be 7.5 seconds. <br /> <br /> Plugging these numbers in, you get: 1.3E13 m/s. This is extremely fast. As you can see, this speaks to how quickly electrons move through substances and how quickly polarization occurs, both in metals and in ionic solutions. <br /> <br /> ===Difficult===<br /> <br /> Summarize the difference between conductors and insulators in the following 4 categories:<br /> <br /> Mobile Charges<br /> Polarization<br /> Equilibrium<br /> Excess Charge<br /> <br /> ====Solution====<br /> <br /> 1) Conductors have mobile charges while insulators do not<br /> <br /> 2) Sea or mass of mobile electrons move when electric field is applied to a conductor. When an electric field is applied to an insulator, INDIVIDUAL atoms polarize. <br /> <br /> 3) Net electric field is 0 in a conductor at equilibrium whereas there is a nonzero electric field in an insulator at equilibrium. <br /> <br /> 4) Excess charge spreads over the surface of a conductor but clumps in patches in an insulator. <br /> <br /> (Adapted from textbook)<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> [http://www.scientificamerican.com/article/bring-science-home-reaction-time/]<br /> <br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Jshah46 http://www.physicsbook.gatech.edu/index.php?title=Polarization_of_a_conductor&diff=23037 2016-04-18T02:40:22Z

<p>Jshah46: </p> <hr /> <div>'''THIS HAS BEEN CLAIMED BY JAY SHAH<br /> '''<br /> Short Description of Topic<br /> <br /> ==The Main Idea==<br /> <br /> Based on the definition of a conductor, it is easily assumed that stronger conductors can have charged particles moving more freely within it and in larger distances. There are two main situations where this can be observed. The first is in ionic solutions:<br /> <br /> ===Ionic Solutions===<br /> <br /> Ionic solutions, such as KCl or NaCl or NaI (solutions in which the ions dissociate), have individual ions of the dissociated particles. For example, a solution of NaI will have Na+, I-, and because it is an aqueous solution, some H+ and OH- as well. When an electric field is applied to this solution, the particles (as you'd imagine) move in the direction of the force applied by the electric field. However, the interesting concept here is that the charged particles move in a direction and accumulate, therefore creating a charge gradient, '''which in turn creates its own electric field!''' This can be shown in Figure 1, taken from the textbook. While ions are constantly moving, this is an accurate snapshot of what would be expected in the event of applied field/force. Furthermore, while ions move around the solution at all times (it is a conductor after all), there is a measurable excess of ions on the edges that generates the field. <br /> <br /> '''The net electric field is the superposition of the applied field and the field generated by the charge gradient and excess ion concentrations on the edges.'''<br /> <br /> ====A Mathematical Model: Drift Speed====<br /> <br /> In the phenomenon described above, when the external field is applied on an ionic solution, the Na+ and I- ions will move and bounce around a good bit, but due to collisions, they do not maintain a specific speed or trajectory. This is in spite of whether or not the force experienced is constant. In order to keep the ions moving at constant speed, also known as the drift speed, a constant electric field must be applied. This is modeled mathematically using the following equation: <br /> <br /> '''v = u*Enet''' <br /> <br /> where v is the drift speed, u is the mobility of the charge ((m/s)/(N/C)), and Enet is the net electric field applied to the ionic solution. The proportionality constant, u, is determined for the ions based on the solution and will be usually given or easy to derive in all practical problem sets using this concept. This is a linear relationship overall, meaning that in the event of no electric field, the ions will stop moving. <br /> <br /> ====Polarization Process in Ionic Solution====<br /> <br /> While polarization is a rapid process once initiated, it is not an on-off binary process. The instant that an electric field is applied, the drift speed is nonzero and the particles start tending towards the direction of the electric field. As ions pile up on the sides of the solution, the electric field inside becomes weaker and the system approaches an equilibrium at a microscopic level. At this equilibrium, drift speed is 0 and there is no NET MOTION of mobile charges in solution<br /> <br /> ===Charge Motion in Metals===<br /> <br /> The second example to look at for conductors is in metals.<br /> <br /> ====Mobile Electron Sea====<br /> <br /> Metals are an interesting idea structurally. Atoms of a metal are arranged in a rigid, ordered structure, sometimes known as a lattice structure (similar to crystal). Due to this, there is a interesting pattern of behavior. The inner electrons of each of these ordered atoms are attracted to the positively charged nucleus. Some of the outer electrons engage in solid atom interactions (ball and spring model), but other outer electrons participate in a pool of electrons that is allowed to move freely across the solid, in an &quot;electron sea&quot;. While they can move across the solid, they are very hard to extract and there are obviously some limitations to its direction of movement (different from liquid ionic solutions), but the mobile electron sea makes metals great conductor candidates (and thus are used in so many practical applications, including wires, microchips, cars, etc.) <br /> <br /> There is a caveat to this, however. You may ask, well won't the electrons repel each other and this not really allow for movement? Yes, but due to the presence of the positive cores, this interaction is neutralized. There is, therefore, no net interaction between the electrons inside a metal. Thus, the sea electrons move freely independent of electron field, positive cores, and appear not to interact with each other. The model of electron motion is defined by the Drude model, the steps of which are shown here:<br /> <br /> 1) When an electric field is applied in a metal, the electrons get excited and accelerate.<br /> <br /> 2) The electrons lose their energy when they collide with the lattices of the positive atomic cores<br /> <br /> 3) After the collision, the electrons again get accelerated and the entire process repeats itself. <br /> <br /> The average speed, then is defined by v, the drift speed, as mentioned earlier. For metals this equation is:<br /> <br /> '''v = (e*Enet*deltaT)/(m)'''<br /> <br /> where v is the drift speed, e is the charge of the electron, Enet is the net applied electric field, deltaT is the average time between collisions, and m is the mass of the electron. The average time between collisions is used because the time between each collision is uncontrollable and inconsistent. This equation is derived from the momentum equation where p = F*deltaT and F = Enet*e.<br /> <br /> ==Examples==<br /> <br /> ===Simple===<br /> <br /> The mobility of electrons in copper is 4.5E-3 (m/s)/(N/C). How much net electric field would be needed in order to give the electrons in copper a drift speed of 1.5E-3 m/s?<br /> <br /> ====Solution====<br /> <br /> This is a simple problem using the formula given for drift speed <br /> <br /> '''v = u*Enet''' <br /> <br /> Thus, Enet = v/u = 1.5E-3/4.5E-3 = 0.333 N/C. <br /> <br /> This also makes sense from a units perspective, as our solution is in N/C, the speed is m/s, and the mobility is given in (m/s)/(N/C). <br /> <br /> ===Middling===<br /> <br /> In a simple metal lattice structure, an electric field of 10 N/C is applied and 15 collisions are observed. The time between collisions increases after each collision, starting with 1 second, from collision 1 to collision 2. After 15 collisions, what is the drift speed of an electron in this metal lattice structure? <br /> <br /> This is a slightly more complex problem that requires a bit of analytical thinking and application of a formula. The formula:<br /> <br /> '''v = (e*Enet*deltaT)/(m)'''<br /> <br /> All of the quantities are known. e = 1.6E-19 C, Enet = 10 N/C, m = 9.1E-31<br /> <br /> However, deltaT is not immediately discernible. The question asks for the drift speed after 15 collisions. It might be some people's thought to just use the time between the 14th and 15th collision as the deltaT in the equation. DeltaT refers to the AVERAGE time between collisions. In this case, the deltaT would therefore be 7.5 seconds. <br /> <br /> Plugging these numbers in, you get: 1.3E13 m/s. This is extremely fast. As you can see, this speaks to how quickly electrons move through substances and how quickly polarization occurs, both in metals and in ionic solutions. <br /> <br /> <br /> ===Difficult===<br /> <br /> <br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> [http://www.scientificamerican.com/article/bring-science-home-reaction-time/]<br /> <br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Jshah46 http://www.physicsbook.gatech.edu/index.php?title=Polarization_of_a_conductor&diff=23010 2016-04-18T02:28:22Z

<p>Jshah46: </p> <hr /> <div>'''THIS HAS BEEN CLAIMED BY JAY SHAH<br /> '''<br /> Short Description of Topic<br /> <br /> ==The Main Idea==<br /> <br /> Based on the definition of a conductor, it is easily assumed that stronger conductors can have charged particles moving more freely within it and in larger distances. There are two main situations where this can be observed. The first is in ionic solutions:<br /> <br /> ===Ionic Solutions===<br /> <br /> Ionic solutions, such as KCl or NaCl or NaI (solutions in which the ions dissociate), have individual ions of the dissociated particles. For example, a solution of NaI will have Na+, I-, and because it is an aqueous solution, some H+ and OH- as well. When an electric field is applied to this solution, the particles (as you'd imagine) move in the direction of the force applied by the electric field. However, the interesting concept here is that the charged particles move in a direction and accumulate, therefore creating a charge gradient, '''which in turn creates its own electric field!''' This can be shown in Figure 1, taken from the textbook. While ions are constantly moving, this is an accurate snapshot of what would be expected in the event of applied field/force. Furthermore, while ions move around the solution at all times (it is a conductor after all), there is a measurable excess of ions on the edges that generates the field. <br /> <br /> '''The net electric field is the superposition of the applied field and the field generated by the charge gradient and excess ion concentrations on the edges.'''<br /> <br /> ====A Mathematical Model: Drift Speed====<br /> <br /> In the phenomenon described above, when the external field is applied on an ionic solution, the Na+ and I- ions will move and bounce around a good bit, but due to collisions, they do not maintain a specific speed or trajectory. This is in spite of whether or not the force experienced is constant. In order to keep the ions moving at constant speed, also known as the drift speed, a constant electric field must be applied. This is modeled mathematically using the following equation: <br /> <br /> '''v = u*Enet''' <br /> <br /> where v is the drift speed, u is the mobility of the charge ((m/s)/(N/C)), and Enet is the net electric field applied to the ionic solution. The proportionality constant, u, is determined for the ions based on the solution and will be usually given or easy to derive in all practical problem sets using this concept. This is a linear relationship overall, meaning that in the event of no electric field, the ions will stop moving. <br /> <br /> ====Polarization Process in Ionic Solution====<br /> <br /> While polarization is a rapid process once initiated, it is not an on-off binary process. The instant that an electric field is applied, the drift speed is nonzero and the particles start tending towards the direction of the electric field. As ions pile up on the sides of the solution, the electric field inside becomes weaker and the system approaches an equilibrium at a microscopic level. At this equilibrium, drift speed is 0 and there is no NET MOTION of mobile charges in solution<br /> <br /> ===Charge Motion in Metals===<br /> <br /> The second example to look at for conductors is in metals.<br /> <br /> ====Mobile Electron Sea====<br /> <br /> Metals are an interesting idea structurally. Atoms of a metal are arranged in a rigid, ordered structure, sometimes known as a lattice structure (similar to crystal). Due to this, there is a interesting pattern of behavior. The inner electrons of each of these ordered atoms are attracted to the positively charged nucleus. Some of the outer electrons engage in solid atom interactions (ball and spring model), but other outer electrons participate in a pool of electrons that is allowed to move freely across the solid, in an &quot;electron sea&quot;. While they can move across the solid, they are very hard to extract and there are obviously some limitations to its direction of movement (different from liquid ionic solutions), but the mobile electron sea makes metals great conductor candidates (and thus are used in so many practical applications, including wires, microchips, cars, etc.) <br /> <br /> There is a caveat to this, however. You may ask, well won't the electrons repel each other and this not really allow for movement? Yes, but due to the presence of the positive cores, this interaction is neutralized. There is, therefore, no net interaction between the electrons inside a metal. Thus, the sea electrons move freely independent of electron field, positive cores, and appear not to interact with each other. The model of electron motion is defined by the Drude model, the steps of which are shown here:<br /> <br /> 1) When an electric field is applied in a metal, the electrons get excited and accelerate.<br /> <br /> 2) The electrons lose their energy when they collide with the lattices of the positive atomic cores<br /> <br /> 3) After the collision, the electrons again get accelerated and the entire process repeats itself. <br /> <br /> The average speed, then is defined by v, the drift speed, as mentioned earlier. For metals this equation is:<br /> <br /> '''v = (e*Enet*deltaT)/(m)'''<br /> <br /> where v is the drift speed, e is the charge of the electron, Enet is the net applied electric field, deltaT is the average time between collisions, and m is the mass of the electron. The average time between collisions is used because the time between each collision is uncontrollable and inconsistent. This equation is derived from the momentum equation where p = F*deltaT and F = Enet*e.<br /> <br /> ==Examples==<br /> <br /> ===Simple===<br /> <br /> The mobility of electrons in copper is 4.5E-3 (m/s)/(N/C). How much net electric field would be needed in order to give the electrons in copper a drift speed of 1.5E-3 m/s?<br /> <br /> ====Solution====<br /> <br /> This is a simple problem using the formula given for drift speed <br /> <br /> '''v = u*Enet''' <br /> <br /> Thus, Enet = v/u = 1.5E-3/4.5E-3 = 0.333 N/C. <br /> <br /> This also makes sense from a units perspective, as our solution is in N/C, the speed is m/s, and the mobility is given in (m/s)/(N/C). <br /> <br /> ===Middling===<br /> <br /> <br /> ===Difficult===<br /> <br /> <br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> [http://www.scientificamerican.com/article/bring-science-home-reaction-time/]<br /> <br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Jshah46 http://www.physicsbook.gatech.edu/index.php?title=Polarization_of_a_conductor&diff=22986 2016-04-18T02:18:47Z

<p>Jshah46: </p> <hr /> <div>'''THIS HAS BEEN CLAIMED BY JAY SHAH<br /> '''<br /> Short Description of Topic<br /> <br /> ==The Main Idea==<br /> <br /> Based on the definition of a conductor, it is easily assumed that stronger conductors can have charged particles moving more freely within it and in larger distances. There are two main situations where this can be observed. The first is in ionic solutions:<br /> <br /> ===Ionic Solutions===<br /> <br /> Ionic solutions, such as KCl or NaCl or NaI (solutions in which the ions dissociate), have individual ions of the dissociated particles. For example, a solution of NaI will have Na+, I-, and because it is an aqueous solution, some H+ and OH- as well. When an electric field is applied to this solution, the particles (as you'd imagine) move in the direction of the force applied by the electric field. However, the interesting concept here is that the charged particles move in a direction and accumulate, therefore creating a charge gradient, '''which in turn creates its own electric field!''' This can be shown in Figure 1, taken from the textbook. While ions are constantly moving, this is an accurate snapshot of what would be expected in the event of applied field/force. Furthermore, while ions move around the solution at all times (it is a conductor after all), there is a measurable excess of ions on the edges that generates the field. <br /> <br /> '''The net electric field is the superposition of the applied field and the field generated by the charge gradient and excess ion concentrations on the edges.'''<br /> <br /> ====A Mathematical Model: Drift Speed====<br /> <br /> In the phenomenon described above, when the external field is applied on an ionic solution, the Na+ and I- ions will move and bounce around a good bit, but due to collisions, they do not maintain a specific speed or trajectory. This is in spite of whether or not the force experienced is constant. In order to keep the ions moving at constant speed, also known as the drift speed, a constant electric field must be applied. This is modeled mathematically using the following equation: <br /> <br /> '''v = u*Enet''' <br /> <br /> where v is the drift speed, u is the mobility of the charge ((m/s)/(N/C)), and Enet is the net electric field applied to the ionic solution. The proportionality constant, u, is determined for the ions based on the solution and will be usually given or easy to derive in all practical problem sets using this concept. This is a linear relationship overall, meaning that in the event of no electric field, the ions will stop moving. <br /> <br /> ====Polarization Process in Ionic Solution====<br /> <br /> While polarization is a rapid process once initiated, it is not an on-off binary process. The instant that an electric field is applied, the drift speed is nonzero and the particles start tending towards the direction of the electric field. As ions pile up on the sides of the solution, the electric field inside becomes weaker and the system approaches an equilibrium at a microscopic level. At this equilibrium, drift speed is 0 and there is no NET MOTION of mobile charges in solution<br /> <br /> ===Charge Motion in Metals===<br /> <br /> The second example to look at for conductors is in metals.<br /> <br /> ====Mobile Electron Sea====<br /> <br /> Metals are an interesting idea structurally. Atoms of a metal are arranged in a rigid, ordered structure, sometimes known as a lattice structure (similar to crystal). Due to this, there is a interesting pattern of behavior. The inner electrons of each of these ordered atoms are attracted to the positively charged nucleus. Some of the outer electrons engage in solid atom interactions (ball and spring model), but other outer electrons participate in a pool of electrons that is allowed to move freely across the solid, in an &quot;electron sea&quot;. While they can move across the solid, they are very hard to extract and there are obviously some limitations to its direction of movement (different from liquid ionic solutions), but the mobile electron sea makes metals great conductor candidates (and thus are used in so many practical applications, including wires, microchips, cars, etc.) <br /> <br /> There is a caveat to this, however. You may ask, well won't the electrons repel each other and this not really allow for movement? Yes, but due to the presence of the positive cores, this interaction is neutralized. There is, therefore, no net interaction between the electrons inside a metal. Thus, the sea electrons move freely independent of electron field, positive cores, and appear not to interact with each other. The model of electron motion is defined by the Drude model, the steps of which are shown here:<br /> <br /> 1) When an electric field is applied in a metal, the electrons get excited and accelerate.<br /> <br /> 2) The electrons lose their energy when they collide with the lattices of the positive atomic cores<br /> <br /> 3) After the collision, the electrons again get accelerated and the entire process repeats itself. <br /> <br /> The average speed, then is defined by v, the drift speed, as mentioned earlier. For metals this equation is:<br /> <br /> '''v = (e*Enet*deltaT)/(m)'''<br /> <br /> where v is the drift speed, e is the charge of the electron, Enet is the net applied electric field, deltaT is the average time between collisions, and m is the mass of the electron. The average time between collisions is used because the time between each collision is uncontrollable and inconsistent. This equation is derived from the momentum equation where p = F*deltaT and F = Enet*e.<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> ===Middling===<br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> [http://www.scientificamerican.com/article/bring-science-home-reaction-time/]<br /> <br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Jshah46 http://www.physicsbook.gatech.edu/index.php?title=Polarization_of_a_conductor&diff=22593 2016-04-17T22:59:45Z

<p>Jshah46: </p> <hr /> <div>'''THIS HAS BEEN CLAIMED BY JAY SHAH<br /> '''<br /> Short Description of Topic<br /> <br /> ==The Main Idea==<br /> <br /> Based on the definition of a conductor, it is easily assumed that stronger conductors can have charged particles moving more freely within it and in larger distances. There are two main situations where this can be observed. The first is in ionic solutions:<br /> <br /> ===Ionic Solutions===<br /> <br /> Ionic solutions, such as KCl or NaCl or NaI (solutions in which the ions dissociate), have individual ions of the dissociated particles. For example, a solution of NaI will have Na+, I-, and because it is an aqueous solution, some H+ and OH- as well. When an electric field is applied to this solution, the particles (as you'd imagine) move in the direction of the force applied by the electric field. However, the interesting concept here is that the charged particles move in a direction and accumulate, therefore creating a charge gradient, '''which in turn creates its own electric field!''' This can be shown in Figure 1, taken from the textbook. While ions are constantly moving, this is an accurate snapshot of what would be expected in the event of applied field/force. Furthermore, while ions move around the solution at all times (it is a conductor after all), there is a measurable excess of ions on the edges that generates the field. <br /> <br /> '''The net electric field is the superposition of the applied field and the field generated by the charge gradient and excess ion concentrations on the edges.'''<br /> <br /> ====A Mathematical Model: Drift Speed====<br /> <br /> In the phenomenon described above, when the external field is applied on an ionic solution, the Na+ and I- ions will move and bounce around a good bit, but due to collisions, they do not maintain a specific speed or trajectory. This is in spite of whether or not the force experienced is constant. In order to keep the ions moving at constant speed, also known as the drift speed, a constant electric field must be applied. This is modeled mathematically using the following equation: <br /> <br /> '''v = u*Enet''' <br /> <br /> where v is the drift speed, u is the mobility of the charge ((m/s)/(N/C)), and Enet is the net electric field applied to the ionic solution. The proportionality constant, u, is determined for the ions based on the solution and will be usually given or easy to derive in all practical problem sets using this concept. This is a linear relationship overall, meaning that in the event of no electric field, the ions will stop moving. <br /> <br /> ====Polarization Process in Ionic Solution====<br /> <br /> While polarization is a rapid process once initiated, it is not an on-off binary process. The instant that an electric field is applied, the drift speed is nonzero and the particles start tending towards the direction of the electric field. As ions pile up on the sides of the solution, the electric field inside becomes weaker and the system approaches an equilibrium at a microscopic level. At this equilibrium, drift speed is 0 and there is no NET MOTION of mobile charges in solution<br /> <br /> ===Charge Motion in Metals===<br /> <br /> The second example to look at for conductors is in metals.<br /> <br /> ====Mobile Electron Sea====<br /> <br /> Metals are an interesting idea structurally. Atoms of a metal are arranged in a rigid, ordered structure, sometimes known as a lattice structure (similar to crystal). Due to this, there is a interesting pattern of behavior. The inner electrons of each of these ordered atoms are attracted to the positively charged nucleus. Some of the outer electrons engage in solid atom interactions (ball and spring model), but other outer electrons participate in a pool of electrons that is allowed to move freely across the solid, in an &quot;electron sea&quot;. While they can move across the solid, they are very hard to extract and there are obviously some limitations to its direction of movement (different from liquid ionic solutions), but the mobile electron sea makes metals great conductor candidates (and thus are used in so many practical applications, including wires, microchips, cars, etc.) <br /> <br /> There is a caveat to this, however. You may ask, well won't the electrons repel each other and this not really allow for movement? Yes, but due to the presence of the positive cores, this interaction is neutralized. There is, therefore, no net interaction between the electrons inside a metal. Thus, the sea electrons move freely independent of electron field, positive cores, and appear not to interact with each other. The model of electron motion is defined by the Drude model, the steps of which are shown here:<br /> <br /> 1) When an electric field is applied in a metal, the electrons get excited and accelerate.<br /> <br /> 2) The electrons lose their energy when they collide with the lattices of the positive atomic cores<br /> <br /> 3) After the collision, the electrons again get accelerated and the entire process repeats itself. <br /> <br /> The average speed, then is defined by v, the drift speed, as mentioned earlier. <br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> ===Middling===<br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> [http://www.scientificamerican.com/article/bring-science-home-reaction-time/]<br /> <br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Jshah46 http://www.physicsbook.gatech.edu/index.php?title=Polarization_of_a_conductor&diff=22592 2016-04-17T22:59:23Z

<p>Jshah46: </p> <hr /> <div>'''THIS HAS BEEN CLAIMED BY JAY SHAH<br /> '''<br /> Short Description of Topic<br /> <br /> ==The Main Idea==<br /> <br /> Based on the definition of a conductor, it is easily assumed that stronger conductors can have charged particles moving more freely within it and in larger distances. There are two main situations where this can be observed. The first is in ionic solutions:<br /> <br /> ===Ionic Solutions===<br /> <br /> Ionic solutions, such as KCl or NaCl or NaI (solutions in which the ions dissociate), have individual ions of the dissociated particles. For example, a solution of NaI will have Na+, I-, and because it is an aqueous solution, some H+ and OH- as well. When an electric field is applied to this solution, the particles (as you'd imagine) move in the direction of the force applied by the electric field. However, the interesting concept here is that the charged particles move in a direction and accumulate, therefore creating a charge gradient, '''which in turn creates its own electric field!''' This can be shown in Figure 1, taken from the textbook. While ions are constantly moving, this is an accurate snapshot of what would be expected in the event of applied field/force. Furthermore, while ions move around the solution at all times (it is a conductor after all), there is a measurable excess of ions on the edges that generates the field. <br /> <br /> '''The net electric field is the superposition of the applied field and the field generated by the charge gradient and excess ion concentrations on the edges.'''<br /> <br /> ====A Mathematical Model: Drift Speed====<br /> <br /> In the phenomenon described above, when the external field is applied on an ionic solution, the Na+ and I- ions will move and bounce around a good bit, but due to collisions, they do not maintain a specific speed or trajectory. This is in spite of whether or not the force experienced is constant. In order to keep the ions moving at constant speed, also known as the drift speed, a constant electric field must be applied. This is modeled mathematically using the following equation: <br /> <br /> '''v = u*Enet''' <br /> <br /> where v is the drift speed, u is the mobility of the charge ((m/s)/(N/C)), and Enet is the net electric field applied to the ionic solution. The proportionality constant, u, is determined for the ions based on the solution and will be usually given or easy to derive in all practical problem sets using this concept. This is a linear relationship overall, meaning that in the event of no electric field, the ions will stop moving. <br /> <br /> ====Polarization Process in Ionic Solution====<br /> <br /> While polarization is a rapid process once initiated, it is not an on-off binary process. The instant that an electric field is applied, the drift speed is nonzero and the particles start tending towards the direction of the electric field. As ions pile up on the sides of the solution, the electric field inside becomes weaker and the system approaches an equilibrium at a microscopic level. At this equilibrium, drift speed is 0 and there is no NET MOTION of mobile charges in solution<br /> <br /> ===Charge Motion in Metals===<br /> <br /> The second example to look at for conductors is in metals.<br /> <br /> ====Mobile Electron Sea====<br /> <br /> Metals are an interesting idea structurally. Atoms of a metal are arranged in a rigid, ordered structure, sometimes known as a lattice structure (similar to crystal). Due to this, there is a interesting pattern of behavior. The inner electrons of each of these ordered atoms are attracted to the positively charged nucleus. Some of the outer electrons engage in solid atom interactions (ball and spring model), but other outer electrons participate in a pool of electrons that is allowed to move freely across the solid, in an &quot;electron sea&quot;. While they can move across the solid, they are very hard to extract and there are obviously some limitations to its direction of movement (different from liquid ionic solutions), but the mobile electron sea makes metals great conductor candidates (and thus are used in so many practical applications, including wires, microchips, cars, etc.) <br /> <br /> There is a caveat to this, however. You may ask, well won't the electrons repel each other and this not really allow for movement? Yes, but due to the presence of the positive cores, this interaction is neutralized. There is, therefore, no net interaction between the electrons inside a metal. Thus, the sea electrons move freely independent of electron field, positive cores, and appear not to interact with each other. The model of electron motion is defined by the Drude model, the steps of which are shown here:<br /> <br /> 1) When an electric field is applied in a metal, the electrons get excited and accelerate.<br /> 2) The electrons lose their energy when they collide with the lattices of the positive atomic cores<br /> 3) After the collision, the electrons again get accelerated and the entire process repeats itself. <br /> <br /> The average speed, then is defined by v, the drift speed, as mentioned earlier. <br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> ===Middling===<br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> [http://www.scientificamerican.com/article/bring-science-home-reaction-time/]<br /> <br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Jshah46 http://www.physicsbook.gatech.edu/index.php?title=Polarization_of_a_conductor&diff=22587 2016-04-17T22:47:07Z

<p>Jshah46: </p> <hr /> <div>'''THIS HAS BEEN CLAIMED BY JAY SHAH<br /> '''<br /> Short Description of Topic<br /> <br /> ==The Main Idea==<br /> <br /> Based on the definition of a conductor, it is easily assumed that stronger conductors can have charged particles moving more freely within it and in larger distances. There are two main situations where this can be observed. The first is in ionic solutions:<br /> <br /> <br /> ===Ionic Solutions===<br /> <br /> Ionic solutions, such as KCl or NaCl or NaI (solutions in which the ions dissociate), have individual ions of the dissociated particles. For example, a solution of NaI will have Na+, I-, and because it is an aqueous solution, some H+ and OH- as well. When an electric field is applied to this solution, the particles (as you'd imagine) move in the direction of the force applied by the electric field. However, the interesting concept here is that the charged particles move in a direction and accumulate, therefore creating a charge gradient, '''which in turn creates its own electric field!''' This can be shown in Figure 1, taken from the textbook. While ions are constantly moving, this is an accurate snapshot of what would be expected in the event of applied field/force. Furthermore, while ions move around the solution at all times (it is a conductor after all), there is a measurable excess of ions on the edges that generates the field. <br /> <br /> '''The net electric field is the superposition of the applied field and the field generated by the charge gradient and excess ion concentrations on the edges.'''<br /> <br /> ====A Mathematical Model: Drift Speed====<br /> <br /> In the phenomenon described above, when the external field is applied on an ionic solution, the Na+ and I- ions will move and bounce around a good bit, but due to collisions, they do not maintain a specific speed or trajectory. This is in spite of whether or not the force experienced is constant. In order to keep the ions moving at constant speed, also known as the drift speed, a constant electric field must be applied. This is modeled mathematically using the following equation: <br /> <br /> '''v = u*Enet''' <br /> <br /> where v is the drift speed, u is the mobility of the charge ((m/s)/(N/C)), and Enet is the net electric field applied to the ionic solution. The proportionality constant, u, is determined for the ions based on the solution and will be usually given or easy to derive in all practical problem sets using this concept. This is a linear relationship overall, meaning that in the event of no electric field, the ions will stop moving. <br /> <br /> ====Polarization Process in Ionic Solution====<br /> <br /> While polarization is a rapid process once initiated, it is not an on-off binary process. The instant that an electric field is applied, the drift speed is nonzero and the particles start tending towards the direction of the electric field. As ions pile up on the sides of the solution, the electric field inside becomes weaker and the system approaches an equilibrium at a microscopic level. At this equilibrium, drift speed is 0 and there is no NET MOTION of mobile charges in solution<br /> <br /> ===Charge Motion in Metals===<br /> <br /> ====Mobile Electron Sea====<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> ===Middling===<br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> [http://www.scientificamerican.com/article/bring-science-home-reaction-time/]<br /> <br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Jshah46 http://www.physicsbook.gatech.edu/index.php?title=Polarization_of_a_conductor&diff=22583 2016-04-17T22:32:45Z

<p>Jshah46: </p> <hr /> <div>'''THIS HAS BEEN CLAIMED BY JAY SHAH<br /> '''<br /> Short Description of Topic<br /> <br /> ==The Main Idea==<br /> <br /> Based on the definition of a conductor, it is easily assumed that stronger conductors can have charged particles moving more freely within it and in larger distances. There are two main situations where this can be observed. The first is in ionic solutions:<br /> <br /> <br /> ===Ionic Solutions===<br /> <br /> Ionic solutions, such as KCl or NaCl or NaI (solutions in which the ions dissociate), have individual ions of the dissociated particles. For example, a solution of NaI will have Na+, I-, and because it is an aqueous solution, some H+ and OH- as well. When an electric field is applied to this solution, the particles (as you'd imagine) move in the direction of the force applied by the electric field. However, the interesting concept here is that the charged particles move in a direction and accumulate, therefore creating a charge gradient, '''which in turn creates its own electric field!''' This can be shown in Figure 1, taken from the textbook. While ions are constantly moving, this is an accurate snapshot of what would be expected in the event of applied field/force. Furthermore, while ions move around the solution at all times (it is a conductor after all), there is a measurable excess of ions on the edges that generates the field. <br /> <br /> '''The net electric field is the superposition of the applied field and the field generated by the charge gradient and excess ion concentrations on the edges.'''<br /> <br /> ===A Mathematical Model===<br /> <br /> In the phenomenon described above, when the external field is applied on an ionic solution, the Na+ and I- ions will move and bounce around a good bit, but due to collisions, they do not maintain a specific speed or trajectory. This is in spite of whether or not the force experienced is constant. In order to keep the ions moving at constant speed, also known as the drift speed, a constant electric field must be applied. This is modeled mathematically using the following equation: <br /> <br /> '''v = u*Enet''' <br /> <br /> where v is the drift speed, u is the mobility of the charge ((m/s)/(N/C)), and Enet is the net electric field applied to the ionic solution. The proportionality constant, u, is determined for the ions based on the solution and will be usually given or easy to derive in all practical problem sets using this concept. This is a linear relationship overall, meaning that in the event of no electric field, the ions will stop moving. <br /> <br /> ===A Computational Model===<br /> <br /> How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> ===Middling===<br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> [http://www.scientificamerican.com/article/bring-science-home-reaction-time/]<br /> <br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Jshah46 http://www.physicsbook.gatech.edu/index.php?title=Polarization_of_a_conductor&diff=22582 2016-04-17T22:30:18Z

<p>Jshah46: </p> <hr /> <div>'''THIS HAS BEEN CLAIMED BY JAY SHAH<br /> '''<br /> Short Description of Topic<br /> <br /> ==The Main Idea==<br /> <br /> Based on the definition of a conductor, it is easily assumed that stronger conductors can have charged particles moving more freely within it and in larger distances. There are two main situations where this can be observed. The first is in ionic solutions:<br /> <br /> <br /> '''Ionic Solutions'''<br /> <br /> Ionic solutions, such as KCl or NaCl or NaI (solutions in which the ions dissociate), have individual ions of the dissociated particles. For example, a solution of NaI will have Na+, I-, and because it is an aqueous solution, some H+ and OH- as well. When an electric field is applied to this solution, the particles (as you'd imagine) move in the direction of the force applied by the electric field. However, the interesting concept here is that the charged particles move in a direction and accumulate, therefore creating a charge gradient, '''which in turn creates its own electric field!''' This can be shown in Figure 1, taken from the textbook. While ions are constantly moving, this is an accurate snapshot of what would be expected in the event of applied field/force. Furthermore, while ions move around the solution at all times (it is a conductor after all), there is a measurable excess of ions on the edges that generates the field. <br /> <br /> '''The net electric field is the superposition of the applied field and the field generated by the charge gradient and excess ion concentrations on the edges.'''<br /> <br /> ===A Mathematical Model===<br /> <br /> In the phenomenon described above, when the external field is applied on an ionic solution, the Na+ and I- ions will move and bounce around a good bit, but due to collisions, they do not maintain a specific speed or trajectory. This is in spite of whether or not the force experienced is constant. In order to keep the ions moving at constant speed, also known as the drift speed, a constant electric field must be applied. This is modeled mathematically using the following equation: <br /> <br /> '''v = u*Enet''' <br /> <br /> where v is the drift speed, u is the mobility of the charge ((m/s)/(N/C)), and Enet is the net electric field applied to the ionic solution. The proportionality constant, u, is determined for the ions based on the solution and will be usually given or easy to derive in all practical problem sets using this concept. This is a linear relationship overall, meaning that in the event of no electric field, the ions will stop moving. <br /> <br /> ===A Computational Model===<br /> <br /> How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> ===Middling===<br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> [http://www.scientificamerican.com/article/bring-science-home-reaction-time/]<br /> <br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Jshah46 http://www.physicsbook.gatech.edu/index.php?title=Polarization_of_a_conductor&diff=22580 2016-04-17T22:28:16Z

<p>Jshah46: </p> <hr /> <div>'''THIS HAS BEEN CLAIMED BY JAY SHAH<br /> '''<br /> Short Description of Topic<br /> <br /> ==The Main Idea==<br /> <br /> Based on the definition of a conductor, it is easily assumed that stronger conductors can have charged particles moving more freely within it and in larger distances. There are two main situations where this can be observed. The first is in ionic solutions:<br /> <br /> <br /> '''Ionic Solutions'''<br /> <br /> Ionic solutions, such as KCl or NaCl or NaI (solutions in which the ions dissociate), have individual ions of the dissociated particles. For example, a solution of NaI will have Na+, I-, and because it is an aqueous solution, some H+ and OH- as well. When an electric field is applied to this solution, the particles (as you'd imagine) move in the direction of the force applied by the electric field. However, the interesting concept here is that the charged particles move in a direction and accumulate, therefore creating a charge gradient, '''which in turn creates its own electric field!''' This can be shown in Figure 1, taken from the textbook. While ions are constantly moving, this is an accurate snapshot of what would be expected in the event of applied field/force. Furthermore, while ions move around the solution at all times (it is a conductor after all), there is a measurable excess of ions on the edges that generates the field. <br /> <br /> '''The net electric field is the superposition of the applied field and the field generated by the charge gradient and excess ion concentrations on the edges.'''<br /> <br /> ===A Mathematical Model===<br /> <br /> In the phenomenon described above, when the external field is applied on an ionic solution, the Na+ and I- ions will move and bounce around a good bit, but due to collisions, they do not maintain a specific speed or trajectory. This is in spite of whether or not the force experienced is constant. In order to keep the ions moving at constant speed, also known as the drift speed, a constant electric field must be applied. This is modeled mathematically using the following equation: <br /> <br /> '''v = u*Enet''' <br /> <br /> where v is the drift speed, u is the mobility of the charge ((m/s)/(N/C)), and Enet is the net electric field applied to the ionic solution. <br /> <br /> What are the mathematical equations that allow us to model this topic. For example &lt;math&gt;{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}&lt;/math&gt; where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.<br /> <br /> ===A Computational Model===<br /> <br /> How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> ===Middling===<br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> [http://www.scientificamerican.com/article/bring-science-home-reaction-time/]<br /> <br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Jshah46 http://www.physicsbook.gatech.edu/index.php?title=Polarization_of_a_conductor&diff=22578 2016-04-17T22:21:04Z

<p>Jshah46: </p> <hr /> <div>'''THIS HAS BEEN CLAIMED BY JAY SHAH<br /> '''<br /> Short Description of Topic<br /> <br /> ==The Main Idea==<br /> <br /> Based on the definition of a conductor, it is easily assumed that stronger conductors can have charged particles moving more freely within it and in larger distances. There are two main situations where this can be observed. The first is in ionic solutions:<br /> <br /> <br /> '''Ionic Solutions'''<br /> <br /> <br /> Ionic solutions, such as KCl or NaCl or NaI (solutions in which the ions dissociate), have individual ions of the dissociated particles. For example, a solution of NaI will have Na+, I-, and because it is an aqueous solution, some H+ and OH- as well. When an electric field is applied to this solution, the particles (as you'd imagine) move in the direction of the force applied by the electric field. However, the interesting concept here is that the charged particles move in a direction and accumulate, therefore creating a charge gradient, '''which in turn creates its own electric field!''' This can be shown in Figure 1, taken from the textbook. While ions are constantly moving, this is an accurate snapshot of what would be expected in the event of applied field/force. Furthermore, while ions move around the solution at all times (it is a conductor after all), there is a measurable excess of ions on the edges that generates the field. <br /> <br /> '''The net electric field is the superposition of the applied field and the field generated by the charge gradient and excess ion concentrations on the edges.'''<br /> <br /> <br /> ===A Mathematical Model===<br /> <br /> What are the mathematical equations that allow us to model this topic. For example &lt;math&gt;{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}&lt;/math&gt; where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.<br /> <br /> ===A Computational Model===<br /> <br /> How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> ===Middling===<br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> [http://www.scientificamerican.com/article/bring-science-home-reaction-time/]<br /> <br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Jshah46 http://www.physicsbook.gatech.edu/index.php?title=Polarization_of_a_conductor&diff=22577 2016-04-17T22:19:40Z

<p>Jshah46: </p> <hr /> <div>'''THIS HAS BEEN CLAIMED BY JAY SHAH<br /> '''<br /> Short Description of Topic<br /> <br /> ==The Main Idea==<br /> <br /> Based on the definition of a conductor, it is easily assumed that stronger conductors can have charged particles moving more freely within it and in larger distances. There are two main situations where this can be observed. The first is in ionic solutions:<br /> <br /> [[Ionic Solutions]]<br /> <br /> Ionic solutions, such as KCl or NaCl or NaI (solutions in which the ions dissociate), have individual ions of the dissociated particles. For example, a solution of NaI will have Na+, I-, and because it is an aqueous solution, some H+ and OH- as well. When an electric field is applied to this solution, the particles (as you'd imagine) move in the direction of the force applied by the electric field. However, the interesting concept here is that the charged particles move in a direction and accumulate, therefore creating a charge gradient, [[which in turn creates its own electric field!]] This can be shown in Figure 1, taken from the textbook. While ions are constantly moving, this is an accurate snapshot of what would be expected in the event of applied field/force. Furthermore, while ions move around the solution at all times (it is a conductor after all), there is a measurable excess of ions on the edges that generates the field. <br /> <br /> [[The net electric field is the superposition of the applied field and the field generated by the charge gradient and excess ion concentrations on the edges.]]<br /> <br /> <br /> ===A Mathematical Model===<br /> <br /> What are the mathematical equations that allow us to model this topic. For example &lt;math&gt;{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}&lt;/math&gt; where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.<br /> <br /> ===A Computational Model===<br /> <br /> How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> ===Middling===<br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> [http://www.scientificamerican.com/article/bring-science-home-reaction-time/]<br /> <br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Jshah46 http://www.physicsbook.gatech.edu/index.php?title=Polarization_of_a_conductor&diff=22573 2016-04-17T22:09:22Z

<p>Jshah46: </p> <hr /> <div>'''THIS HAS BEEN CLAIMED BY JAY SHAH<br /> '''<br /> Short Description of Topic<br /> <br /> ==The Main Idea==<br /> <br /> State, in your own words, the main idea for this topic<br /> <br /> <br /> ===A Mathematical Model===<br /> <br /> What are the mathematical equations that allow us to model this topic. For example &lt;math&gt;{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}&lt;/math&gt; where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.<br /> <br /> ===A Computational Model===<br /> <br /> How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> ===Middling===<br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> [http://www.scientificamerican.com/article/bring-science-home-reaction-time/]<br /> <br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Jshah46 http://www.physicsbook.gatech.edu/index.php?title=Charged_Conductor_and_Charged_Insulator&diff=22563 2016-04-17T22:03:21Z

<p>Jshah46: </p> <hr /> <div>RESERVED by JAY SHAH<br /> <br /> Understanding the Conductor and Insulator is the foundation and crucial to fully understand the polarization problem. <br /> <br /> <br /> ==Basic==<br /> <br /> All materials are made of atoms that contains electrons and protons. However, at the microscopic level there can be difference in structure that lead to very different behavior when they are exposed to electric field. Conductor and Insulator is what are discussed in the physics 2 classes. <br /> <br /> ===Conductor===<br /> <br /> <br /> A conductor is an object or type of material that allows the flow of electrical current in one or more directions. <br /> <br /> ===Insulator===<br /> An electrical insulator is a material whose internal electric charges do not flow freely, and therefore make it nearly impossible to conduct an electric current under the influence of an electric field.<br /> <br /> ==Charge on Conductor==<br /> [[File:Inschargedist.gif|thumb|Sphere Conductor]]<br /> An object made of a conducting material will permit charge to be transferred across the entire surface of the object. If charge is transferred to the object at a given location, that charge is quickly distributed across the entire surface of the object. The distribution of charge is the result of electron movement. Since conductors allow for electrons to be transported from particle to particle, a charged object will always distribute its charge until the overall repulsive forces between excess electrons is minimized.<br /> <br /> If the conductor is spherical, charge is evenly distributed on the outside surface.<br /> <br /> <br /> If the conductor is not spherical, surface charge density is higher where radius of curvature is smaller. (i.e on sharp points or corner of conductor.)<br /> <br /> [[File:hollow.png]]<br /> <br /> ==Insulator==<br /> In contrast to conductors, insulators are materials that impede the free flow of electrons from atom to atom and molecule to molecule. If charge is transferred to an insulator at a given location, the excess charge will remain at the initial location of charging. The particles of the insulator do not permit the free flow of electrons; subsequently charge is seldom distributed evenly across the surface of an insulator.<br /> [[File:insulator.png]]<br /> <br /> The electrons don't need to spread out evenly. Instead, they stay at where they were.<br /> <br /> <br /> <br /> While insulators are not useful for transferring charge, they do serve a critical role in electrostatic experiments and demonstrations. Conductive objects are often mounted upon insulating objects. This arrangement of a conductor on top of an insulator prevents charge from being transferred from the conductive object to its surroundings.<br /> <br /> == See also ==<br /> [http://www.physicsbook.gatech.edu/Charge_Transfer Charge Transfer] This topic talk about the charge transfer between objects<br /> <br /> ===External links===<br /> [http://www.schoolphysics.co.uk/age16-19/Electricity%20and%20magnetism/Electrostatics/text/Electric_charge_distribution/index.html Explenation of why does charge concentrate at a point on a conductor]<br /> <br /> ==References==<br /> [http://www.physicsclassroom.com/class/estatics/Lesson-1/Conductors-and-Insulators http://www.physicsclassroom.com/class/estatics/Lesson-1/Conductors-and-Insulators]<br /> <br /> [http://www.schoolphysics.co.uk/age16-19/Electricity%20and%20magnetism/Electrostatics/text/Electric_charge_distribution/index.html http://www.schoolphysics.co.uk/age16-19/Electricity%20and%20magnetism/Electrostatics/text/Electric_charge_distribution/index.html</div>

Jshah46 http://www.physicsbook.gatech.edu/index.php?title=Electric_Field&diff=20775 2016-04-09T18:55:00Z

<p>Jshah46: </p> <hr /> <div>'''CLAIMED BY JAY SHAH PHYS 2212 3/13/2016'''<br /> <br /> <br /> This page discusses the general properties of electric fields<br /> <br /> == Electric Field==<br /> <br /> Electric Field is a [[field]] created by an electric charge. It is measured in units of Newtons per Coulomb (N/C) and has a direction, making it a vector quantity. The electric field created by a charge exists at all points in space and exerts a force on other charged objects. The field can be drawn as an arrow with tail at the observation location pointing in the direction of the field. The Electric field obeys superposition, so the net Electric field at a point in space can be determined by summing all the individual fields present at that location.<br /> <br /> <br /> == Mathematical Concept of a Field==<br /> <br /> In mathematics, a field is a value that exists at all points in space. It can be a scalar or a vector. Other examples of fields are [[graviational fields]] and [[magnetic fields]].<br /> <br /> == Electric Field and Force==<br /> <br /> The force due to an external electric field on a charged particle is given by the equation &lt;math&gt; \vec{F} = q\vec{E}&lt;/math&gt; where q is the charge of the observed particle and E is the electric field. The field created by a charged particle exerts no force on itself. This is to say that the force on a given particle is defined as the charge on that particle multiplied the combined electric fields of the external environment. Since force is measured in Newtons (N) and charge in Coulombs (C), Electric field is measured in Newtons per Coulomb (N/C) as mentioned earlier. Furthermore, the electric field is not dependent on the sign of q (i.e. whether the charge is positive or negative.) The sign only helps determine the direction that the electric field points. <br /> <br /> == Electric Field and Superposition==<br /> <br /> The electric field contributed by a charged particle is unaffected by the electric field contributed by other charged particles. To that end, the principle of superposition, as mentioned earlier, states that the net electric field at a location is determined by the sum of all individual electric fields on charged particles. The principle of superposition is very useful to determine the force on a given charged particle. By being able to define electric field as a vector and simply adding up the various components of individual electric fields, the force on a particle is easily calculated using &lt;math&gt; \vec{F} = q\vec{E}&lt;/math&gt;<br /> <br /> == Electric Field and Electric Potential==<br /> <br /> Another way to define electric field is using the electric potential over a certain distance to determine field. In this case, Electric field is shown in units volts (V) per meter (m) (V/m).<br /> <br /> <br /> <br /> This page pioneered by<br /> --[[User:Spennell3|Spennell3]] ([[User talk:Spennell3|talk]]) 13:36, 19 October 2015 (EDT)</div>

Jshah46 http://www.physicsbook.gatech.edu/index.php?title=Electric_Field&diff=20613 2016-03-13T16:53:10Z

<p>Jshah46: </p> <hr /> <div>'''CLAIMED BY JAY SHAH PHYS 2212 3/13/2016'''<br /> <br /> <br /> This page discusses the general properties of electric fields<br /> <br /> == Electric Field==<br /> <br /> Electric Field is a [[field]] created by an electric charge. It is measured in units of Newtons per Coulomb (N/C) and has a direction, making it a vector quantity. The electric field created by a charge exists at all points in space and exerts a force on other charged objects. The field can be drawn as an arrow with tail at the observation location pointing in the direction of the field. The Electric field obeys superposition, so the net Electric field at a point in space can be determined by summing all the individual fields present at that location.<br /> <br /> <br /> == Mathematical Concept of a Field==<br /> <br /> In mathematics, a field is a value that exists at all points in space. It can be a scalar or a vector. Other examples of fields are [[graviational fields]] and [[magnetic fields]].<br /> <br /> == Electric Field and Force==<br /> <br /> The force due to an external electric field on a charged particle is given by the equation &lt;math&gt; \vec{F} = q\vec{E}&lt;/math&gt; where q is the charge of the observed particle and E is the electric field. The field created by a charged particle exerts no force on itself.<br /> <br /> This page pioneered by<br /> --[[User:Spennell3|Spennell3]] ([[User talk:Spennell3|talk]]) 13:36, 19 October 2015 (EDT)</div>

Jshah46 http://www.physicsbook.gatech.edu/index.php?title=Electric_Field&diff=20612 2016-03-13T16:52:41Z

<p>Jshah46: </p> <hr /> <div>CLAIMED BY JAY SHAH PHYS 2212 3/13/2016<br /> This page discusses the general properties of electric fields<br /> <br /> == Electric Field==<br /> <br /> Electric Field is a [[field]] created by an electric charge. It is measured in units of Newtons per Coulomb (N/C) and has a direction, making it a vector quantity. The electric field created by a charge exists at all points in space and exerts a force on other charged objects. The field can be drawn as an arrow with tail at the observation location pointing in the direction of the field. The Electric field obeys superposition, so the net Electric field at a point in space can be determined by summing all the individual fields present at that location.<br /> <br /> <br /> == Mathematical Concept of a Field==<br /> <br /> In mathematics, a field is a value that exists at all points in space. It can be a scalar or a vector. Other examples of fields are [[graviational fields]] and [[magnetic fields]].<br /> <br /> == Electric Field and Force==<br /> <br /> The force due to an external electric field on a charged particle is given by the equation &lt;math&gt; \vec{F} = q\vec{E}&lt;/math&gt; where q is the charge of the observed particle and E is the electric field. The field created by a charged particle exerts no force on itself.<br /> <br /> This page pioneered by<br /> --[[User:Spennell3|Spennell3]] ([[User talk:Spennell3|talk]]) 13:36, 19 October 2015 (EDT)</div>

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