http://www.physicsbook.gatech.edu/api.php?action=feedcontributions&feedformat=atom&user=Vramanan3Physics Book - User contributions [en]2026-04-26T08:48:36ZUser contributionsMediaWiki 1.42.7http://www.physicsbook.gatech.edu/index.php?title=Biot-Savart_Law_for_Currents&diff=32916Biot-Savart Law for Currents2018-12-13T16:50:31Z<p>Vramanan3: </p>
<hr />
<div>Vaishnavi Ramanan - Fall 2018<br />
<br />
==Biot-Savart Law==<br />
<br />
The Biot-Savart Law can be used for more than just single moving charges; a notable application of this law is its ability to calculate the magnetic field for an extremely large number of charges - an example of thousands of charges moving together is within a current carrying wire (current being the amount of charges moving over a specific amount of time). <br />
<br />
When using Biot-Savart Law to find the magnetic field of a short wire, we can extend this concept to a variety of different shapes - long current carrying wires, current carrying loops, etc. <br />
<br />
*One main point to note is that the application of the Biot-Savart law is specifically for steady state current (current that is not changing over time ----- <math> dI/dt = 0 </math> )!<br />
<br />
<br />
====A Mathematical Model====<br />
First We start off with the original version of the Biot-Savart Law. <br />
<math>\vec B=\frac{\mu_0}{4 \pi } \frac{q\vec v\times\hat r}{r^2}</math>, where <math> \frac{\mu_0}{4 \pi } = 1 \times 10^{-7}\frac{Tm^2}{Cm/s}, </math><br />
<br />
Because we are dealing with a portion of wire <math>\mathrm{d}\boldsymbol{\ell}</math> long with an Area A containing n moving particles with charge q, we find that the total number of moving charges is equal to |q|(nAv) which is also equal to I, the current in the wire.<br />
<br />
<math>B = \frac{\mu_0I}{4\pi}\frac{\mathrm{d}\boldsymbol{\ell} \times \mathbf{\hat r}}{r^2},</math><br />
<br />
Because the shape of the current carrying wire can vary from a straight wire to a loop, we must integrate over the region of the wire.<br />
<br />
<math>\Delta B = \frac{\mu_0I}{4\pi}\int_{\mathrm{wire}}\frac{\mathrm{d}\boldsymbol{\ell} \times \mathbf{\hat r}}{r^2},</math><br />
<br />
The key point is that there are <math> nA\Delta l </math> electrons in a short length of wire, each moving with average speed <math>\vec v </math>, so that the sum of all the <math> q\vec v </math> contributions is <math> nA \Delta l|q|\vec v = I\Delta l. </math><br />
<br />
<br />
<br />
When applying the Biot-Savart Law to a Long Straight Wire, we follow a set of steps,<br />
<br />
Step 1: Cut Up the Distribution into Pieces (<math> \Delta l </math>) and Draw <math> \Delta B </math>.<br />
<br />
Step 2: Write an Expression for the Magnetic Field Due to One Piece.<br />
<br />
Step 3: Add Up the Contributions of All the Pieces (each <math> \Delta l </math> adds together to make the entirety of the length).<br />
<br />
Step 4: Check the Result.<br />
<br />
Where the Magnetic Field of a Straight Wire is shown by,<br />
<br />
<math> B = \frac{\mu_0}{4\pi}\frac{LI}{r(r^2 + (L/2)^2)^{1/2}} </math> for length <math> L </math>, conventional current <math> I </math>, a perpendicular distance <math> r </math> from the center of the wire, or,<br />
<math> B = \frac{\mu_0}{4\pi}\frac{2I}{r} </math> if <math> L\>>\>> r. </math><br />
<br />
<br />
==Right Hand Rule== [[File:IMG_2467.jpg|200px|thumb|alt text]]<br />
<br />
When using the Biot-Savart Law for Currents, it is crucial to understand the direction of the magnetic field created by a current. <br />
<br />
In order to get the direction of the Magnetic Field, as shown in the image on the right, we:<br />
<br />
1. Point our thumb in the direction of the current, and<br />
<br />
2. automatically curl our fingers around in one direction. <br />
<br />
This curling direction is the direction of the magnetic field itself.<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
==Long Wire Integration Example==<br />
[[File:IMG_2469.jpg|200px|thumb|alt text]]<br />
====For a long wire of length L positioned along the x axis with current flowing in the positive x direction (as shown by image on right)====<br />
First, we start off with our adjusted Biot-Savart Formula for a slice of wire.<br />
<br />
<math>\Delta B = \frac{\mu_0I}{4\pi}\int_{\mathrm{wire}}\frac{\mathrm{d}\boldsymbol{\ell} \times \mathbf{\hat r}}{r^2},</math><br />
<br />
Second, we must find <math>r</math>, the vector pointing from the source to the observation location. In this case, we will choose an observation location y above the rod.<br />
<br />
<math> r = obs - source = <0,y,0> - < x,0,0> = <-x,y,0> </math>. which has a magnitude of <math>\sqrt(x^2+y^2)</math><br />
<br />
We see that <math>\hat r = \frac{r}{|r|} </math> .<br />
<br />
<math>\hat r = \frac{<-x,y,0>}{\sqrt(x^2+y^2))}</math><br />
<br />
We then have to express <math> \Delta \boldsymbol{\ell}</math> in terms of our variable of integration, x.<br />
<math> \Delta \boldsymbol{\ell}</math> = <math> \Delta x<1,0,0,></math><br />
<br />
Our new equation after substituting our new variables is <br />
<math> \Delta B = \frac{\mu_0I\Delta x<1,0,0,>}{4\pi(x^2+y^2)} \times \frac{<-x,y,0>}{\sqrt(x^2+y^2))} </math><br />
<br />
Finding the cross product of the above vectors gives us a product in the +z direction.<br />
<math> \Delta B = \frac{\mu_0I\Delta x}{4\pi(x^2+y^2)^(\frac{3}{2})} </math><br />
<br />
We are finally ready to integrate. Because we are integrating the entire rod our limits are<br />
<br />
<br />
<math> \int\limits_{-L/2}^{L/2}\ </math> <math> \int\limits_{-L/2}^{L/2}\ = \frac{\mu_0I\Delta x}{4\pi(x^2+y^2)^(\frac{3}{2})} </math><br />
<br />
We find that our final answer is <math> B= \frac{\mu_0}{4\pi}\frac{LI}{y\sqrt(y^2+(L/2)^2)}\hat z </math><br />
<br />
==Current Loop Integration Example==<br />
<br />
==A Computational Model==<br />
The following link shows the magnetic field produced by small segments of wire in a loop individually.<br />
For a long straight wire, we see that there is a circular magnetic field surrounding the wire with current. The following link does a stepwise visual of the contributions of each part of the wire at an observation location a distance r from the wire.<br />
<br />
http://www.glowscript.org/#/user/matterandinteractions/folder/matterandinteractions/program/17-Bwire-with-r<br />
<br />
We see that along the axis of the wire, each contribution not on the axis is negated due to symmetry and the resulting magnetic field is all along the wire.<br />
<br />
http://www.glowscript.org/#/user/matterandinteractions/folder/matterandinteractions/program/17-B-loop-with-r-dB.<br />
<br />
== See also ==<br />
[Right Hand Rule[http://www.physicsbook.gatech.edu/Right-Hand_Rule]]<br />
<br />
[Direction of magnetic fields[http://www.physicsbook.gatech.edu/Direction_of_Magnetic_Field]]<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 />
==External Links==<br />
[[Category:Which Category did you place this in?]]</div>Vramanan3http://www.physicsbook.gatech.edu/index.php?title=Biot-Savart_Law_for_Currents&diff=32915Biot-Savart Law for Currents2018-12-13T16:49:03Z<p>Vramanan3: </p>
<hr />
<div>Vaishnavi Ramanan - Fall 2018<br />
<br />
==Biot-Savart Law==<br />
<br />
The Biot-Savart Law can be used for more than just single moving charges; a notable application of this law is its ability to calculate the magnetic field for an extremely large number of charges - an example of thousands of charges moving together is within a current carrying wire (current being the amount of charges moving over a specific amount of time). <br />
<br />
When using Biot-Savart Law to find the magnetic field of a short wire, we can extend this concept to a variety of different shapes - long current carrying wires, current carrying loops, etc. <br />
<br />
*One main point to note is that the application of the Biot-Savart law is specifically for steady state current (current that is not changing over time ----- <math> dI/dt = 0 </math> )!<br />
<br />
<br />
====A Mathematical Model====<br />
First We start off with the original version of the Biot-Savart Law. <br />
<math>\vec B=\frac{\mu_0}{4 \pi } \frac{q\vec v\times\hat r}{r^2}</math>, where <math> \frac{\mu_0}{4 \pi } = 1 \times 10^{-7}\frac{Tm^2}{Cm/s}, </math><br />
<br />
Because we are dealing with a portion of wire <math>\mathrm{d}\boldsymbol{\ell}</math> long with an Area A containing n moving particles with charge q, we find that the total number of moving charges is equal to |q|(nAv) which is also equal to I, the current in the wire.<br />
<br />
<math>B = \frac{\mu_0I}{4\pi}\frac{\mathrm{d}\boldsymbol{\ell} \times \mathbf{\hat r}}{r^2},</math><br />
<br />
Because the shape of the current carrying wire can vary from a straight wire to a loop, we must integrate over the region of the wire.<br />
<br />
<math>\Delta B = \frac{\mu_0I}{4\pi}\int_{\mathrm{wire}}\frac{\mathrm{d}\boldsymbol{\ell} \times \mathbf{\hat r}}{r^2},</math><br />
<br />
The key point is that there are <math> nA\Delta l </math> electrons in a short length of wire, each moving with average speed <math>\vec v </math>, so that the sum of all the <math> q\vec v </math> contributions is <math> nA \Delta l|q|\vec v = I\Delta l. </math><br />
<br />
<br />
<br />
When applying the Biot-Savart Law to a Long Straight Wire, we follow a set of steps,<br />
<br />
Step 1: Cut Up the Distribution into Pieces (<math> \Delta l </math>) and Draw <math> \Delta B </math>.<br />
<br />
Step 2: Write an Expression for the Magnetic Field Due to One Piece.<br />
<br />
Step 3: Add Up the Contributions of All the Pieces (each <math> \Delta l </math> adds together to make the entirety of the length).<br />
<br />
Step 4: Check the Result.<br />
<br />
Where the Magnetic Field of a Straight Wire is shown by,<br />
<br />
<math> B = \frac{\mu_0}{4\pi}\frac{LI}{r(r^2 + (L/2)^2)^{1/2}} </math> for length <math> L </math>, conventional current <math> I </math>, a perpendicular distance <math> r </math> from the center of the wire, or,<br />
<math> B = \frac{\mu_0}{4\pi}\frac{2I}{r} </math> if <math> L\>>\>> r. </math><br />
<br />
<br />
'''Right Hand Rule''' [[File:IMG_2467.jpg|200px|thumb|alt text]]<br />
<br />
When using the Biot-Savart Law for Currents, it is crucial to understand the direction of the magnetic field created by a current. <br />
<br />
In order to get the direction of the Magnetic Field, as shown in the image on the right, we:<br />
<br />
1. Point our thumb in the direction of the current, and<br />
<br />
2. automatically curl our fingers around in one direction. <br />
<br />
This curling direction is the direction of the magnetic field itself.<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
==Long Wire Integration Example==<br />
[[File:IMG_2469.jpg|200px|thumb|alt text]]<br />
====For a long wire of length L positioned along the x axis with current flowing in the positive x direction====<br />
First, we start off with our adjusted Biot-Savart Formula for a slice of wire.<br />
<br />
<math>\Delta B = \frac{\mu_0I}{4\pi}\int_{\mathrm{wire}}\frac{\mathrm{d}\boldsymbol{\ell} \times \mathbf{\hat r}}{r^2},</math><br />
<br />
Second, we must find <math>r</math>, the vector pointing from the source to the observation location. In this case, we will choose an observation location y above the rod.<br />
<br />
<math> r = obs - source = <0,y,0> - < x,0,0> = <-x,y,0> </math>. which has a magnitude of <math>\sqrt(x^2+y^2)</math><br />
<br />
We see that <math>\hat r = \frac{r}{|r|} </math> .<br />
<br />
<math>\hat r = \frac{<-x,y,0>}{\sqrt(x^2+y^2))}</math><br />
<br />
We then have to express <math> \Delta \boldsymbol{\ell}</math> in terms of our variable of integration, x.<br />
<math> \Delta \boldsymbol{\ell}</math> = <math> \Delta x<1,0,0,></math><br />
<br />
Our new equation after substituting our new variables is <br />
<math> \Delta B = \frac{\mu_0I\Delta x<1,0,0,>}{4\pi(x^2+y^2)} \times \frac{<-x,y,0>}{\sqrt(x^2+y^2))} </math><br />
<br />
Finding the cross product of the above vectors gives us a product in the +z direction.<br />
<math> \Delta B = \frac{\mu_0I\Delta x}{4\pi(x^2+y^2)^(\frac{3}{2})} </math><br />
<br />
We are finally ready to integrate. Because we are integrating the entire rod our limits are<br />
<br />
<br />
<math> \int\limits_{-L/2}^{L/2}\ </math> <math> \int\limits_{-L/2}^{L/2}\ = \frac{\mu_0I\Delta x}{4\pi(x^2+y^2)^(\frac{3}{2})} </math><br />
<br />
We find that our final answer is <math> B= \frac{\mu_0}{4\pi}\frac{LI}{y\sqrt(y^2+(L/2)^2)}\hat z </math><br />
<br />
==A Computational Model==<br />
The following link shows the magnetic field produced by small segments of wire in a loop individually.<br />
For a long straight wire, we see that there is a circular magnetic field surrounding the wire with current. The following link does a stepwise visual of the contributions of each part of the wire at an observation location a distance r from the wire.<br />
<br />
http://www.glowscript.org/#/user/matterandinteractions/folder/matterandinteractions/program/17-Bwire-with-r<br />
<br />
We see that along the axis of the wire, each contribution not on the axis is negated due to symmetry and the resulting magnetic field is all along the wire.<br />
<br />
http://www.glowscript.org/#/user/matterandinteractions/folder/matterandinteractions/program/17-B-loop-with-r-dB.<br />
<br />
== See also ==<br />
[Right Hand Rule[http://www.physicsbook.gatech.edu/Right-Hand_Rule]]<br />
<br />
[Direction of magnetic fields[http://www.physicsbook.gatech.edu/Direction_of_Magnetic_Field]]<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 />
==External Links==<br />
[[Category:Which Category did you place this in?]]</div>Vramanan3http://www.physicsbook.gatech.edu/index.php?title=File:IMG_2469.jpg&diff=32914File:IMG 2469.jpg2018-12-13T16:48:08Z<p>Vramanan3: </p>
<hr />
<div></div>Vramanan3http://www.physicsbook.gatech.edu/index.php?title=Biot-Savart_Law_for_Currents&diff=32913Biot-Savart Law for Currents2018-12-13T16:33:57Z<p>Vramanan3: </p>
<hr />
<div>Vaishnavi Ramanan - Fall 2018<br />
<br />
==Biot-Savart Law==<br />
<br />
The Biot-Savart Law can be used for more than just single moving charges; a notable application of this law is its ability to calculate the magnetic field for an extremely large number of charges - an example of thousands of charges moving together is within a current carrying wire (current being the amount of charges moving over a specific amount of time). <br />
<br />
When using Biot-Savart Law to find the magnetic field of a short wire, we can extend this concept to a variety of different shapes - long current carrying wires, current carrying loops, etc. <br />
<br />
*One main point to note is that the application of the Biot-Savart law is specifically for steady state current (current that is not changing over time ----- <math> dI/dt = 0 </math> )!<br />
<br />
<br />
====A Mathematical Model====<br />
First We start off with the original version of the Biot-Savart Law. <br />
<math>\vec B=\frac{\mu_0}{4 \pi } \frac{q\vec v\times\hat r}{r^2}</math>, where <math> \frac{\mu_0}{4 \pi } = 1 \times 10^{-7}\frac{Tm^2}{Cm/s}, </math><br />
<br />
Because we are dealing with a portion of wire <math>\mathrm{d}\boldsymbol{\ell}</math> long with an Area A containing n moving particles with charge q, we find that the total number of moving charges is equal to |q|(nAv) which is also equal to I, the current in the wire.<br />
<br />
<math>B = \frac{\mu_0I}{4\pi}\frac{\mathrm{d}\boldsymbol{\ell} \times \mathbf{\hat r}}{r^2},</math><br />
<br />
Because the shape of the current carrying wire can vary from a straight wire to a loop, we must integrate over the region of the wire.<br />
<br />
<math>\Delta B = \frac{\mu_0I}{4\pi}\int_{\mathrm{wire}}\frac{\mathrm{d}\boldsymbol{\ell} \times \mathbf{\hat r}}{r^2},</math><br />
<br />
The key point is that there are <math> nA\Delta l </math> electrons in a short length of wire, each moving with average speed <math>\vec v </math>, so that the sum of all the <math> q\vec v </math> contributions is <math> nA \Delta l|q|\vec v = I\Delta l. </math><br />
<br />
<br />
<br />
When applying the Biot-Savart Law to a Long Straight Wire, we follow a set of steps,<br />
<br />
Step 1: Cut Up the Distribution into Pieces (<math> \Delta l </math>) and Draw <math> \Delta B </math>.<br />
<br />
Step 2: Write an Expression for the Magnetic Field Due to One Piece.<br />
<br />
Step 3: Add Up the Contributions of All the Pieces (each <math> \Delta l </math> adds together to make the entirety of the length).<br />
<br />
Step 4: Check the Result.<br />
<br />
Where the Magnetic Field of a Straight Wire is shown by,<br />
<br />
<math> B = \frac{\mu_0}{4\pi}\frac{LI}{r(r^2 + (L/2)^2)^{1/2}} </math> for length <math> L </math>, conventional current <math> I </math>, a perpendicular distance <math> r </math> from the center of the wire, or,<br />
<math> B = \frac{\mu_0}{4\pi}\frac{2I}{r} </math> if <math> L\>>\>> r. </math><br />
<br />
<br />
'''Right Hand Rule''' [[File:IMG_2467.jpg|200px|thumb|alt text]]<br />
<br />
When using the Biot-Savart Law for Currents, it is crucial to understand the direction of the magnetic field created by a current. <br />
<br />
In order to get the direction of the Magnetic Field, as shown in the image on the right, we:<br />
<br />
1. Point our thumb in the direction of the current, and<br />
<br />
2. automatically curl our fingers around in one direction. <br />
<br />
This curling direction is the direction of the magnetic field itself.<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
==Long Wire Integration Example==<br />
====For a long wire of length L positioned along the x axis with current flowing in the positive x direction====<br />
First, we start off with our adjusted Biot-Savart Formula for a slice of wire.<br />
<br />
<math>\Delta B = \frac{\mu_0I}{4\pi}\int_{\mathrm{wire}}\frac{\mathrm{d}\boldsymbol{\ell} \times \mathbf{\hat r}}{r^2},</math><br />
<br />
Second, we must find <math>r</math>, the vector pointing from the source to the observation location. In this case, we will choose an observation location y above the rod.<br />
<br />
<math> r = obs - source = <0,y,0> - < x,0,0> = <-x,y,0> </math>. which has a magnitude of <math>\sqrt(x^2+y^2)</math><br />
<br />
We see that <math>\hat r = \frac{r}{|r|} </math> .<br />
<br />
<math>\hat r = \frac{<-x,y,0>}{\sqrt(x^2+y^2))}</math><br />
<br />
We then have to express <math> \Delta \boldsymbol{\ell}</math> in terms of our variable of integration, x.<br />
<math> \Delta \boldsymbol{\ell}</math> = <math> \Delta x<1,0,0,></math><br />
<br />
Our new equation after substituting our new variables is <br />
<math> \Delta B = \frac{\mu_0I\Delta x<1,0,0,>}{4\pi(x^2+y^2)} \times \frac{<-x,y,0>}{\sqrt(x^2+y^2))} </math><br />
<br />
Finding the cross product of the above vectors gives us a product in the +z direction.<br />
<math> \Delta B = \frac{\mu_0I\Delta x}{4\pi(x^2+y^2)^(\frac{3}{2})} </math><br />
<br />
We are finally ready to integrate. Because we are integrating the entire rod our limits are<br />
<br />
<br />
<math> \int\limits_{-L/2}^{L/2}\ </math> <math> \int\limits_{-L/2}^{L/2}\ = \frac{\mu_0I\Delta x}{4\pi(x^2+y^2)^(\frac{3}{2})} </math><br />
<br />
We find that our final answer is <math> B= \frac{\mu_0}{4\pi}\frac{LI}{y\sqrt(y^2+(L/2)^2)}\hat z </math><br />
<br />
==A Computational Model==<br />
The following link shows the magnetic field produced by small segments of wire in a loop individually.<br />
For a long straight wire, we see that there is a circular magnetic field surrounding the wire with current. The following link does a stepwise visual of the contributions of each part of the wire at an observation location a distance r from the wire.<br />
<br />
http://www.glowscript.org/#/user/matterandinteractions/folder/matterandinteractions/program/17-Bwire-with-r<br />
<br />
We see that along the axis of the wire, each contribution not on the axis is negated due to symmetry and the resulting magnetic field is all along the wire.<br />
<br />
http://www.glowscript.org/#/user/matterandinteractions/folder/matterandinteractions/program/17-B-loop-with-r-dB.<br />
<br />
== See also ==<br />
[Right Hand Rule[http://www.physicsbook.gatech.edu/Right-Hand_Rule]]<br />
<br />
[Direction of magnetic fields[http://www.physicsbook.gatech.edu/Direction_of_Magnetic_Field]]<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 />
==External Links==<br />
[[Category:Which Category did you place this in?]]</div>Vramanan3http://www.physicsbook.gatech.edu/index.php?title=Biot-Savart_Law_for_Currents&diff=32912Biot-Savart Law for Currents2018-12-13T16:31:19Z<p>Vramanan3: </p>
<hr />
<div>Vaishnavi Ramanan - Fall 2018<br />
<br />
==Biot-Savart Law==<br />
<br />
The Biot-Savart Law can be used for more than just single moving charges; a notable application of this law is its ability to calculate the magnetic field for an extremely large number of charges - an example of thousands of charges moving together is within a current carrying wire (current being the amount of charges moving over a specific amount of time). <br />
<br />
When using Biot-Savart Law to find the magnetic field of a short wire, we can extend this concept to a variety of different shapes - long current carrying wires, current carrying loops, etc. <br />
<br />
*One main point to note is that the application of the Biot-Savart law is specifically for steady state current (current that is not change over time - dI/dt = 0)!<br />
<br />
<br />
====A Mathematical Model====<br />
First We start off with the original version of the Biot-Savart Law. <br />
<math>\vec B=\frac{\mu_0}{4 \pi } \frac{q\vec v\times\hat r}{r^2}</math>, where <math> \frac{\mu_0}{4 \pi } = 1 \times 10^{-7}\frac{Tm^2}{Cm/s}, </math><br />
<br />
Because we are dealing with a portion of wire <math>\mathrm{d}\boldsymbol{\ell}</math> long with an Area A containing n moving particles with charge q, we find that the total number of moving charges is equal to |q|(nAv) which is also equal to I, the current in the wire.<br />
<br />
<math>B = \frac{\mu_0I}{4\pi}\frac{\mathrm{d}\boldsymbol{\ell} \times \mathbf{\hat r}}{r^2},</math><br />
<br />
Because the shape of the current carrying wire can vary from a straight wire to a loop, we must integrate over the region of the wire.<br />
<br />
<math>\Delta B = \frac{\mu_0I}{4\pi}\int_{\mathrm{wire}}\frac{\mathrm{d}\boldsymbol{\ell} \times \mathbf{\hat r}}{r^2},</math><br />
<br />
The key point is that there are <math> nA\Delta l </math> electrons in a short length of wire, each moving with average speed <math>\vec v </math>, so that the sum of all the <math> q\vec v </math> contributions is <math> nA \Delta l|q|\vec v = I\Delta l. </math><br />
<br />
<br />
<br />
When applying the Biot-Savart Law to a Long Straight Wire, we follow a set of steps,<br />
<br />
Step 1: Cut Up the Distribution into Pieces (<math> \Delta l </math>) and Draw <math> \Delta B </math>.<br />
<br />
Step 2: Write an Expression for the Magnetic Field Due to One Piece.<br />
<br />
Step 3: Add Up the Contributions of All the Pieces (each <math> \Delta l </math> adds together to make the entirety of the length).<br />
<br />
Step 4: Check the Result.<br />
<br />
Where the Magnetic Field of a Straight Wire is shown by,<br />
<br />
<math> B = \frac{\mu_0}{4\pi}\frac{LI}{r(r^2 + (L/2)^2)^{1/2}} </math> for length <math> L </math>, conventional current <math> I </math>, a perpendicular distance <math> r </math> from the center of the wire, or,<br />
<math> B = \frac{\mu_0}{4\pi}\frac{2I}{r} </math> if <math> L\>>\>> r. </math><br />
<br />
<br />
'''Right Hand Rule''' [[File:IMG_2467.jpg|200px|thumb|alt text]]<br />
<br />
When using the Biot-Savart Law for Currents, it is crucial to understand the direction of the magnetic field created by a current. <br />
<br />
In order to get the direction of the Magnetic Field, as shown in the image on the right, we:<br />
<br />
1. Point our thumb in the direction of the current, and<br />
<br />
2. automatically curl our fingers around in one direction. <br />
<br />
This curling direction is the direction of the magnetic field itself.<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
==Long Wire Integration Example==<br />
====For a long wire of length L positioned along the x axis with current flowing in the positive x direction====<br />
First, we start off with our adjusted Biot-Savart Formula for a slice of wire.<br />
<br />
<math>\Delta B = \frac{\mu_0I}{4\pi}\int_{\mathrm{wire}}\frac{\mathrm{d}\boldsymbol{\ell} \times \mathbf{\hat r}}{r^2},</math><br />
<br />
Second, we must find <math>r</math>, the vector pointing from the source to the observation location. In this case, we will choose an observation location y above the rod.<br />
<br />
<math> r = obs - source = <0,y,0> - < x,0,0> = <-x,y,0> </math>. which has a magnitude of <math>\sqrt(x^2+y^2)</math><br />
<br />
We see that <math>\hat r = \frac{r}{|r|} </math> .<br />
<br />
<math>\hat r = \frac{<-x,y,0>}{\sqrt(x^2+y^2))}</math><br />
<br />
We then have to express <math> \Delta \boldsymbol{\ell}</math> in terms of our variable of integration, x.<br />
<math> \Delta \boldsymbol{\ell}</math> = <math> \Delta x<1,0,0,></math><br />
<br />
Our new equation after substituting our new variables is <br />
<math> \Delta B = \frac{\mu_0I\Delta x<1,0,0,>}{4\pi(x^2+y^2)} \times \frac{<-x,y,0>}{\sqrt(x^2+y^2))} </math><br />
<br />
Finding the cross product of the above vectors gives us a product in the +z direction.<br />
<math> \Delta B = \frac{\mu_0I\Delta x}{4\pi(x^2+y^2)^(\frac{3}{2})} </math><br />
<br />
We are finally ready to integrate. Because we are integrating the entire rod our limits are<br />
<br />
<br />
<math> \int\limits_{-L/2}^{L/2}\ </math> <math> \int\limits_{-L/2}^{L/2}\ = \frac{\mu_0I\Delta x}{4\pi(x^2+y^2)^(\frac{3}{2})} </math><br />
<br />
We find that our final answer is <math> B= \frac{\mu_0}{4\pi}\frac{LI}{y\sqrt(y^2+(L/2)^2)}\hat z </math><br />
<br />
==A Computational Model==<br />
The following link shows the magnetic field produced by small segments of wire in a loop individually.<br />
For a long straight wire, we see that there is a circular magnetic field surrounding the wire with current. The following link does a stepwise visual of the contributions of each part of the wire at an observation location a distance r from the wire.<br />
<br />
http://www.glowscript.org/#/user/matterandinteractions/folder/matterandinteractions/program/17-Bwire-with-r<br />
<br />
We see that along the axis of the wire, each contribution not on the axis is negated due to symmetry and the resulting magnetic field is all along the wire.<br />
<br />
http://www.glowscript.org/#/user/matterandinteractions/folder/matterandinteractions/program/17-B-loop-with-r-dB.<br />
<br />
== See also ==<br />
[Right Hand Rule[http://www.physicsbook.gatech.edu/Right-Hand_Rule]]<br />
<br />
[Direction of magnetic fields[http://www.physicsbook.gatech.edu/Direction_of_Magnetic_Field]]<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 />
==External Links==<br />
[[Category:Which Category did you place this in?]]</div>Vramanan3http://www.physicsbook.gatech.edu/index.php?title=Biot-Savart_Law_for_Currents&diff=32911Biot-Savart Law for Currents2018-12-13T16:28:59Z<p>Vramanan3: </p>
<hr />
<div>Vaishnavi Ramanan - Fall 2018<br />
<br />
==Biot-Savart Law==<br />
<br />
The Biot-Savart Law can be used for more than just single moving charges; a notable application of this law is its ability to calculate the magnetic field for an extremely large number of charges - an example of thousands of currents moving together is within a current carrying wire (current being the amount of charges moving over a specific amount of time). <br />
<br />
When using Biot-Savart Law to find the magnetic field of a short wire, we can extend this concept to a variety of different shapes - long current carrying wires, current carrying loops, etc. <br />
<br />
*One main point to note is that the application of the Biot-Savart law is specifically for steady state current!<br />
<br />
<br />
====A Mathematical Model====<br />
First We start off with the original version of the Biot-Savart Law. <br />
<math>\vec B=\frac{\mu_0}{4 \pi } \frac{q\vec v\times\hat r}{r^2}</math>, where <math> \frac{\mu_0}{4 \pi } = 1 \times 10^{-7}\frac{Tm^2}{Cm/s}, </math><br />
<br />
Because we are dealing with a portion of wire <math>\mathrm{d}\boldsymbol{\ell}</math> long with an Area A containing n moving particles with charge q, we find that the total number of moving charges is equal to |q|(nAv) which is also equal to I, the current in the wire.<br />
<br />
<math>B = \frac{\mu_0I}{4\pi}\frac{\mathrm{d}\boldsymbol{\ell} \times \mathbf{\hat r}}{r^2},</math><br />
<br />
Because the shape of the current carrying wire can vary from a straight wire to a loop, we must integrate over the region of the wire.<br />
<br />
<math>\Delta B = \frac{\mu_0I}{4\pi}\int_{\mathrm{wire}}\frac{\mathrm{d}\boldsymbol{\ell} \times \mathbf{\hat r}}{r^2},</math><br />
<br />
The key point is that there are <math> nA\Delta l </math> electrons in a short length of wire, each moving with average speed <math>\vec v </math>, so that the sum of all the <math> q\vec v </math> contributions is <math> nA \Delta l|q|\vec v = I\Delta l. </math><br />
<br />
<br />
<br />
When applying the Biot-Savart Law to a Long Straight Wire, we follow a set of steps,<br />
<br />
Step 1: Cut Up the Distribution into Pieces (<math> \Delta l </math>) and Draw <math> \Delta B </math>.<br />
<br />
Step 2: Write an Expression for the Magnetic Field Due to One Piece.<br />
<br />
Step 3: Add Up the Contributions of All the Pieces (each <math> \Delta l </math> adds together to make the entirety of the length).<br />
<br />
Step 4: Check the Result.<br />
<br />
Where the Magnetic Field of a Straight Wire is shown by,<br />
<br />
<math> B = \frac{\mu_0}{4\pi}\frac{LI}{r(r^2 + (L/2)^2)^{1/2}} </math> for length <math> L </math>, conventional current <math> I </math>, a perpendicular distance <math> r </math> from the center of the wire, or,<br />
<math> B = \frac{\mu_0}{4\pi}\frac{2I}{r} </math> if <math> L\>>\>> r. </math><br />
<br />
<br />
'''Right Hand Rule''' [[File:IMG_2467.jpg|200px|thumb|alt text]]<br />
<br />
When using the Biot-Savart Law for Currents, it is crucial to understand the direction of the magnetic field created by a current. In order to get the direction of the Magnetic Field, as shown in the image on the right, we point our thumb in the direction of the current, and our fingers automatically curl around in one direction. This curling direction is the direction of the magnetic field itself.<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
==Long Wire Integration Example==<br />
====For a long wire of length L positioned along the x axis with current flowing in the positive x direction====<br />
First, we start off with our adjusted Biot-Savart Formula for a slice of wire.<br />
<br />
<math>\Delta B = \frac{\mu_0I}{4\pi}\int_{\mathrm{wire}}\frac{\mathrm{d}\boldsymbol{\ell} \times \mathbf{\hat r}}{r^2},</math><br />
<br />
Second, we must find <math>r</math>, the vector pointing from the source to the observation location. In this case, we will choose an observation location y above the rod.<br />
<br />
<math> r = obs - source = <0,y,0> - < x,0,0> = <-x,y,0> </math>. which has a magnitude of <math>\sqrt(x^2+y^2)</math><br />
<br />
We see that <math>\hat r = \frac{r}{|r|} </math> .<br />
<br />
<math>\hat r = \frac{<-x,y,0>}{\sqrt(x^2+y^2))}</math><br />
<br />
We then have to express <math> \Delta \boldsymbol{\ell}</math> in terms of our variable of integration, x.<br />
<math> \Delta \boldsymbol{\ell}</math> = <math> \Delta x<1,0,0,></math><br />
<br />
Our new equation after substituting our new variables is <br />
<math> \Delta B = \frac{\mu_0I\Delta x<1,0,0,>}{4\pi(x^2+y^2)} \times \frac{<-x,y,0>}{\sqrt(x^2+y^2))} </math><br />
<br />
Finding the cross product of the above vectors gives us a product in the +z direction.<br />
<math> \Delta B = \frac{\mu_0I\Delta x}{4\pi(x^2+y^2)^(\frac{3}{2})} </math><br />
<br />
We are finally ready to integrate. Because we are integrating the entire rod our limits are<br />
<br />
<br />
<math> \int\limits_{-L/2}^{L/2}\ </math> <math> \int\limits_{-L/2}^{L/2}\ = \frac{\mu_0I\Delta x}{4\pi(x^2+y^2)^(\frac{3}{2})} </math><br />
<br />
We find that our final answer is <math> B= \frac{\mu_0}{4\pi}\frac{LI}{y\sqrt(y^2+(L/2)^2)}\hat z </math><br />
<br />
==A Computational Model==<br />
The following link shows the magnetic field produced by small segments of wire in a loop individually.<br />
For a long straight wire, we see that there is a circular magnetic field surrounding the wire with current. The following link does a stepwise visual of the contributions of each part of the wire at an observation location a distance r from the wire.<br />
<br />
http://www.glowscript.org/#/user/matterandinteractions/folder/matterandinteractions/program/17-Bwire-with-r<br />
<br />
We see that along the axis of the wire, each contribution not on the axis is negated due to symmetry and the resulting magnetic field is all along the wire.<br />
<br />
http://www.glowscript.org/#/user/matterandinteractions/folder/matterandinteractions/program/17-B-loop-with-r-dB.<br />
<br />
== See also ==<br />
[Right Hand Rule[http://www.physicsbook.gatech.edu/Right-Hand_Rule]]<br />
<br />
[Direction of magnetic fields[http://www.physicsbook.gatech.edu/Direction_of_Magnetic_Field]]<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 />
==External Links==<br />
[[Category:Which Category did you place this in?]]</div>Vramanan3http://www.physicsbook.gatech.edu/index.php?title=Biot-Savart_Law_for_Currents&diff=32910Biot-Savart Law for Currents2018-12-13T16:28:30Z<p>Vramanan3: </p>
<hr />
<div>Vaishnavi Ramanan - Fall 2018<br />
<br />
==Biot-Savart Law==<br />
<br />
The Biot-Savart Law can be used for more than just single moving charges; a notable application of this law is its ability to calculate the magnetic field for an extremely large number of charges - an example of thousands of currents moving together is within a current carrying wire (current being the amount of charges moving over a specific amount of time). <br />
<br />
When using Biot-Savart Law to find the magnetic field of a short wire, we can extend this concept to a variety of different shapes - long current carrying wires, current carrying loops, etc. <br />
<br />
*One main point to note is that the application of the Biot-Savart law is specifically for steady state current!<br />
<br />
<br />
====A Mathematical Model====<br />
First We start off with the original version of the Biot-Savart Law. <br />
<math>\vec B=\frac{\mu_0}{4 \pi } \frac{q\vec v\times\hat r}{r^2}</math>, where <math> \frac{\mu_0}{4 \pi } = 1 \times 10^{-7}\frac{Tm^2}{Cm/s}, </math><br />
<br />
Because we are dealing with a portion of wire <math>\mathrm{d}\boldsymbol{\ell}</math> long with an Area A containing n moving particles with charge q, we find that the total number of moving charges is equal to |q|(nAv) which is also equal to I, the current in the wire.<br />
<br />
<math>B = \frac{\mu_0I}{4\pi}\frac{\mathrm{d}\boldsymbol{\ell} \times \mathbf{\hat r}}{r^2},</math><br />
<br />
Because the shape of the current carrying wire can vary from a straight wire to a loop, we must integrate over the region of the wire.<br />
<br />
<math>\Delta B = \frac{\mu_0I}{4\pi}\int_{\mathrm{wire}}\frac{\mathrm{d}\boldsymbol{\ell} \times \mathbf{\hat r}}{r^2},</math><br />
<br />
The key point is that there are <math> nA\Delta l </math> electrons in a short length of wire, each moving with average speed <math>\vec v </math>, so that the sum of all the <math> q\vec v </math> contributions is <math> nA \Delta l|q|\vec v = I\Delta l. </math><br />
<br />
<br />
<br />
When applying the Biot-Savart Law to a Long Straight Wire, we follow a set of steps,<br />
<br />
Step 1: Cut Up the Distribution into Pieces (<math> \Delta l </math>) and Draw <math> \Delta B </math>.<br />
<br />
Step 2: Write an Expression for the Magnetic Field Due to One Piece.<br />
<br />
Step 3: Add Up the Contributions of All the Pieces (each <math> \Delta l </math> adds together to make the entirety of the length).<br />
<br />
Step 4: Check the Result.<br />
<br />
Where the Magnetic Field of a Straight Wire is shown by,<br />
<br />
<math> B = \frac{\mu_0}{4\pi}\frac{LI}{r(r^2 + (L/2)^2)^{1/2}} </math> for length <math> L </math>, conventional current <math> I </math>, a perpendicular distance <math> r </math> from the center of the wire, or,<br />
<math> B = \frac{\mu_0}{4\pi}\frac{2I}{r} </math> if <math> L\>>\>> r. </math><br />
<br />
<br />
'''Right Hand Rule''' [[File:IMG_2467.jpg|200px|thumb|alt text]]<br />
<br />
When using the Biot-Savart Law for Currents, it is crucial to understand the direction of the magnetic field created by a current. In order to get the direction of the Magnetic Field, as shown in the image on the right, we point our thumb in the direction of the current, and our fingers automatically curl around in one direction. This curling direction is the direction of the magnetic field itself.<br />
<br />
<br />
<br />
<br />
<br />
==Long Wire Integration Example==<br />
====For a long wire of length L positioned along the x axis with current flowing in the positive x direction====<br />
First, we start off with our adjusted Biot-Savart Formula for a slice of wire.<br />
<br />
<math>\Delta B = \frac{\mu_0I}{4\pi}\int_{\mathrm{wire}}\frac{\mathrm{d}\boldsymbol{\ell} \times \mathbf{\hat r}}{r^2},</math><br />
<br />
Second, we must find <math>r</math>, the vector pointing from the source to the observation location. In this case, we will choose an observation location y above the rod.<br />
<br />
<math> r = obs - source = <0,y,0> - < x,0,0> = <-x,y,0> </math>. which has a magnitude of <math>\sqrt(x^2+y^2)</math><br />
<br />
We see that <math>\hat r = \frac{r}{|r|} </math> .<br />
<br />
<math>\hat r = \frac{<-x,y,0>}{\sqrt(x^2+y^2))}</math><br />
<br />
We then have to express <math> \Delta \boldsymbol{\ell}</math> in terms of our variable of integration, x.<br />
<math> \Delta \boldsymbol{\ell}</math> = <math> \Delta x<1,0,0,></math><br />
<br />
Our new equation after substituting our new variables is <br />
<math> \Delta B = \frac{\mu_0I\Delta x<1,0,0,>}{4\pi(x^2+y^2)} \times \frac{<-x,y,0>}{\sqrt(x^2+y^2))} </math><br />
<br />
Finding the cross product of the above vectors gives us a product in the +z direction.<br />
<math> \Delta B = \frac{\mu_0I\Delta x}{4\pi(x^2+y^2)^(\frac{3}{2})} </math><br />
<br />
We are finally ready to integrate. Because we are integrating the entire rod our limits are<br />
<br />
<br />
<math> \int\limits_{-L/2}^{L/2}\ </math> <math> \int\limits_{-L/2}^{L/2}\ = \frac{\mu_0I\Delta x}{4\pi(x^2+y^2)^(\frac{3}{2})} </math><br />
<br />
We find that our final answer is <math> B= \frac{\mu_0}{4\pi}\frac{LI}{y\sqrt(y^2+(L/2)^2)}\hat z </math><br />
<br />
==A Computational Model==<br />
The following link shows the magnetic field produced by small segments of wire in a loop individually.<br />
For a long straight wire, we see that there is a circular magnetic field surrounding the wire with current. The following link does a stepwise visual of the contributions of each part of the wire at an observation location a distance r from the wire.<br />
<br />
http://www.glowscript.org/#/user/matterandinteractions/folder/matterandinteractions/program/17-Bwire-with-r<br />
<br />
We see that along the axis of the wire, each contribution not on the axis is negated due to symmetry and the resulting magnetic field is all along the wire.<br />
<br />
http://www.glowscript.org/#/user/matterandinteractions/folder/matterandinteractions/program/17-B-loop-with-r-dB.<br />
<br />
== See also ==<br />
[Right Hand Rule[http://www.physicsbook.gatech.edu/Right-Hand_Rule]]<br />
<br />
[Direction of magnetic fields[http://www.physicsbook.gatech.edu/Direction_of_Magnetic_Field]]<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 />
==External Links==<br />
[[Category:Which Category did you place this in?]]</div>Vramanan3http://www.physicsbook.gatech.edu/index.php?title=Biot-Savart_Law_for_Currents&diff=32909Biot-Savart Law for Currents2018-12-13T16:26:19Z<p>Vramanan3: </p>
<hr />
<div>Vaishnavi Ramanan - Fall 2018<br />
<br />
==Biot-Savart Law==<br />
<br />
The Biot-Savart Law can be used for more than just single moving charges; a notable application of this law is its ability to calculate the magnetic field for an extremely large number of charges - an example of thousands of currents moving together is within a current carrying wire (current being the amount of charges moving over a specific amount of time). <br />
<br />
When using Biot-Savart Law to find the magnetic field of a short wire, we can extend this concept to a variety of different shapes - long current carrying wires, current carrying loops, etc. <br />
<br />
*One main point to note is that the application of the Biot-Savart law is specifically for steady state current!<br />
<br />
<br />
====A Mathematical Model====<br />
First We start off with the original version of the Biot-Savart Law. <br />
<math>\vec B=\frac{\mu_0}{4 \pi } \frac{q\vec v\times\hat r}{r^2}</math>, where <math> \frac{\mu_0}{4 \pi } = 1 \times 10^{-7}\frac{Tm^2}{Cm/s}, </math><br />
<br />
Because we are dealing with a portion of wire <math>\mathrm{d}\boldsymbol{\ell}</math> long with an Area A containing n moving particles with charge q, we find that the total number of moving charges is equal to |q|(nAv) which is also equal to I, the current in the wire.<br />
<br />
<math>B = \frac{\mu_0I}{4\pi}\frac{\mathrm{d}\boldsymbol{\ell} \times \mathbf{\hat r}}{r^2},</math><br />
<br />
Because the shape of the current carrying wire can vary from a straight wire to a loop, we must integrate over the region of the wire.<br />
<br />
<math>\Delta B = \frac{\mu_0I}{4\pi}\int_{\mathrm{wire}}\frac{\mathrm{d}\boldsymbol{\ell} \times \mathbf{\hat r}}{r^2},</math><br />
<br />
The key point is that there are <math> nA\Delta l </math> electrons in a short length of wire, each moving with average speed <math>\vec v </math>, so that the sum of all the <math> q\vec v </math> contributions is <math> nA \Delta l|q|\vec v = I\Delta l. </math><br />
<br />
<br />
<br />
When applying the Biot-Savart Law to a Long Straight Wire, we follow a set of steps,<br />
<br />
Step 1: Cut Up the Distribution into Pieces (<math> \Delta l </math>) and Draw <math> \Delta B </math>.<br />
<br />
Step 2: Write an Expression for the Magnetic Field Due to One Piece.<br />
<br />
Step 3: Add Up the Contributions of All the Pieces (each <math> \Delta l </math> adds together to make the entirety of the length).<br />
<br />
Step 4: Check the Result.<br />
<br />
Where the Magnetic Field of a Straight Wire is shown by,<br />
<br />
<math> B = \frac{\mu_0}{4\pi}\frac{LI}{r(r^2 + (L/2)^2)^{1/2}} </math> for length <math> L </math>, conventional current <math> I </math>, a perpendicular distance <math> r </math> from the center of the wire, or,<br />
<math> B = \frac{\mu_0}{4\pi}\frac{2I}{r} </math> if <math> L\>>\>> r. </math><br />
<br />
<br />
'''Right Hand Rule'''<br />
<br />
<br />
When using the Biot-Savart Law for Currents, it is crucial to understand the direction of the magnetic field created by a current. In order to get the direction of the Magnetic Field, as shown in the image below, we point our thumb in the direction of the current, and our fingers automatically curl around in one direction. This curling direction is the direction of the magnetic field itself.<br />
<br />
[[File:IMG_2467.jpg|200px|thumb|left|alt text]]<br />
<br />
==Example==<br />
====For a long wire of length L positioned along the x axis with current flowing in the positive x direction====<br />
First, we start off with our adjusted Biot-Savart Formula for a slice of wire.<br />
<br />
<math>\Delta B = \frac{\mu_0I}{4\pi}\int_{\mathrm{wire}}\frac{\mathrm{d}\boldsymbol{\ell} \times \mathbf{\hat r}}{r^2},</math><br />
<br />
Second, we must find <math>r</math>, the vector pointing from the source to the observation location. In this case, we will choose an observation location y above the rod.<br />
<br />
<math> r = obs - source = <0,y,0> - < x,0,0> = <-x,y,0> </math>. which has a magnitude of <math>\sqrt(x^2+y^2)</math><br />
<br />
We see that <math>\hat r = \frac{r}{|r|} </math> .<br />
<br />
<math>\hat r = \frac{<-x,y,0>}{\sqrt(x^2+y^2))}</math><br />
<br />
We then have to express <math> \Delta \boldsymbol{\ell}</math> in terms of our variable of integration, x.<br />
<math> \Delta \boldsymbol{\ell}</math> = <math> \Delta x<1,0,0,></math><br />
<br />
Our new equation after substituting our new variables is <br />
<math> \Delta B = \frac{\mu_0I\Delta x<1,0,0,>}{4\pi(x^2+y^2)} \times \frac{<-x,y,0>}{\sqrt(x^2+y^2))} </math><br />
<br />
Finding the cross product of the above vectors gives us a product in the +z direction.<br />
<math> \Delta B = \frac{\mu_0I\Delta x}{4\pi(x^2+y^2)^(\frac{3}{2})} </math><br />
<br />
We are finally ready to integrate. Because we are integrating the entire rod our limits are<br />
<br />
<br />
<math> \int\limits_{-L/2}^{L/2}\ </math> <math> \int\limits_{-L/2}^{L/2}\ = \frac{\mu_0I\Delta x}{4\pi(x^2+y^2)^(\frac{3}{2})} </math><br />
<br />
We find that our final answer is <math> B= \frac{\mu_0}{4\pi}\frac{LI}{y\sqrt(y^2+(L/2)^2)}\hat z </math><br />
<br />
==A Computational Model==<br />
The following link shows the magnetic field produced by small segments of wire in a loop individually.<br />
For a long straight wire, we see that there is a circular magnetic field surrounding the wire with current. The following link does a stepwise visual of the contributions of each part of the wire at an observation location a distance r from the wire.<br />
<br />
http://www.glowscript.org/#/user/matterandinteractions/folder/matterandinteractions/program/17-Bwire-with-r<br />
<br />
We see that along the axis of the wire, each contribution not on the axis is negated due to symmetry and the resulting magnetic field is all along the wire.<br />
<br />
http://www.glowscript.org/#/user/matterandinteractions/folder/matterandinteractions/program/17-B-loop-with-r-dB.<br />
<br />
== See also ==<br />
[Right Hand Rule[http://www.physicsbook.gatech.edu/Right-Hand_Rule]]<br />
<br />
[Direction of magnetic fields[http://www.physicsbook.gatech.edu/Direction_of_Magnetic_Field]]<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 />
==External Links==<br />
[[Category:Which Category did you place this in?]]</div>Vramanan3http://www.physicsbook.gatech.edu/index.php?title=Biot-Savart_Law_for_Currents&diff=32908Biot-Savart Law for Currents2018-12-13T16:21:46Z<p>Vramanan3: </p>
<hr />
<div>Vaishnavi Ramanan - Fall 2018<br />
<br />
==Biot-Savart Law==<br />
<br />
The Biot-Savart Law can be used for more than just single moving charges; a notable application of this law is its ability to calculate the magnetic field for an extremely large number of charges - an example of thousands of currents moving together is within a current carrying wire (current being the amount of charges moving over a specific amount of time). <br />
<br />
When using Biot-Savart Law to find the magnetic field of a short wire, we can extend this concept to a variety of different shapes - long current carrying wires, current carrying loops, etc. <br />
<br />
*One main point to note is that the application of the Biot-Savart law is specifically for steady state current!<br />
<br />
<br />
====A Mathematical Model====<br />
First We start off with the original version of the Biot-Savart Law. <br />
<math>\vec B=\frac{\mu_0}{4 \pi } \frac{q\vec v\times\hat r}{r^2}</math>, where <math> \frac{\mu_0}{4 \pi } = 1 \times 10^{-7}\frac{Tm^2}{Cm/s}, </math><br />
<br />
Because we are dealing with a portion of wire <math>\mathrm{d}\boldsymbol{\ell}</math> long with an Area A containing n moving particles with charge q, we find that the total number of moving charges is equal to |q|(nAv) which is also equal to I, the current in the wire.<br />
<br />
<math>B = \frac{\mu_0I}{4\pi}\frac{\mathrm{d}\boldsymbol{\ell} \times \mathbf{\hat r}}{r^2},</math><br />
<br />
Because the shape of the current carrying wire can vary from a straight wire to a loop, we must integrate over the region of the wire.<br />
<br />
<math>\Delta B = \frac{\mu_0I}{4\pi}\int_{\mathrm{wire}}\frac{\mathrm{d}\boldsymbol{\ell} \times \mathbf{\hat r}}{r^2},</math><br />
<br />
The key point is that there are <math> nA\Delta l </math> electrons in a short length of wire, each moving with average speed <math>\vec v </math>, so that the sum of all the <math> q\vec v </math> contributions is <math> nA \Delta l|q|\vec v = I\Delta l. </math><br />
<br />
<br />
<br />
When applying the Biot-Savart Law to a Long Straight Wire, we follow a set of steps,<br />
<br />
Step 1: Cut Up the Distribution into Pieces (<math> \Delta l </math>) and Draw <math> \Delta B </math>.<br />
<br />
Step 2: Write an Expression for the Magnetic Field Due to One Piece.<br />
<br />
Step 3: Add Up the Contributions of All the Pieces (each <math> \Delta l </math> adds together to make the entirety of the length).<br />
<br />
Step 4: Check the Result.<br />
<br />
Where the Magnetic Field of a Straight Wire is shown by,<br />
<br />
<math> B = \frac{\mu_0}{4\pi}\frac{LI}{r(r^2 + (L/2)^2)^{1/2}} </math> for length <math> L </math>, conventional current <math> I </math>, a perpendicular distance <math> r </math> from the center of the wire, or,<br />
<math> B = \frac{\mu_0}{4\pi}\frac{2I}{r} </math> if <math> L\>>\>> r. </math><br />
<br />
<br />
'''Right Hand Rule'''<br />
<br />
<br />
When using the Biot-Savart Law for Currents, it is crucial to understand the direction of the magnetic field created by a current. In order to get the direction of the Magnetic Field, as shown in the image below, we point our thumb in the direction of the current, and our fingers automatically curl around in one direction. This curling direction is the direction of the magnetic field itself.<br />
<br />
[[File:IMG_2467.jpg]]<br />
<br />
==Example==<br />
====For a long wire of length L positioned along the x axis with current flowing in the positive x direction====<br />
First, we start off with our adjusted Biot-Savart Formula for a slice of wire.<br />
<br />
<math>\Delta B = \frac{\mu_0I}{4\pi}\int_{\mathrm{wire}}\frac{\mathrm{d}\boldsymbol{\ell} \times \mathbf{\hat r}}{r^2},</math><br />
<br />
Second, we must find <math>r</math>, the vector pointing from the source to the observation location. In this case, we will choose an observation location y above the rod.<br />
<br />
<math> r = obs - source = <0,y,0> - < x,0,0> = <-x,y,0> </math>. which has a magnitude of <math>\sqrt(x^2+y^2)</math><br />
<br />
We see that <math>\hat r = \frac{r}{|r|} </math> .<br />
<br />
<math>\hat r = \frac{<-x,y,0>}{\sqrt(x^2+y^2))}</math><br />
<br />
We then have to express <math> \Delta \boldsymbol{\ell}</math> in terms of our variable of integration, x.<br />
<math> \Delta \boldsymbol{\ell}</math> = <math> \Delta x<1,0,0,></math><br />
<br />
Our new equation after substituting our new variables is <br />
<math> \Delta B = \frac{\mu_0I\Delta x<1,0,0,>}{4\pi(x^2+y^2)} \times \frac{<-x,y,0>}{\sqrt(x^2+y^2))} </math><br />
<br />
Finding the cross product of the above vectors gives us a product in the +z direction.<br />
<math> \Delta B = \frac{\mu_0I\Delta x}{4\pi(x^2+y^2)^(\frac{3}{2})} </math><br />
<br />
We are finally ready to integrate. Because we are integrating the entire rod our limits are<br />
<br />
<br />
<math> \int\limits_{-L/2}^{L/2}\ </math> <math> \int\limits_{-L/2}^{L/2}\ = \frac{\mu_0I\Delta x}{4\pi(x^2+y^2)^(\frac{3}{2})} </math><br />
<br />
We find that our final answer is <math> B= \frac{\mu_0}{4\pi}\frac{LI}{y\sqrt(y^2+(L/2)^2)}\hat z </math><br />
<br />
==A Computational Model==<br />
The following link shows the magnetic field produced by small segments of wire in a loop individually.<br />
For a long straight wire, we see that there is a circular magnetic field surrounding the wire with current. The following link does a stepwise visual of the contributions of each part of the wire at an observation location a distance r from the wire.<br />
<br />
http://www.glowscript.org/#/user/matterandinteractions/folder/matterandinteractions/program/17-Bwire-with-r<br />
<br />
We see that along the axis of the wire, each contribution not on the axis is negated due to symmetry and the resulting magnetic field is all along the wire.<br />
<br />
http://www.glowscript.org/#/user/matterandinteractions/folder/matterandinteractions/program/17-B-loop-with-r-dB.<br />
<br />
== See also ==<br />
[Right Hand Rule[http://www.physicsbook.gatech.edu/Right-Hand_Rule]]<br />
<br />
[Direction of magnetic fields[http://www.physicsbook.gatech.edu/Direction_of_Magnetic_Field]]<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 />
==External Links==<br />
[[Category:Which Category did you place this in?]]</div>Vramanan3http://www.physicsbook.gatech.edu/index.php?title=Biot-Savart_Law_for_Currents&diff=32907Biot-Savart Law for Currents2018-12-13T16:20:34Z<p>Vramanan3: </p>
<hr />
<div>Vaishnavi Ramanan - Fall 2018<br />
<br />
==Biot-Savart Law==<br />
<br />
The Biot-Savart Law can be used for more than just single moving charges; a notable application of this law is its ability to calculate the magnetic field for an extremely large number of charges - an example of thousands of currents moving together is within a current carrying wire (current being the amount of charges moving over a specific amount of time). <br />
<br />
When using Biot-Savart Law to find the magnetic field of a short wire, we can extend this concept to a variety of different shapes - long current carrying wires, current carrying loops, etc. <br />
<br />
*One main point to note is that the application of the Biot-Savart law is specifically for steady state current!<br />
<br />
<br />
====A Mathematical Model====<br />
First We start off with the original version of the Biot-Savart Law. <br />
<math>\vec B=\frac{\mu_0}{4 \pi } \frac{q\vec v\times\hat r}{r^2}</math>, where <math> \frac{\mu_0}{4 \pi } = 1 \times 10^{-7}\frac{Tm^2}{Cm/s}, </math><br />
<br />
Because we are dealing with a portion of wire <math>\mathrm{d}\boldsymbol{\ell}</math> long with an Area A containing n moving particles with charge q, we find that the total number of moving charges is equal to |q|(nAv) which is also equal to I, the current in the wire.<br />
<br />
<math>B = \frac{\mu_0I}{4\pi}\frac{\mathrm{d}\boldsymbol{\ell} \times \mathbf{\hat r}}{r^2},</math><br />
<br />
Because the shape of the current carrying wire can vary from a straight wire to a loop, we must integrate over the region of the wire.<br />
<br />
<math>\Delta B = \frac{\mu_0I}{4\pi}\int_{\mathrm{wire}}\frac{\mathrm{d}\boldsymbol{\ell} \times \mathbf{\hat r}}{r^2},</math><br />
<br />
The key point is that there are <math> nA\Delta l </math> electrons in a short length of wire, each moving with average speed <math>\vec v </math>, so that the sum of all the <math> q\vec v </math> contributions is <math> nA \Delta l|q|\vec v = I\Delta l. </math><br />
<br />
<br />
<br />
When applying the Biot-Savart Law to a Long Straight Wire, we follow a set of steps,<br />
<br />
Step 1: Cut Up the Distribution into Pieces (<math> \Delta l </math>) and Draw <math> \Delta B </math>.<br />
<br />
Step 2: Write an Expression for the Magnetic Field Due to One Piece.<br />
<br />
Step 3: Add Up the Contributions of All the Pieces (each <math> \Delta l </math> adds together to make the entirety of the length).<br />
<br />
Step 4: Check the Result.<br />
<br />
Where the Magnetic Field of a Straight Wire is shown by,<br />
<br />
<math> B = \frac{\mu_0}{4\pi}\frac{LI}{r(r^2 + (L/2)^2)^{1/2}} </math> for length <math> L </math>, conventional current <math> I </math>, a perpendicular distance <math> r </math> from the center of the wire, or,<br />
<math> B = \frac{\mu_0}{4\pi}\frac{2I}{r} </math> if <math> L\>>\>> r. </math><br />
<br />
<br />
'''Right Hand Rule'''<br />
<br />
<br />
When using the Biot-Savart Law for Currents, it is crucial to understand the direction of the magnetic field created by a current. In order to get the direction of the Magnetic Field, as shown in the image below, we point our thumb in the direction of the current, and our fingers automatically curl around in one direction. This curling direction is the direction of the magnetic field itself.<br />
<br />
[[File:IMG_2467.jpg]]<br />
<br />
==Example==<br />
====For a long wire of length L positioned along the x axis with current flowing in the positive x direction====<br />
First, we start off with our adjusted Biot-Savart Formula for a slice of wire.<br />
<br />
<math>\Delta B = \frac{\mu_0I}{4\pi}\int_{\mathrm{wire}}\frac{\mathrm{d}\boldsymbol{\ell} \times \mathbf{\hat r}}{r^2},</math><br />
<br />
Second, we must find <math>r</math>, the vector pointing from the source to the observation location. In this case, we will choose an observation location y above the rod.<br />
<br />
<math> r = obs - source = <0,y,0> - < x,0,0> = <-x,y,0> </math>. which has a magnitude of <math>\sqrt(x^2+y^2)</math><br />
<br />
We see that <math>\hat r = \frac{r}{|r|} </math> .<br />
<br />
<math>\hat r = \frac{<-x,y,0>}{\sqrt(x^2+y^2))}</math><br />
<br />
We then have to express <math> \Delta \boldsymbol{\ell}</math> in terms of our variable of integration, x.<br />
<math> \Delta \boldsymbol{\ell}</math> = <math> \Delta x<1,0,0,></math><br />
<br />
Our new equation after substituting our new variables is <br />
<math> \Delta B = \frac{\mu_0I\Delta x<1,0,0,>}{4\pi(x^2+y^2)} \times \frac{<-x,y,0>}{\sqrt(x^2+y^2))} </math><br />
<br />
Finding the cross product of the above vectors gives us a product in the +z direction.<br />
<math> \Delta B = \frac{\mu_0I\Delta x}{4\pi(x^2+y^2)^(\frac{3}{2})} </math><br />
<br />
We are finally ready to integrate. Because we are integrating the entire rod our limits are<br />
<math> \int\limits_{-L/2}^{L/2}\ </math><br />
<br />
<math> \int\limits_{-L/2}^{L/2}\ = \frac{\mu_0I\Delta x}{4\pi(x^2+y^2)^(\frac{3}{2})} </math><br />
<br />
We find that our final answer is <math> B= \frac{\mu_0}{4\pi}\frac{LI}{y\sqrt(y^2+(L/2)^2)}\hat z </math><br />
<br />
==A Computational Model==<br />
The following link shows the magnetic field produced by small segments of wire in a loop individually.<br />
For a long straight wire, we see that there is a circular magnetic field surrounding the wire with current. The following link does a stepwise visual of the contributions of each part of the wire at an observation location a distance r from the wire.<br />
<br />
http://www.glowscript.org/#/user/matterandinteractions/folder/matterandinteractions/program/17-Bwire-with-r<br />
<br />
We see that along the axis of the wire, each contribution not on the axis is negated due to symmetry and the resulting magnetic field is all along the wire.<br />
<br />
http://www.glowscript.org/#/user/matterandinteractions/folder/matterandinteractions/program/17-B-loop-with-r-dB.<br />
<br />
== See also ==<br />
[Right Hand Rule[http://www.physicsbook.gatech.edu/Right-Hand_Rule]]<br />
<br />
[Direction of magnetic fields[http://www.physicsbook.gatech.edu/Direction_of_Magnetic_Field]]<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 />
==External Links==<br />
[[Category:Which Category did you place this in?]]</div>Vramanan3http://www.physicsbook.gatech.edu/index.php?title=Biot-Savart_Law_for_Currents&diff=32906Biot-Savart Law for Currents2018-12-13T16:19:46Z<p>Vramanan3: </p>
<hr />
<div>Vaishnavi Ramanan - Fall 2018<br />
<br />
==Biot-Savart Law==<br />
<br />
The Biot-Savart Law can be used for more than just single moving charges; a notable application of this law is its ability to calculate the magnetic field for an extremely large number of charges - an example of thousands of currents moving together is within a current carrying wire (current being the amount of charges moving over a specific amount of time). <br />
<br />
When using Biot-Savart Law to find the magnetic field of a short wire, we can extend this concept to a variety of different shapes - long current carrying wires, current carrying loops, etc. <br />
<br />
*One main point to note is that the application of the Biot-Savart law is specifically for steady state current!<br />
<br />
<br />
====A Mathematical Model====<br />
First We start off with the original version of the Biot-Savart Law. <br />
<math>\vec B=\frac{\mu_0}{4 \pi } \frac{q\vec v\times\hat r}{r^2}</math>, where <math> \frac{\mu_0}{4 \pi } = 1 \times 10^{-7}\frac{Tm^2}{Cm/s}, </math><br />
<br />
Because we are dealing with a portion of wire <math>\mathrm{d}\boldsymbol{\ell}</math> long with an Area A containing n moving particles with charge q, we find that the total number of moving charges is equal to |q|(nAv) which is also equal to I, the current in the wire.<br />
<br />
<math>B = \frac{\mu_0I}{4\pi}\frac{\mathrm{d}\boldsymbol{\ell} \times \mathbf{\hat r}}{r^2},</math><br />
<br />
Because the shape of the current carrying wire can vary from a straight wire to a loop, we must integrate over the region of the wire.<br />
<br />
<math>\Delta B = \frac{\mu_0I}{4\pi}\int_{\mathrm{wire}}\frac{\mathrm{d}\boldsymbol{\ell} \times \mathbf{\hat r}}{r^2},</math><br />
<br />
The key point is that there are <math> nA\Delta l </math> electrons in a short length of wire, each moving with average speed <math>\vec v </math>, so that the sum of all the <math> q\vec v </math> contributions is <math> nA \Delta l|q|\vec v = I\Delta l. </math><br />
<br />
<br />
<br />
When applying the Biot-Savart Law to a Long Straight Wire, we follow a set of steps,<br />
<br />
Step 1: Cut Up the Distribution into Pieces (<math> \Delta l </math>) and Draw <math> \Delta B </math>.<br />
<br />
Step 2: Write an Expression for the Magnetic Field Due to One Piece.<br />
<br />
Step 3: Add Up the Contributions of All the Pieces (each <math> \Delta l </math> adds together to make the entirety of the length).<br />
<br />
Step 4: Check the Result.<br />
<br />
Where the Magnetic Field of a Straight Wire is shown by,<br />
<br />
<math> B = \frac{\mu_0}{4\pi}\frac{LI}{r(r^2 + (L/2)^2)^{1/2}} </math> for length <math> L </math>, conventional current <math> I </math>, a perpendicular distance <math> r </math> from the center of the wire, or,<br />
<math> B = \frac{\mu_0}{4\pi}\frac{2I}{r} </math> if <math> L\>>\>> r. </math><br />
<br />
<br />
'''Right Hand Rule'''<br />
<br />
<br />
When using the Biot-Savart Law for Currents, it is crucial to understand the direction of the magnetic field created by a current. In order to get the direction of the Magnetic Field, as shown in the image below, we point our thumb in the direction of the current, and our fingers automatically curl around in one direction. This curling direction is the direction of the magnetic field itself.<br />
<br />
[[File:IMG_2467.jpg]]<br />
==Example==<br />
====For a long wire of length L positioned along the x axis with current flowing in the positive x direction====<br />
First, we start off with our adjusted Biot-Savart Formula for a slice of wire.<br />
<br />
<math>\Delta B = \frac{\mu_0I}{4\pi}\int_{\mathrm{wire}}\frac{\mathrm{d}\boldsymbol{\ell} \times \mathbf{\hat r}}{r^2},</math><br />
<br />
Second, we must find <math>r</math>, the vector pointing from the source to the observation location. In this case, we will choose an observation location y above the rod.<br />
<br />
<math> r = obs - source = <0,y,0> - < x,0,0> = <-x,y,0> </math>. which has a magnitude of <math>\sqrt(x^2+y^2)</math><br />
<br />
We see that <math>\hat r = \frac{r}{|r|} </math> .<br />
<br />
<math>\hat r = \frac{<-x,y,0>}{\sqrt(x^2+y^2))}</math><br />
<br />
We then have to express <math> \Delta \boldsymbol{\ell}</math> in terms of our variable of integration, x.<br />
<math> \Delta \boldsymbol{\ell}</math> = <math> \Delta x<1,0,0,></math><br />
<br />
Our new equation after substituting our new variables is <br />
<math> \Delta B = \frac{\mu_0I\Delta x<1,0,0,>}{4\pi(x^2+y^2)} \times \frac{<-x,y,0>}{\sqrt(x^2+y^2))} </math><br />
<br />
Finding the cross product of the above vectors gives us a product in the +z direction.<br />
<math> \Delta B = \frac{\mu_0I\Delta x}{4\pi(x^2+y^2)^(\frac{3}{2})} </math><br />
<br />
We are finally ready to integrate. Because we are integrating the entire rod our limits are<br />
<math> \int\limits_{-L/2}^{L/2}\ </math><br />
<br />
<math> \int\limits_{-L/2}^{L/2}\ = \frac{\mu_0I\Delta x}{4\pi(x^2+y^2)^(\frac{3}{2})} </math><br />
<br />
We find that our final answer is <math> B= \frac{\mu_0}{4\pi}\frac{LI}{y\sqrt(y^2+(L/2)^2)}\hat z </math><br />
<br />
==A Computational Model==<br />
The following link shows the magnetic field produced by small segments of wire in a loop individually.<br />
For a long straight wire, we see that there is a circular magnetic field surrounding the wire with current. The following link does a stepwise visual of the contributions of each part of the wire at an observation location a distance r from the wire.<br />
<br />
http://www.glowscript.org/#/user/matterandinteractions/folder/matterandinteractions/program/17-Bwire-with-r<br />
<br />
We see that along the axis of the wire, each contribution not on the axis is negated due to symmetry and the resulting magnetic field is all along the wire.<br />
<br />
http://www.glowscript.org/#/user/matterandinteractions/folder/matterandinteractions/program/17-B-loop-with-r-dB.<br />
<br />
== See also ==<br />
[Right Hand Rule[http://www.physicsbook.gatech.edu/Right-Hand_Rule]]<br />
<br />
[Direction of magnetic fields[http://www.physicsbook.gatech.edu/Direction_of_Magnetic_Field]]<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 />
==External Links==<br />
[[Category:Which Category did you place this in?]]</div>Vramanan3http://www.physicsbook.gatech.edu/index.php?title=File:IMG_2467.jpg&diff=32905File:IMG 2467.jpg2018-12-13T16:19:11Z<p>Vramanan3: </p>
<hr />
<div></div>Vramanan3http://www.physicsbook.gatech.edu/index.php?title=Biot-Savart_Law_for_Currents&diff=32904Biot-Savart Law for Currents2018-12-13T16:14:16Z<p>Vramanan3: </p>
<hr />
<div>Vaishnavi Ramanan - Fall 2018<br />
<br />
==Biot-Savart Law==<br />
<br />
The Biot-Savart Law can be used for more than just single moving charges; a notable application of this law is its ability to calculate the magnetic field for an extremely large number of charges - an example of thousands of currents moving together is within a current carrying wire (current being the amount of charges moving over a specific amount of time). <br />
<br />
When using Biot-Savart Law to find the magnetic field of a short wire, we can extend this concept to a variety of different shapes - long current carrying wires, current carrying loops, etc. <br />
<br />
*One main point to note is that the application of the Biot-Savart law is specifically for steady state current!<br />
<br />
<br />
====A Mathematical Model====<br />
First We start off with the original version of the Biot-Savart Law. <br />
<math>\vec B=\frac{\mu_0}{4 \pi } \frac{q\vec v\times\hat r}{r^2}</math>, where <math> \frac{\mu_0}{4 \pi } = 1 \times 10^{-7}\frac{Tm^2}{Cm/s}, </math><br />
<br />
Because we are dealing with a portion of wire <math>\mathrm{d}\boldsymbol{\ell}</math> long with an Area A containing n moving particles with charge q, we find that the total number of moving charges is equal to |q|(nAv) which is also equal to I, the current in the wire.<br />
<br />
<math>B = \frac{\mu_0I}{4\pi}\frac{\mathrm{d}\boldsymbol{\ell} \times \mathbf{\hat r}}{r^2},</math><br />
<br />
Because the shape of the current carrying wire can vary from a straight wire to a loop, we must integrate over the region of the wire.<br />
<br />
<math>\Delta B = \frac{\mu_0I}{4\pi}\int_{\mathrm{wire}}\frac{\mathrm{d}\boldsymbol{\ell} \times \mathbf{\hat r}}{r^2},</math><br />
<br />
The key point is that there are <math> nA\Delta l </math> electrons in a short length of wire, each moving with average speed <math>\vec v </math>, so that the sum of all the <math> q\vec v </math> contributions is <math> nA \Delta l|q|\vec v = I\Delta l. </math><br />
<br />
<br />
<br />
When applying the Biot-Savart Law to a Long Straight Wire, we follow a set of steps,<br />
<br />
Step 1: Cut Up the Distribution into Pieces (<math> \Delta l </math>) and Draw <math> \Delta B </math>.<br />
<br />
Step 2: Write an Expression for the Magnetic Field Due to One Piece.<br />
<br />
Step 3: Add Up the Contributions of All the Pieces (each <math> \Delta l </math> adds together to make the entirety of the length).<br />
<br />
Step 4: Check the Result.<br />
<br />
Where the Magnetic Field of a Straight Wire is shown by,<br />
<br />
<math> B = \frac{\mu_0}{4\pi}\frac{LI}{r(r^2 + (L/2)^2)^{1/2}} </math> for length <math> L </math>, conventional current <math> I </math>, a perpendicular distance <math> r </math> from the center of the wire, or,<br />
<math> B = \frac{\mu_0}{4\pi}\frac{2I}{r} </math> if <math> L\>>\>> r. </math><br />
<br />
<br />
'''Right Hand Rule'''<br />
<br />
<br />
When using the Biot-Savart Law for Currents, it is crucial to understand the direction of the magnetic field created by a current. In order to get the direction of the Magnetic Field, as shown in the image below, we point our thumb in the direction of the current, and our fingers automatically curl around in one direction. This curling direction is the direction of the magnetic field itself.<br />
<br />
[[File:Right Hand Rule.jpg]]<br />
==Example==<br />
====For a long wire of length L positioned along the x axis with current flowing in the positive x direction====<br />
First, we start off with our adjusted Biot-Savart Formula for a slice of wire.<br />
<br />
<math>\Delta B = \frac{\mu_0I}{4\pi}\int_{\mathrm{wire}}\frac{\mathrm{d}\boldsymbol{\ell} \times \mathbf{\hat r}}{r^2},</math><br />
<br />
Second, we must find <math>r</math>, the vector pointing from the source to the observation location. In this case, we will choose an observation location y above the rod.<br />
<br />
<math> r = obs - source = <0,y,0> - < x,0,0> = <-x,y,0> </math>. which has a magnitude of <math>\sqrt(x^2+y^2)</math><br />
<br />
We see that <math>\hat r = \frac{r}{|r|} </math> .<br />
<br />
<math>\hat r = \frac{<-x,y,0>}{\sqrt(x^2+y^2))}</math><br />
<br />
We then have to express <math> \Delta \boldsymbol{\ell}</math> in terms of our variable of integration, x.<br />
<math> \Delta \boldsymbol{\ell}</math> = <math> \Delta x<1,0,0,></math><br />
<br />
Our new equation after substituting our new variables is <br />
<math> \Delta B = \frac{\mu_0I\Delta x<1,0,0,>}{4\pi(x^2+y^2)} \times \frac{<-x,y,0>}{\sqrt(x^2+y^2))} </math><br />
<br />
Finding the cross product of the above vectors gives us a product in the +z direction.<br />
<math> \Delta B = \frac{\mu_0I\Delta x}{4\pi(x^2+y^2)^(\frac{3}{2})} </math><br />
<br />
We are finally ready to integrate. Because we are integrating the entire rod our limits are<br />
<math> \int\limits_{-L/2}^{L/2}\ </math><br />
<br />
<math> \int\limits_{-L/2}^{L/2}\ = \frac{\mu_0I\Delta x}{4\pi(x^2+y^2)^(\frac{3}{2})} </math><br />
<br />
We find that our final answer is <math> B= \frac{\mu_0}{4\pi}\frac{LI}{y\sqrt(y^2+(L/2)^2)}\hat z </math><br />
<br />
==A Computational Model==<br />
The following link shows the magnetic field produced by small segments of wire in a loop individually.<br />
For a long straight wire, we see that there is a circular magnetic field surrounding the wire with current. The following link does a stepwise visual of the contributions of each part of the wire at an observation location a distance r from the wire.<br />
<br />
http://www.glowscript.org/#/user/matterandinteractions/folder/matterandinteractions/program/17-Bwire-with-r<br />
<br />
We see that along the axis of the wire, each contribution not on the axis is negated due to symmetry and the resulting magnetic field is all along the wire.<br />
<br />
http://www.glowscript.org/#/user/matterandinteractions/folder/matterandinteractions/program/17-B-loop-with-r-dB.<br />
<br />
== See also ==<br />
[Right Hand Rule[http://www.physicsbook.gatech.edu/Right-Hand_Rule]]<br />
<br />
[Direction of magnetic fields[http://www.physicsbook.gatech.edu/Direction_of_Magnetic_Field]]<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 />
==External Links==<br />
[[Category:Which Category did you place this in?]]</div>Vramanan3http://www.physicsbook.gatech.edu/index.php?title=Biot-Savart_Law_for_Currents&diff=32903Biot-Savart Law for Currents2018-12-13T16:09:17Z<p>Vramanan3: </p>
<hr />
<div>Vaishnavi Ramanan - Fall 2018<br />
<br />
==Biot-Savart Law==<br />
<br />
The Biot-Savart Law can be used for more than just single moving charges; a notable application of this law is its ability to calculate the magnetic field for an extremely large number of charges - an example of thousands of currents moving together is within a current carrying wire (current being the amount of charges moving over a specific amount of time). <br />
<br />
When using Biot-Savart Law to find the magnetic field of a short wire, we can extend this concept to a variety of different shapes - long current carrying wires, current carrying loops, etc. <br />
<br />
One main point to note is that the application of the Bio-Savart law is specifically for steady state current!<br />
<br />
<br />
====A Mathematical Model====<br />
First We start off with the original version of the Biot-Savart Law. <br />
<math>\vec B=\frac{\mu_0}{4 \pi } \frac{q\vec v\times\hat r}{r^2}</math>, where <math> \frac{\mu_0}{4 \pi } = 1 \times 10^{-7}\frac{Tm^2}{Cm/s}, </math><br />
<br />
Because we are dealing with a portion of wire <math>\mathrm{d}\boldsymbol{\ell}</math> long with an Area A containing n moving particles with charge q, we find that the total number of moving charges is equal to |q|(nAv) which is also equal to I, the current in the wire.<br />
<br />
<math>B = \frac{\mu_0I}{4\pi}\frac{\mathrm{d}\boldsymbol{\ell} \times \mathbf{\hat r}}{r^2},</math><br />
<br />
Because the shape of the current carrying wire can vary from a straight wire to a loop, we must integrate over the region of the wire.<br />
<br />
<math>\Delta B = \frac{\mu_0I}{4\pi}\int_{\mathrm{wire}}\frac{\mathrm{d}\boldsymbol{\ell} \times \mathbf{\hat r}}{r^2},</math><br />
<br />
The key point is that there are <math> nA\Delta l </math> electrons in a short length of wire, each moving with average speed <math>\vec v </math>, so that the sum of all the <math> q\vec v </math> contributions is <math> nA \Delta l|q|\vec v = I\Delta l. </math><br />
<br />
When applying the Biot-Savart Law to a Long Straight Wire, we follow a set of steps,<br />
<br />
Step 1: Cut Up the Distribution into Pieces and Draw <math> \Delta B </math>.<br />
<br />
Step 2: Write an Expression for the Magnetic Field Due to One Piece.<br />
<br />
Step 3: Add Up the Contributions of All the Pieces.<br />
<br />
Step 4: Check the Result.<br />
<br />
Where the Magnetic Field of a Straight Wire is shown by,<br />
<br />
<math> B = \frac{\mu_0}{4\pi}\frac{LI}{r(r^2 + (L/2)^2)^{1/2}} </math> for length <math> L </math>, conventional current <math> I </math>, a perpendicular distance <math> r </math> from the center of the wire, or,<br />
<math> B = \frac{\mu_0}{4\pi}\frac{2I}{r} </math> if <math> L\>>\>> r. </math><br />
<br />
<br />
'''Right Hand Rule'''<br />
<br />
<br />
When using the Biot-Savart Law for Currents, it is crucial to understand the direction of the magnetic field created by a current. For this, we use the right hand rule. If we curl our fingers and extend our thumb, similar to a thumbs up position, and point our thumb in the direction of the current, our fingers curl in the direction of the magnetic field.<br />
<br />
[[File:Example.jpg]]<br />
[[File:Right Hand Rule.jpg]]<br />
==Example==<br />
====For a long wire of length L positioned along the x axis with current flowing in the positive x direction====<br />
First, we start off with our adjusted Biot-Savart Formula for a slice of wire.<br />
<br />
<math>\Delta B = \frac{\mu_0I}{4\pi}\int_{\mathrm{wire}}\frac{\mathrm{d}\boldsymbol{\ell} \times \mathbf{\hat r}}{r^2},</math><br />
<br />
Second, we must find <math>r</math>, the vector pointing from the source to the observation location. In this case, we will choose an observation location y above the rod.<br />
<br />
<math> r = obs - source = <0,y,0> - < x,0,0> = <-x,y,0> </math>. which has a magnitude of <math>\sqrt(x^2+y^2)</math><br />
<br />
We see that <math>\hat r = \frac{r}{|r|} </math> .<br />
<br />
<math>\hat r = \frac{<-x,y,0>}{\sqrt(x^2+y^2))}</math><br />
<br />
We then have to express <math> \Delta \boldsymbol{\ell}</math> in terms of our variable of integration, x.<br />
<math> \Delta \boldsymbol{\ell}</math> = <math> \Delta x<1,0,0,></math><br />
<br />
Our new equation after substituting our new variables is <br />
<math> \Delta B = \frac{\mu_0I\Delta x<1,0,0,>}{4\pi(x^2+y^2)} \times \frac{<-x,y,0>}{\sqrt(x^2+y^2))} </math><br />
<br />
Finding the cross product of the above vectors gives us a product in the +z direction.<br />
<math> \Delta B = \frac{\mu_0I\Delta x}{4\pi(x^2+y^2)^(\frac{3}{2})} </math><br />
<br />
We are finally ready to integrate. Because we are integrating the entire rod our limits are<br />
<math> \int\limits_{-L/2}^{L/2}\ </math><br />
<br />
<math> \int\limits_{-L/2}^{L/2}\ = \frac{\mu_0I\Delta x}{4\pi(x^2+y^2)^(\frac{3}{2})} </math><br />
<br />
We find that our final answer is <math> B= \frac{\mu_0}{4\pi}\frac{LI}{y\sqrt(y^2+(L/2)^2)}\hat z </math><br />
<br />
==A Computational Model==<br />
The following link shows the magnetic field produced by small segments of wire in a loop individually.<br />
For a long straight wire, we see that there is a circular magnetic field surrounding the wire with current. The following link does a stepwise visual of the contributions of each part of the wire at an observation location a distance r from the wire.<br />
<br />
http://www.glowscript.org/#/user/matterandinteractions/folder/matterandinteractions/program/17-Bwire-with-r<br />
<br />
We see that along the axis of the wire, each contribution not on the axis is negated due to symmetry and the resulting magnetic field is all along the wire.<br />
<br />
http://www.glowscript.org/#/user/matterandinteractions/folder/matterandinteractions/program/17-B-loop-with-r-dB.<br />
<br />
== See also ==<br />
[Right Hand Rule[http://www.physicsbook.gatech.edu/Right-Hand_Rule]]<br />
<br />
[Direction of magnetic fields[http://www.physicsbook.gatech.edu/Direction_of_Magnetic_Field]]<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 />
==External Links==<br />
[[Category:Which Category did you place this in?]]</div>Vramanan3http://www.physicsbook.gatech.edu/index.php?title=Biot-Savart_Law_for_Currents&diff=32901Biot-Savart Law for Currents2018-12-07T07:31:24Z<p>Vramanan3: </p>
<hr />
<div>Vaishnavi Ramanan - Fall 2018<br />
<br />
==Biot-Savart Law==<br />
<br />
The Biot-Savart Law can be used for more than just single moving charges; a notable application of this law is its ability to calculate the magnetic field for an extremely large number of charges - an example of thousands of currents moving together is within a current carrying wire (current being the amount of charges moving over a specific amount of time). <br />
<br />
When using Biot-Savart Law to find the magnetic field of a short wire, we can extend this concept to a variety of different shapes - long current carrying wires, current carrying loops, etc. <br />
<br />
One main point to note is that the application of the Bio-Savart law is specifically for steady state current!<br />
<br />
<br />
====A Mathematical Model====<br />
First We start off with the original version of the Biot-Savart Law. <br />
<math>\vec B=\frac{\mu_0}{4 \pi } \frac{q\vec v\times\hat r}{r^2}</math>, where <math> \frac{\mu_0}{4 \pi } = 1 \times 10^{-7}\frac{Tm^2}{Cm/s}, </math><br />
<br />
Because we are dealing with a portion of wire <math>\mathrm{d}\boldsymbol{\ell}</math> long with an Area A containing n moving particles with charge q, we find that the total number of moving charges is equal to |q|(nAv) which is also equal to I, the current in the wire.<br />
<br />
<math>B = \frac{\mu_0I}{4\pi}\frac{\mathrm{d}\boldsymbol{\ell} \times \mathbf{\hat r}}{r^2},</math><br />
<br />
Because the shape of the current carrying wire can vary from a straight wire to a loop, we must integrate over the region of the wire.<br />
<br />
<math>\Delta B = \frac{\mu_0I}{4\pi}\int_{\mathrm{wire}}\frac{\mathrm{d}\boldsymbol{\ell} \times \mathbf{\hat r}}{r^2},</math><br />
<br />
The key point is that there are <math> nA\Delta l </math> electrons in a short length of wire, each moving with average speed <math>\vec v </math>, so that the sum of all the <math> q\vec v </math> contributions is <math> nA \Delta l|q|\vec v = I\Delta l. </math><br />
<br />
When applying the Biot-Savart Law to a Long Straight Wire, we follow a set of steps,<br />
<br />
Step 1: Cut Up the Distribution into Pieces and Draw <math> \Delta B </math>.<br />
<br />
Step 2: Write an Expression for the Magnetic Field Due to One Piece.<br />
<br />
Step 3: Add Up the Contributions of All the Pieces.<br />
<br />
Step 4: Check the Result.<br />
<br />
Where the Magnetic Field of a Straight Wire is shown by,<br />
<br />
<math> B = \frac{\mu_0}{4\pi}\frac{LI}{r(r^2 + (L/2)^2)^{1/2}} </math> for length <math> L </math>, conventional current <math> I </math>, a perpendicular distance <math> r </math> from the center of the wire, or,<br />
<math> B = \frac{\mu_0}{4\pi}\frac{2I}{r} </math> if <math> L\>>\>> r. </math><br />
<br />
<br />
'''Right Hand Rule'''<br />
<br />
<br />
When using the Biot-Savart Law for Currents, it is crucial to understand the direction of the magnetic field created by a current. For this, we use the right hand rule. If we curl our fingers and extend our thumb, similar to a thumbs up position, and point our thumb in the direction of the current, our fingers curl in the direction of the magnetic field.<br />
<br />
[[File:Example.jpg]]<br />
<br />
==Example==<br />
====For a long wire of length L positioned along the x axis with current flowing in the positive x direction====<br />
First, we start off with our adjusted Biot-Savart Formula for a slice of wire.<br />
<br />
<math>\Delta B = \frac{\mu_0I}{4\pi}\int_{\mathrm{wire}}\frac{\mathrm{d}\boldsymbol{\ell} \times \mathbf{\hat r}}{r^2},</math><br />
<br />
Second, we must find <math>r</math>, the vector pointing from the source to the observation location. In this case, we will choose an observation location y above the rod.<br />
<br />
<math> r = obs - source = <0,y,0> - < x,0,0> = <-x,y,0> </math>. which has a magnitude of <math>\sqrt(x^2+y^2)</math><br />
<br />
We see that <math>\hat r = \frac{r}{|r|} </math> .<br />
<br />
<math>\hat r = \frac{<-x,y,0>}{\sqrt(x^2+y^2))}</math><br />
<br />
We then have to express <math> \Delta \boldsymbol{\ell}</math> in terms of our variable of integration, x.<br />
<math> \Delta \boldsymbol{\ell}</math> = <math> \Delta x<1,0,0,></math><br />
<br />
Our new equation after substituting our new variables is <br />
<math> \Delta B = \frac{\mu_0I\Delta x<1,0,0,>}{4\pi(x^2+y^2)} \times \frac{<-x,y,0>}{\sqrt(x^2+y^2))} </math><br />
<br />
Finding the cross product of the above vectors gives us a product in the +z direction.<br />
<math> \Delta B = \frac{\mu_0I\Delta x}{4\pi(x^2+y^2)^(\frac{3}{2})} </math><br />
<br />
We are finally ready to integrate. Because we are integrating the entire rod our limits are<br />
<math> \int\limits_{-L/2}^{L/2}\ </math><br />
<br />
<math> \int\limits_{-L/2}^{L/2}\ = \frac{\mu_0I\Delta x}{4\pi(x^2+y^2)^(\frac{3}{2})} </math><br />
<br />
We find that our final answer is <math> B= \frac{\mu_0}{4\pi}\frac{LI}{y\sqrt(y^2+(L/2)^2)}\hat z </math><br />
<br />
==A Computational Model==<br />
The following link shows the magnetic field produced by small segments of wire in a loop individually.<br />
For a long straight wire, we see that there is a circular magnetic field surrounding the wire with current. The following link does a stepwise visual of the contributions of each part of the wire at an observation location a distance r from the wire.<br />
<br />
http://www.glowscript.org/#/user/matterandinteractions/folder/matterandinteractions/program/17-Bwire-with-r<br />
<br />
We see that along the axis of the wire, each contribution not on the axis is negated due to symmetry and the resulting magnetic field is all along the wire.<br />
<br />
http://www.glowscript.org/#/user/matterandinteractions/folder/matterandinteractions/program/17-B-loop-with-r-dB.<br />
<br />
== See also ==<br />
[Right Hand Rule[http://www.physicsbook.gatech.edu/Right-Hand_Rule]]<br />
<br />
[Direction of magnetic fields[http://www.physicsbook.gatech.edu/Direction_of_Magnetic_Field]]<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 />
==External Links==<br />
[[Category:Which Category did you place this in?]]</div>Vramanan3http://www.physicsbook.gatech.edu/index.php?title=Biot-Savart_Law_for_Currents&diff=32900Biot-Savart Law for Currents2018-12-07T07:30:56Z<p>Vramanan3: </p>
<hr />
<div>Vaishnavi Ramanan - Fall 2018<br />
<br />
==Biot-Savart Law==<br />
<br />
The Biot-Savart Law can be used for more than just single moving charges; a notable application of this law is its ability to calculate the magnetic field for an extremely large number of charges - an example of thousands of currents moving together is within a current carrying wire (current being the amount of charges moving over a specific amount of time). <br />
<br />
When using Biot-Savart Law to find the magnetic field of a short wire, we can extend this concept to a variety of different shapes - long current carrying wires, current carrying loops, etc. <br />
<br />
One main point to note is that the application of the Bio-Savart law is specifically for steady state current!<br />
<br />
<br />
====A Mathematical Model====<br />
First We start off with the original version of the Biot-Savart Law. <br />
<math>\vec B=\frac{\mu_0}{4 \pi } \frac{q\vec v\times\hat r}{r^2}</math>, where <math> \frac{\mu_0}{4 \pi } = 1 \times 10^{-7}\frac{Tm^2}{Cm/s}, </math><br />
<br />
Because we are dealing with a portion of wire <math>\mathrm{d}\boldsymbol{\ell}</math> long with an Area A containing n moving particles with charge q, we find that the total number of moving charges is equal to |q|(nAv) which is also equal to I, the current in the wire.<br />
<br />
<math>B = \frac{\mu_0I}{4\pi}\frac{\mathrm{d}\boldsymbol{\ell} \times \mathbf{\hat r}}{r^2},</math><br />
<br />
Because the shape of the current carrying wire can vary from a straight wire to a loop, we must integrate over the region of the wire.<br />
<br />
<math>\Delta B = \frac{\mu_0I}{4\pi}\int_{\mathrm{wire}}\frac{\mathrm{d}\boldsymbol{\ell} \times \mathbf{\hat r}}{r^2},</math><br />
<br />
The key point is that there are <math> nA\Delta l </math> electrons in a short length of wire, each moving with average speed <math>\vec v </math>, so that the sum of all the <math> q\vec v </math> contributions is <math> nA \Delta l|q|\vec v = I\Delta l. </math><br />
<br />
When applying the Biot-Savart Law to a Long Straight Wire, we follow a set of steps,<br />
<br />
Step 1: Cut Up the Distribution into Pieces and Draw <math> \Delta B </math>.<br />
<br />
Step 2: Write an Expression for the Magnetic Field Due to One Piece.<br />
<br />
Step 3: Add Up the Contributions of All the Pieces.<br />
<br />
Step 4: Check the Result.<br />
<br />
Where the Magnetic Field of a Straight Wire is shown by,<br />
<br />
<math> B = \frac{\mu_0}{4\pi}\frac{LI}{r(r^2 + (L/2)^2)^{1/2}} </math> for length <math> L </math>, conventional current <math> I </math>, a perpendicular distance <math> r </math> from the center of the wire, or,<br />
<math> B = \frac{\mu_0}{4\pi}\frac{2I}{r} </math> if <math> L\>>\>> r. </math><br />
<br />
<br />
'''Right Hand Rule'''<br />
When using the Biot-Savart Law for Currents, it is crucial to understand the direction of the magnetic field created by a current. For this, we use the right hand rule. If we curl our fingers and extend our thumb, similar to a thumbs up position, and point our thumb in the direction of the current, our fingers curl in the direction of the magnetic field.<br />
<br />
[[File:Example.jpg]]<br />
<br />
==Example==<br />
====For a long wire of length L positioned along the x axis with current flowing in the positive x direction====<br />
First, we start off with our adjusted Biot-Savart Formula for a slice of wire.<br />
<br />
<math>\Delta B = \frac{\mu_0I}{4\pi}\int_{\mathrm{wire}}\frac{\mathrm{d}\boldsymbol{\ell} \times \mathbf{\hat r}}{r^2},</math><br />
<br />
Second, we must find <math>r</math>, the vector pointing from the source to the observation location. In this case, we will choose an observation location y above the rod.<br />
<br />
<math> r = obs - source = <0,y,0> - < x,0,0> = <-x,y,0> </math>. which has a magnitude of <math>\sqrt(x^2+y^2)</math><br />
<br />
We see that <math>\hat r = \frac{r}{|r|} </math> .<br />
<br />
<math>\hat r = \frac{<-x,y,0>}{\sqrt(x^2+y^2))}</math><br />
<br />
We then have to express <math> \Delta \boldsymbol{\ell}</math> in terms of our variable of integration, x.<br />
<math> \Delta \boldsymbol{\ell}</math> = <math> \Delta x<1,0,0,></math><br />
<br />
Our new equation after substituting our new variables is <br />
<math> \Delta B = \frac{\mu_0I\Delta x<1,0,0,>}{4\pi(x^2+y^2)} \times \frac{<-x,y,0>}{\sqrt(x^2+y^2))} </math><br />
<br />
Finding the cross product of the above vectors gives us a product in the +z direction.<br />
<math> \Delta B = \frac{\mu_0I\Delta x}{4\pi(x^2+y^2)^(\frac{3}{2})} </math><br />
<br />
We are finally ready to integrate. Because we are integrating the entire rod our limits are<br />
<math> \int\limits_{-L/2}^{L/2}\ </math><br />
<br />
<math> \int\limits_{-L/2}^{L/2}\ = \frac{\mu_0I\Delta x}{4\pi(x^2+y^2)^(\frac{3}{2})} </math><br />
<br />
We find that our final answer is <math> B= \frac{\mu_0}{4\pi}\frac{LI}{y\sqrt(y^2+(L/2)^2)}\hat z </math><br />
<br />
==A Computational Model==<br />
The following link shows the magnetic field produced by small segments of wire in a loop individually.<br />
For a long straight wire, we see that there is a circular magnetic field surrounding the wire with current. The following link does a stepwise visual of the contributions of each part of the wire at an observation location a distance r from the wire.<br />
<br />
http://www.glowscript.org/#/user/matterandinteractions/folder/matterandinteractions/program/17-Bwire-with-r<br />
<br />
We see that along the axis of the wire, each contribution not on the axis is negated due to symmetry and the resulting magnetic field is all along the wire.<br />
<br />
http://www.glowscript.org/#/user/matterandinteractions/folder/matterandinteractions/program/17-B-loop-with-r-dB.<br />
<br />
== See also ==<br />
[Right Hand Rule[http://www.physicsbook.gatech.edu/Right-Hand_Rule]]<br />
<br />
[Direction of magnetic fields[http://www.physicsbook.gatech.edu/Direction_of_Magnetic_Field]]<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 />
==External Links==<br />
[[Category:Which Category did you place this in?]]</div>Vramanan3http://www.physicsbook.gatech.edu/index.php?title=Biot-Savart_Law_for_Currents&diff=32899Biot-Savart Law for Currents2018-12-07T06:43:10Z<p>Vramanan3: </p>
<hr />
<div>Vaishnavi Ramanan - Fall 2018<br />
<br />
==Biot-Savart Law==<br />
<br />
The Biot-Savart Law can be used for more than just single moving charges; a notable application of this law is its ability to calculate the magnetic field for an extremely large number of charges - an example of thousands of currents moving together is within a current carrying wire (current being the amount of charges moving over a specific amount of time). <br />
<br />
When using Biot-Savart Law to find the magnetic field of a short wire, we can extend this concept to a variety of different shapes - long current carrying wires, current carrying loops, etc. <br />
<br />
One main point to note is that the application of the Bio-Savart law is specifically for steady state current!<br />
<br />
<br />
====A Mathematical Model====<br />
First We start off with the original version of the Biot-Savart Law. <br />
<math>\vec B=\frac{\mu_0}{4 \pi } \frac{q\vec v\times\hat r}{r^2}</math>, where <math> \frac{\mu_0}{4 \pi } = 1 \times 10^{-7}\frac{Tm^2}{Cm/s}, </math><br />
<br />
Because we are dealing with a portion of wire <math>\mathrm{d}\boldsymbol{\ell}</math> long with an Area A containing n moving particles with charge q, we find that the total number of moving charges is equal to |q|(nAv) which is also equal to I, the current in the wire.<br />
<br />
<math>B = \frac{\mu_0I}{4\pi}\frac{\mathrm{d}\boldsymbol{\ell} \times \mathbf{\hat r}}{r^2},</math><br />
<br />
Because the shape of the current carrying wire can vary from a straight wire to a loop, we must integrate over the region of the wire.<br />
<br />
<math>\Delta B = \frac{\mu_0I}{4\pi}\int_{\mathrm{wire}}\frac{\mathrm{d}\boldsymbol{\ell} \times \mathbf{\hat r}}{r^2},</math><br />
<br />
The key point is that there are <math> nA\Delta l </math> electrons in a short length of wire, each moving with average speed <math>\vec v </math>, so that the sum of all the <math> q\vec v </math> contributions is <math> nA \Delta l|q|\vec v = I\Delta l. </math><br />
<br />
When applying the Biot-Savart Law to a Long Straight Wire, we follow a set of steps,<br />
<br />
Step 1: Cut Up the Distribution into Pieces and Draw <math> \Delta B </math>.<br />
<br />
Step 2: Write an Expression for the Magnetic Field Due to One Piece.<br />
<br />
Step 3: Add Up the Contributions of All the Pieces.<br />
<br />
Step 4: Check the Result.<br />
<br />
Where the Magnetic Field of a Straight Wire is shown by,<br />
<br />
<math> B = \frac{\mu_0}{4\pi}\frac{LI}{r(r^2 + (L/2)^2)^{1/2}} </math> for length <math> L </math>, conventional current <math> I </math>, a perpendicular distance <math> r </math> from the center of the wire, or,<br />
<math> B = \frac{\mu_0}{4\pi}\frac{2I}{r} </math> if <math> L\>>\>> r. </math><br />
<br />
When using the Biot-Savart Law for Currents, it is crucial to understand the direction of the magnetic field created by a current. For this, we use the right hand rule. If we curl our fingers and extend our thumb, similar to a thumbs up position, and point our thumb in the direction of the current, our fingers curl in the direction of the magnetic field.<br />
<br />
==Example==<br />
====For a long wire of length L positioned along the x axis with current flowing in the positive x direction====<br />
First, we start off with our adjusted Biot-Savart Formula for a slice of wire.<br />
<br />
<math>\Delta B = \frac{\mu_0I}{4\pi}\int_{\mathrm{wire}}\frac{\mathrm{d}\boldsymbol{\ell} \times \mathbf{\hat r}}{r^2},</math><br />
<br />
Second, we must find <math>r</math>, the vector pointing from the source to the observation location. In this case, we will choose an observation location y above the rod.<br />
<br />
<math> r = obs - source = <0,y,0> - < x,0,0> = <-x,y,0> </math>. which has a magnitude of <math>\sqrt(x^2+y^2)</math><br />
<br />
We see that <math>\hat r = \frac{r}{|r|} </math> .<br />
<br />
<math>\hat r = \frac{<-x,y,0>}{\sqrt(x^2+y^2))}</math><br />
<br />
We then have to express <math> \Delta \boldsymbol{\ell}</math> in terms of our variable of integration, x.<br />
<math> \Delta \boldsymbol{\ell}</math> = <math> \Delta x<1,0,0,></math><br />
<br />
Our new equation after substituting our new variables is <br />
<math> \Delta B = \frac{\mu_0I\Delta x<1,0,0,>}{4\pi(x^2+y^2)} \times \frac{<-x,y,0>}{\sqrt(x^2+y^2))} </math><br />
<br />
Finding the cross product of the above vectors gives us a product in the +z direction.<br />
<math> \Delta B = \frac{\mu_0I\Delta x}{4\pi(x^2+y^2)^(\frac{3}{2})} </math><br />
<br />
We are finally ready to integrate. Because we are integrating the entire rod our limits are<br />
<math> \int\limits_{-L/2}^{L/2}\ </math><br />
<br />
<math> \int\limits_{-L/2}^{L/2}\ = \frac{\mu_0I\Delta x}{4\pi(x^2+y^2)^(\frac{3}{2})} </math><br />
<br />
We find that our final answer is <math> B= \frac{\mu_0}{4\pi}\frac{LI}{y\sqrt(y^2+(L/2)^2)}\hat z </math><br />
<br />
==A Computational Model==<br />
The following link shows the magnetic field produced by small segments of wire in a loop individually.<br />
For a long straight wire, we see that there is a circular magnetic field surrounding the wire with current. The following link does a stepwise visual of the contributions of each part of the wire at an observation location a distance r from the wire.<br />
<br />
http://www.glowscript.org/#/user/matterandinteractions/folder/matterandinteractions/program/17-Bwire-with-r<br />
<br />
We see that along the axis of the wire, each contribution not on the axis is negated due to symmetry and the resulting magnetic field is all along the wire.<br />
<br />
http://www.glowscript.org/#/user/matterandinteractions/folder/matterandinteractions/program/17-B-loop-with-r-dB.<br />
<br />
== See also ==<br />
[Right Hand Rule[http://www.physicsbook.gatech.edu/Right-Hand_Rule]]<br />
<br />
[Direction of magnetic fields[http://www.physicsbook.gatech.edu/Direction_of_Magnetic_Field]]<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 />
==External Links==<br />
[[Category:Which Category did you place this in?]]</div>Vramanan3http://www.physicsbook.gatech.edu/index.php?title=Biot-Savart_Law_for_Currents&diff=32898Biot-Savart Law for Currents2018-12-07T06:22:57Z<p>Vramanan3: </p>
<hr />
<div>Vaishnavi Ramanan - Fall 2018<br />
<br />
==Biot-Savart Law==<br />
<br />
The Biot-Savart Law can be used for more than just single moving charges; it can also be used to calculate the magnetic field for a large number of charges. One notable reason to do so is to find the magnetic field of a portion of a wire where there can be many moving charges. When we use Biot-Savart Law to find the magnetic field of a short wire, we can apply it to a variety of shapes.<br />
<br />
<br />
====A Mathematical Model====<br />
First We start off with the original version of the Biot-Savart Law. <br />
<math>\vec B=\frac{\mu_0}{4 \pi } \frac{q\vec v\times\hat r}{r^2}</math>, where <math> \frac{\mu_0}{4 \pi } = 1 \times 10^{-7}\frac{Tm^2}{Cm/s}, </math><br />
<br />
Because we are dealing with a portion of wire <math>\mathrm{d}\boldsymbol{\ell}</math> long with an Area A containing n moving particles with charge q, we find that the total number of moving charges is equal to |q|(nAv) which is also equal to I, the current in the wire.<br />
<math>B = \frac{\mu_0I}{4\pi}\frac{\mathrm{d}\boldsymbol{\ell} \times \mathbf{\hat r}}{r^2},</math><br />
<br />
Because the shape of the current carrying wire can vary from a straight wire to a loop, we must integrate over the region of the wire.<br />
<br />
<math>\Delta B = \frac{\mu_0I}{4\pi}\int_{\mathrm{wire}}\frac{\mathrm{d}\boldsymbol{\ell} \times \mathbf{\hat r}}{r^2},</math><br />
<br />
The key point is that there are <math> nA\Delta l </math> electrons in a short length of wire, each moving with average speed <math>\vec v </math>, so that the sum of all the <math> q\vec v </math> contributions is <math> nA \Delta l|q|\vec v = I\Delta l. </math><br />
<br />
When applying the Biot-Savart Law to a Long Straight Wire, we follow a set of steps,<br />
<br />
Step 1: Cut Up the Distribution into Pieces and Draw <math> \Delta B </math>.<br />
<br />
Step 2: Write an Expression for the Magnetic Field Due to One Piece.<br />
<br />
Step 3: Add Up the Contributions of All the Pieces.<br />
<br />
Step 4: Check the Result.<br />
<br />
Where the Magnetic Field of a Straight Wire is shown by,<br />
<br />
<math> B = \frac{\mu_0}{4\pi}\frac{LI}{r(r^2 + (L/2)^2)^{1/2}} </math> for length <math> L </math>, conventional current <math> I </math>, a perpendicular distance <math> r </math> from the center of the wire, or,<br />
<math> B = \frac{\mu_0}{4\pi}\frac{2I}{r} </math> if <math> L\>>\>> r. </math><br />
<br />
When using the Biot-Savart Law for Currents, it is crucial to understand the direction of the magnetic field created by a current. For this, we use the right hand rule. If we curl our fingers and extend our thumb, similar to a thumbs up position, and point our thumb in the direction of the current, our fingers curl in the direction of the magnetic field.<br />
<br />
==Example==<br />
====For a long wire of length L positioned along the x axis with current flowing in the positive x direction====<br />
First, we start off with our adjusted Biot-Savart Formula for a slice of wire.<br />
<br />
<math>\Delta B = \frac{\mu_0I}{4\pi}\int_{\mathrm{wire}}\frac{\mathrm{d}\boldsymbol{\ell} \times \mathbf{\hat r}}{r^2},</math><br />
<br />
Second, we must find <math>r</math>, the vector pointing from the source to the observation location. In this case, we will choose an observation location y above the rod.<br />
<br />
<math> r = obs - source = <0,y,0> - < x,0,0> = <-x,y,0> </math>. which has a magnitude of <math>\sqrt(x^2+y^2)</math><br />
<br />
We see that <math>\hat r = \frac{r}{|r|} </math> .<br />
<br />
<math>\hat r = \frac{<-x,y,0>}{\sqrt(x^2+y^2))}</math><br />
<br />
We then have to express <math> \Delta \boldsymbol{\ell}</math> in terms of our variable of integration, x.<br />
<math> \Delta \boldsymbol{\ell}</math> = <math> \Delta x<1,0,0,></math><br />
<br />
Our new equation after substituting our new variables is <br />
<math> \Delta B = \frac{\mu_0I\Delta x<1,0,0,>}{4\pi(x^2+y^2)} \times \frac{<-x,y,0>}{\sqrt(x^2+y^2))} </math><br />
<br />
Finding the cross product of the above vectors gives us a product in the +z direction.<br />
<math> \Delta B = \frac{\mu_0I\Delta x}{4\pi(x^2+y^2)^(\frac{3}{2})} </math><br />
<br />
We are finally ready to integrate. Because we are integrating the entire rod our limits are<br />
<math> \int\limits_{-L/2}^{L/2}\ </math><br />
<br />
<math> \int\limits_{-L/2}^{L/2}\ = \frac{\mu_0I\Delta x}{4\pi(x^2+y^2)^(\frac{3}{2})} </math><br />
<br />
We find that our final answer is <math> B= \frac{\mu_0}{4\pi}\frac{LI}{y\sqrt(y^2+(L/2)^2)}\hat z </math><br />
<br />
==A Computational Model==<br />
The following link shows the magnetic field produced by small segments of wire in a loop individually.<br />
For a long straight wire, we see that there is a circular magnetic field surrounding the wire with current. The following link does a stepwise visual of the contributions of each part of the wire at an observation location a distance r from the wire.<br />
<br />
http://www.glowscript.org/#/user/matterandinteractions/folder/matterandinteractions/program/17-Bwire-with-r<br />
<br />
We see that along the axis of the wire, each contribution not on the axis is negated due to symmetry and the resulting magnetic field is all along the wire.<br />
<br />
http://www.glowscript.org/#/user/matterandinteractions/folder/matterandinteractions/program/17-B-loop-with-r-dB.<br />
<br />
== See also ==<br />
[Right Hand Rule[http://www.physicsbook.gatech.edu/Right-Hand_Rule]]<br />
<br />
[Direction of magnetic fields[http://www.physicsbook.gatech.edu/Direction_of_Magnetic_Field]]<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 />
==External Links==<br />
[[Category:Which Category did you place this in?]]</div>Vramanan3http://www.physicsbook.gatech.edu/index.php?title=Biot-Savart_Law_for_Currents&diff=32213Biot-Savart Law for Currents2018-10-10T02:31:47Z<p>Vramanan3: </p>
<hr />
<div>Claimed by David Medrano<br />
<br />
Vaishnavi Ramanan - Fall 2018<br />
<br />
==Biot-Savart Law==<br />
<br />
The Biot-Savart Law can be used for more than just single moving charges; it can also be used to calculate the magnetic field for a large number of charges. One notable reason to do so is to find the magnetic field of a portion of a wire where there can be many moving charges. When we use Biot-Savart Law to find the magnetic field of a short wire, we can apply it to a variety of shapes.<br />
<br />
<br />
====A Mathematical Model====<br />
First We start off with the original version of the Biot-Savart Law. <br />
<math>\vec B=\frac{\mu_0}{4 \pi } \frac{q\vec v\times\hat r}{r^2}</math>, where <math> \frac{\mu_0}{4 \pi } = 1 \times 10^{-7}\frac{Tm^2}{Cm/s}, </math><br />
<br />
Because we are dealing with a portion of wire <math>\mathrm{d}\boldsymbol{\ell}</math> long with an Area A containing n moving particles with charge q, we find that the total number of moving charges is equal to |q|(nAv) which is also equal to I, the current in the wire.<br />
<math>B = \frac{\mu_0I}{4\pi}\frac{\mathrm{d}\boldsymbol{\ell} \times \mathbf{\hat r}}{r^2},</math><br />
<br />
Because the shape of the current carrying wire can vary from a straight wire to a loop, we must integrate over the region of the wire.<br />
<br />
<math>\Delta B = \frac{\mu_0I}{4\pi}\int_{\mathrm{wire}}\frac{\mathrm{d}\boldsymbol{\ell} \times \mathbf{\hat r}}{r^2},</math><br />
<br />
The key point is that there are <math> nA\Delta l </math> electrons in a short length of wire, each moving with average speed <math>\vec v </math>, so that the sum of all the <math> q\vec v </math> contributions is <math> nA \Delta l|q|\vec v = I\Delta l. </math><br />
<br />
When applying the Biot-Savart Law to a Long Straight Wire, we follow a set of steps,<br />
<br />
Step 1: Cut Up the Distribution into Pieces and Draw <math> \Delta B </math>.<br />
<br />
Step 2: Write an Expression for the Magnetic Field Due to One Piece.<br />
<br />
Step 3: Add Up the Contributions of All the Pieces.<br />
<br />
Step 4: Check the Result.<br />
<br />
Where the Magnetic Field of a Straight Wire is shown by,<br />
<br />
<math> B = \frac{\mu_0}{4\pi}\frac{LI}{r(r^2 + (L/2)^2)^{1/2}} </math> for length <math> L </math>, conventional current <math> I </math>, a perpendicular distance <math> r </math> from the center of the wire, or,<br />
<math> B = \frac{\mu_0}{4\pi}\frac{2I}{r} </math> if <math> L\>>\>> r. </math><br />
<br />
When using the Biot-Savart Law for Currents, it is crucial to understand the direction of the magnetic field created by a current. For this, we use the right hand rule. If we curl our fingers and extend our thumb, similar to a thumbs up position, and point our thumb in the direction of the current, our fingers curl in the direction of the magnetic field.<br />
<br />
==Example==<br />
====For a long wire of length L positioned along the x axis with current flowing in the positive x direction====<br />
First, we start off with our adjusted Biot-Savart Formula for a slice of wire.<br />
<br />
<math>\Delta B = \frac{\mu_0I}{4\pi}\int_{\mathrm{wire}}\frac{\mathrm{d}\boldsymbol{\ell} \times \mathbf{\hat r}}{r^2},</math><br />
<br />
Second, we must find <math>r</math>, the vector pointing from the source to the observation location. In this case, we will choose an observation location y above the rod.<br />
<br />
<math> r = obs - source = <0,y,0> - < x,0,0> = <-x,y,0> </math>. which has a magnitude of <math>\sqrt(x^2+y^2)</math><br />
<br />
We see that <math>\hat r = \frac{r}{|r|} </math> .<br />
<br />
<math>\hat r = \frac{<-x,y,0>}{\sqrt(x^2+y^2))}</math><br />
<br />
We then have to express <math> \Delta \boldsymbol{\ell}</math> in terms of our variable of integration, x.<br />
<math> \Delta \boldsymbol{\ell}</math> = <math> \Delta x<1,0,0,></math><br />
<br />
Our new equation after substituting our new variables is <br />
<math> \Delta B = \frac{\mu_0I\Delta x<1,0,0,>}{4\pi(x^2+y^2)} \times \frac{<-x,y,0>}{\sqrt(x^2+y^2))} </math><br />
<br />
Finding the cross product of the above vectors gives us a product in the +z direction.<br />
<math> \Delta B = \frac{\mu_0I\Delta x}{4\pi(x^2+y^2)^(\frac{3}{2})} </math><br />
<br />
We are finally ready to integrate. Because we are integrating the entire rod our limits are<br />
<math> \int\limits_{-L/2}^{L/2}\ </math><br />
<br />
<math> \int\limits_{-L/2}^{L/2}\ = \frac{\mu_0I\Delta x}{4\pi(x^2+y^2)^(\frac{3}{2})} </math><br />
<br />
We find that our final answer is <math> B= \frac{\mu_0}{4\pi}\frac{LI}{y\sqrt(y^2+(L/2)^2)}\hat z </math><br />
<br />
==A Computational Model==<br />
The following link shows the magnetic field produced by small segments of wire in a loop individually.<br />
For a long straight wire, we see that there is a circular magnetic field surrounding the wire with current. The following link does a stepwise visual of the contributions of each part of the wire at an observation location a distance r from the wire.<br />
<br />
http://www.glowscript.org/#/user/matterandinteractions/folder/matterandinteractions/program/17-Bwire-with-r<br />
<br />
We see that along the axis of the wire, each contribution not on the axis is negated due to symmetry and the resulting magnetic field is all along the wire.<br />
<br />
http://www.glowscript.org/#/user/matterandinteractions/folder/matterandinteractions/program/17-B-loop-with-r-dB.<br />
<br />
== See also ==<br />
[Right Hand Rule[http://www.physicsbook.gatech.edu/Right-Hand_Rule]]<br />
<br />
[Direction of magnetic fields[http://www.physicsbook.gatech.edu/Direction_of_Magnetic_Field]]<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 />
==External Links==<br />
[[Category:Which Category did you place this in?]]</div>Vramanan3http://www.physicsbook.gatech.edu/index.php?title=Main_Page&diff=32212Main Page2018-10-10T02:28:44Z<p>Vramanan3: /* 3D Vectors */</p>
<hr />
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*[[Types of Interactions and How to Detect Them]]<br />
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====Velocity and Momentum====<br />
<div class="mw-collapsible-content"><br />
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*[[Derivation of Average Velocity]]<br />
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</div><br />
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====Momentum and the Momentum Principle====<br />
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</div><br />
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====Fundamental Interactions====<br />
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==Main Idea==<br />
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*[[Gravitational Force]]<br />
*[[Fluid Mechanics]]<br />
*[[An Application of Gravitational Potential]]<br />
*[[Electric Force]]<br />
*[[Reciprocity]]<br />
</div><br />
</div><br />
<br />
===Week 5===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Conservation of Momentum====<br />
<div class="mw-collapsible-content"><br />
*[[Conservation of Momentum]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Properties of Matter====<br />
<div class="mw-collapsible-content"><br />
*[[Kinds of Matter]]<br />
*[[Ball and Spring Model of Matter]]<br />
*[[Density]]<br />
*[[Length and Stiffness of an Interatomic Bond]]<br />
*[[Young's Modulus]]<br />
*[[Speed of Sound in Solids]]<br />
*[[Malleability]]<br />
*[[Ductility]]<br />
*[[Weight]]<br />
*[[Hardness]]<br />
*[[Boiling Point]]<br />
*[[Melting Point]]<br />
*[[Change of State]]<br />
</div><br />
</div><br />
<br />
===Week 6===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Identifying Forces====<br />
<div class="mw-collapsible-content"><br />
*[[Free Body Diagram]]<br />
*[[Inclined Plane]]<br />
*[[Compression or Normal Force]]<br />
*[[Tension]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Curving Motion====<br />
<div class="mw-collapsible-content"><br />
*[[Curving Motion]]<br />
*[[Centripetal Force and Curving Motion]]<br />
*[[Perpetual Freefall (Orbit)]]<br />
</div><br />
</div><br />
<br />
===Week 7===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Energy Principle====<br />
<div class="mw-collapsible-content"><br />
*[[The Energy Principle]]<br />
*[[Conservation of Energy]]<br />
*[[Kinetic Energy]]<br />
*[[Work]]<br />
*[[Power (Mechanical)]]<br />
</div><br />
</div><br />
<br />
===Week 8===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Work by Non-Constant Forces====<br />
<div class="mw-collapsible-content"><br />
*[[Work Done By A Nonconstant Force]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Potential Energy====<br />
<div class="mw-collapsible-content"><br />
*[[Potential Energy]]<br />
*[[Potential Energy of Macroscopic Springs]]<br />
*[[Spring Potential Energy]]<br />
*[[Ball and Spring Model]]<br />
*[[Gravitational Potential Energy]]<br />
*[[Energy Graphs]]<br />
*[[Escape Velocity]]<br />
</div><br />
</div><br />
<br />
===Week 9===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Multiparticle Systems====<br />
<div class="mw-collapsible-content"><br />
*[[Center of Mass]]<br />
*[[Multi-particle analysis of Momentum]]<br />
*[[Momentum with respect to external Forces]]<br />
*[[Potential Energy of a Multiparticle System]]<br />
*[[Work and Energy for an Extended System]]<br />
*[[Internal Energy]]<br />
**[[Potential Energy of a Pair of Neutral Atoms]]<br />
</div><br />
</div><br />
<br />
===Week 10===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Choice of System====<br />
<div class="mw-collapsible-content"><br />
*[[System & Surroundings]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Thermal Energy, Dissipation, and Transfer of Energy====<br />
<div class="mw-collapsible-content"><br />
*[[Thermal Energy]]<br />
*[[Specific Heat]]<br />
*[[Heat Capacity]]<br />
*[[Calorific Value(Heat of combustion)]]<br />
*[[Specific Heat Capacity]]<br />
*[[First Law of Thermodynamics]]<br />
*[[Second Law of Thermodynamics and Entropy]]<br />
*[[Temperature]]<br />
*[[Predicting Change]]<br />
*[[Energy Transfer due to a Temperature Difference]]<br />
*[[Transformation of Energy]]<br />
*[[The Maxwell-Boltzmann Distribution]]<br />
*[[Air Resistance]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Rotational and Vibrational Energy====<br />
<div class="mw-collapsible-content"><br />
*[[Translational, Rotational and Vibrational Energy]]<br />
</div><br />
</div><br />
<br />
===Week 11===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Different Models of a System====<br />
<div class="mw-collapsible-content"><br />
*[[Point Particle Systems]]<br />
*[[Real Systems]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Models of Friction====<br />
<div class="mw-collapsible-content"><br />
*[[Friction]]<br />
*[[Static Friction]]<br />
</div><br />
</div><br />
<br />
===Week 12===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Collisions====<br />
<div class="mw-collapsible-content"><br />
*[[Newton's Third Law of Motion]]<br />
*[[Collisions]]<br />
*[[Elastic Collisions]]<br />
*[[Inelastic Collisions]]<br />
*[[Maximally Inelastic Collision]]<br />
*[[Head-on Collision of Equal Masses]]<br />
*[[Head-on Collision of Unequal Masses]]<br />
*[[Scattering: Collisions in 2D and 3D]]<br />
*[[Rutherford Experiment and Atomic Collisions]]<br />
*[[Coefficient of Restitution]]<br />
</div><br />
</div><br />
<br />
===Week 13===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Rotations====<br />
<div class="mw-collapsible-content"><br />
*[[Rotation]]<br />
*[[Angular Velocity]]<br />
*[[Eulerian Angles]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Angular Momentum====<br />
<div class="mw-collapsible-content"><br />
*[[Total Angular Momentum]]<br />
*[[Translational Angular Momentum]]<br />
*[[Rotational Angular Momentum]]<br />
*[[The Angular Momentum Principle]]<br />
*[[Angular Momentum Compared to Linear Momentum]]<br />
*[[Angular Impulse]]<br />
*[[Predicting the Position of a Rotating System]]<br />
*[[Angular Momentum of Multiparticle Systems]]<br />
*[[The Moments of Inertia]]<br />
*[[Moment of Inertia for a cylinder]]<br />
*[[Right Hand Rule]]<br />
</div><br />
</div><br />
<br />
===Week 14===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Analyzing Motion with and without Torque====<br />
<div class="mw-collapsible-content"><br />
*[[Torque]]<br />
*[[Torque 2]]<br />
*[[Systems with Zero Torque]]<br />
*[[Systems with Nonzero Torque]]<br />
*[[Torque vs Work]]<br />
*[[Gyroscopes]]<br />
</div><br />
</div><br />
<br />
===Week 15===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Introduction to Quantum Concepts====<br />
<div class="mw-collapsible-content"><br />
*[[Bohr Model]]<br />
*[[Energy graphs and the Bohr model]]<br />
*[[Quantized energy levels]]<br />
*[[Quantized energy levels part II]]<br />
*[[Entropy]]<br />
</div><br />
</div><br />
</div><br />
<br />
<div style="float:left; width:30%; padding:1%;"><br />
<br />
==Physics 2==<br />
===Week 1===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====3D Vectors====<br />
<br />
<div class="mw-collapsible-content"><br />
*[[Vectors]]<br />
*[[Right-Hand Rule]]<br />
*[[Right Hand Rule]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Electric field====<br />
<div class="mw-collapsible-content"><br />
*[[Electric Field]]<br />
*[[Electric Field and Electric Potential]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Electric force====<br />
<div class="mw-collapsible-content"><br />
*[[Electric Force]]<br />
*[[Lorentz Force]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Electric field of a point particle====<br />
<div class="mw-collapsible-content"><br />
*[[Point Charge]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Superposition====<br />
<div class="mw-collapsible-content"><br />
*[[Superposition Principle]]<br />
*[[Superposition principle]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Dipoles====<br />
<div class="mw-collapsible-content"><br />
*[[Electric Dipole]]<br />
*[[Magnetic Dipole]]<br />
</div><br />
</div><br />
<br />
===Week 2===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Interactions of charged objects====<br />
<div class="mw-collapsible-content"><br />
*[[Electric Field]]<br />
*[[Electric Potential]]<br />
*[[Electric Force]]<br />
*[[Lorentz Force]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Tape experiments====<br />
<div class="mw-collapsible-content"><br />
*[[Polarization]]<br />
*[[Electric Polarization]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Polarization====<br />
<div class="mw-collapsible-content"><br />
*[[Polarization]]<br />
*[[Electric Polarization]]<br />
*[[Polarization of an Atom]]<br />
</div><br />
</div><br />
<br />
===Week 3===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Insulators====<br />
<div class="mw-collapsible-content"><br />
*[[Insulators]]<br />
*[[Potential Difference in an Insulator]]<br />
*[[Charged Conductor and Charged Insulator]]<br />
*[[Charged conductor and charged insulator]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Conductors====<br />
<div class="mw-collapsible-content"><br />
*[[Conductivity]]<br />
*[[Charge Transfer]]<br />
*[[Resistivity]]<br />
*[[Polarization of a conductor]]<br />
*[[Charged Conductor and Charged Insulator]]<br />
*[[Charged conductor and charged insulator]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Charging and Discharging====<br />
<div class="mw-collapsible-content"><br />
*[[Charge Transfer]]<br />
*[[Electrostatic Discharge]]<br />
*[[Charged Conductor and Charged Insulator]]<br />
*[[Charged conductor and charged insulator]]<br />
</div><br />
</div><br />
<br />
===Week 4===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Field of a charged rod====<br />
<div class="mw-collapsible-content"><br />
*[[Charged Rod]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Field of a charged ring/disk/capacitor====<br />
<div class="mw-collapsible-content"><br />
*[[Charged Ring]]<br />
*[[Charged Disk]]<br />
*[[Charged Capacitor]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Field of a charged sphere====<br />
<div class="mw-collapsible-content"><br />
*[[Charged Spherical Shell]]<br />
*[[Field of a Charged Ball]]<br />
</div><br />
</div><br />
<br />
===Week 5===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Potential energy====<br />
<div class="mw-collapsible-content"><br />
*[[Potential Energy]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Electric potential====<br />
<div class="mw-collapsible-content"><br />
*[[Electric Potential]]<br />
*[[Path Independence of Electric Potential]]<br />
*[[Potential Difference Path Independence, claimed by Aditya Mohile]] <br />
*[[Potential Difference in a Uniform Field]]<br />
*[[Potential Difference of Point Charge in a Non-Uniform Field]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Sign of a potential difference====<br />
<div class="mw-collapsible-content"><br />
*[[Sign of a Potential Difference]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Potential at a single location====<br />
<div class="mw-collapsible-content"><br />
*[[Electric Potential]]<br />
*[[Potential Difference at One Location]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Path independence and round trip potential====<br />
<div class="mw-collapsible-content"><br />
*[[Path Independence of Electric Potential]]<br />
*[[Potential Difference Path Independence, claimed by Aditya Mohile]]<br />
</div><br />
</div><br />
<br />
===Week 6===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Electric field and potential in an insulator====<br />
<div class="mw-collapsible-content"><br />
*[[Potential Difference in an Insulator]]<br />
*[[Electric Field in an Insulator]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Moving charges in a magnetic field====<br />
<div class="mw-collapsible-content"><br />
*[[Magnetic Field]]<br />
*[[Magnetic Force]]<br />
*[[Lorentz Force]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Biot-Savart Law====<br />
<div class="mw-collapsible-content"><br />
*[[Biot-Savart Law]]<br />
*[[Biot-Savart Law for Currents]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Moving charges, electron current, and conventional current====<br />
<div class="mw-collapsible-content"><br />
*[[Moving Point Charge]]<br />
*[[Current]]<br />
</div><br />
</div><br />
<br />
===Week 7===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Magnetic field of a wire====<br />
<div class="mw-collapsible-content"><br />
*[[Magnetic Field of a Long Straight Wire]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Magnetic field of a current-carrying loop====<br />
<div class="mw-collapsible-content"><br />
*[[Magnetic Field of a Loop]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Magnetic field of a Charged Disk====<br />
<div class="mw-collapsible-content"><br />
*[[Magnetic Field of a Disk]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Magnetic dipoles====<br />
<div class="mw-collapsible-content"><br />
*[[Magnetic Dipole Moment]]<br />
*[[Bar Magnet]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Atomic structure of magnets====<br />
<div class="mw-collapsible-content"><br />
*[[Atomic Structure of Magnets]]<br />
</div><br />
</div><br />
<br />
===Week 8===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Steady state current====<br />
<div class="mw-collapsible-content"><br />
*[[Steady State]]<br />
*[[Non Steady State]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Kirchoff's Laws====<br />
<div class="mw-collapsible-content"><br />
*[[Kirchoff's Laws]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Electric fields and energy in circuits====<br />
<div class="mw-collapsible-content"><br />
*[[Series circuit]]<br />
*[[Node Rule]]<br />
*[[Loop Rule]]<br />
*[[Electric Potential Difference]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Macroscopic analysis of circuits====<br />
<div class="mw-collapsible-content"><br />
*[[Series Circuits]]<br />
*[[Parallel Circuits]]<br />
*[[Parallel Circuits vs. Series Circuits*]]<br />
*[[Loop Rule]]<br />
*[[Node Rule]]<br />
*[[Fundamentals of Resistance]]<br />
*[[Problem Solving]]<br />
</div><br />
</div><br />
<br />
===Week 9===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Electric field and potential in circuits with capacitors====<br />
<div class="mw-collapsible-content"><br />
*[[Charging and Discharging a Capacitor]]<br />
*[[RC Circuit]] <br />
*[[R Circuit]]<br />
*[[AC and DC]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Magnetic forces on charges and currents====<br />
<div class="mw-collapsible-content"><br />
*[[Magnetic Force]]<br />
*[[Lorentz Force]]<br />
*[[Motors and Generators]]<br />
*[[Applying Magnetic Force to Currents]]<br />
*[[Magnetic Force in a Moving Reference Frame]]<br />
*[[Right-Hand Rule]]<br />
*[[Analysis of Railgun vs Coil gun technologies]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Electric and magnetic forces====<br />
<div class="mw-collapsible-content"><br />
*[[Electric Force]]<br />
*[[Magnetic Force]]<br />
*[[Lorentz Force]]<br />
*[[VPython Modelling of Electric and Magnetic Forces]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Velocity selector====<br />
<div class="mw-collapsible-content"><br />
*[[Lorentz Force]]<br />
*[[Combining Electric and Magnetic Forces]]<br />
</div><br />
</div><br />
<br />
===Week 10===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Hall Effect====<br />
<div class="mw-collapsible-content"><br />
*[[Hall Effect]]<br />
*[[Right-Hand Rule]]<br />
*[[Motional Emf]]<br />
*[[Magnetic Force]]<br />
*[[Magnetic Torque]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Motional EMF====<br />
<div class="mw-collapsible-content"><br />
*[[Motional Emf]]<br />
*[[Motional Emf using Faraday's Law]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Magnetic force====<br />
<div class="mw-collapsible-content"><br />
*[[Magnetic Force]]<br />
*[[Lorentz Force]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Magnetic torque====<br />
<div class="mw-collapsible-content"><br />
*[[Magnetic Torque]]<br />
*[[Right-Hand Rule]]<br />
</div><br />
</div><br />
<br />
===Week 12===<br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Gauss's Law====<br />
<div class="mw-collapsible-content"><br />
*[[Gauss's Flux Theorem]]<br />
*[[Gauss's Law]]<br />
*[[Magnetic Flux]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Ampere's Law====<br />
<div class="mw-collapsible-content"><br />
*[[Ampere's Law]]<br />
*[[Ampere-Maxwell Law]]<br />
*[[Magnetic Field of Coaxial Cable Using Ampere's Law]]<br />
*[[Magnetic Field of a Long Thick Wire Using Ampere's Law]]<br />
*[[Magnetic Field of a Toroid Using Ampere's Law]]<br />
*[[Magnetic Field of a Solenoid Using Ampere's Law]]<br />
*[[The Differential Form of Ampere's Law]]<br />
</div><br />
</div><br />
<br />
===Week 13===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Semiconductors====<br />
<div class="mw-collapsible-content"><br />
*[[Semiconductor Devices]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Faraday's Law====<br />
<div class="mw-collapsible-content"><br />
*[[Faraday's Law]]<br />
*[[Motional Emf using Faraday's Law]]<br />
*[[Lenz's Law]]<br />
<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Maxwell's equations====<br />
<div class="mw-collapsible-content"><br />
*[[Gauss's Law]]<br />
*[[Magnetic Flux]]<br />
*[[Ampere's Law]]<br />
*[[Faraday's Law]]<br />
*[[Maxwell's Electromagnetic Theory]]<br />
</div><br />
</div><br />
<br />
===Week 14===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Circuits revisited====<br />
<div class="mw-collapsible-content"><br />
<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Inductors====<br />
<div class="mw-collapsible-content"><br />
*[[Inductors]]<br />
*[[Current in an LC Circuit]]<br />
*[[Current in an RL Circuit]]<br />
</div><br />
</div><br />
<br />
===Week 15===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
==== Electromagnetic Radiation ====<br />
<div class="mw-collapsible-content"><br />
*[[Electromagnetic Radiation]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Sparks in the air====<br />
<div class="mw-collapsible-content"><br />
*[[Sparks in Air]]<br />
*[[Spark Plugs]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Superconductors====<br />
<div class="mw-collapsible-content"><br />
*[[Superconducters]]<br />
*[[Superconductors]]<br />
*[[Meissner effect]]<br />
</div><br />
</div><br />
</div><br />
<br />
<div style="float:left; width:30%; padding:1%;"><br />
<br />
==Physics 3==<br />
<br />
===Week 1===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Classical Physics====<br />
<div class="mw-collapsible-content"><br />
</div><br />
</div><br />
<br />
===Week 2===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Special Relativity====<br />
<div class="mw-collapsible-content"><br />
*[[Frame of Reference]]<br />
*[[Einstein's Theory of Special Relativity]]<br />
*[[Time Dilation]]<br />
*[[Einstein's Theory of General Relativity]]<br />
*[[Albert A. Micheleson & Edward W. Morley]]<br />
*[[Magnetic Force in a Moving Reference Frame]]<br />
</div><br />
</div><br />
<br />
===Week 3===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Photons====<br />
<div class="mw-collapsible-content"><br />
*[[Spontaneous Photon Emission]]<br />
*[[Light Scattering: Why is the Sky Blue]]<br />
*[[Lasers]]<br />
*[[Electronic Energy Levels and Photons]]<br />
*[[Quantum Properties of Light]]<br />
</div><br />
</div><br />
<br />
===Week 4===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Matter Waves====<br />
<div class="mw-collapsible-content"><br />
*[[Wave-Particle Duality]]<br />
</div><br />
</div><br />
<br />
===Week 5===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Wave Mechanics====<br />
<div class="mw-collapsible-content"><br />
*[[Standing Waves]]<br />
*[[Wavelength]]<br />
*[[Wavelength and Frequency]]<br />
*[[Mechanical Waves]]<br />
*[[Transverse and Longitudinal Waves]]<br />
</div><br />
</div><br />
<br />
===Week 6===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Rutherford-Bohr Model====<br />
<div class="mw-collapsible-content"><br />
*[[Rutherford Experiment and Atomic Collisions]]<br />
*[[Bohr Model]]<br />
*[[Quantized energy levels]]<br />
*[[Energy graphs and the Bohr model]]<br />
</div><br />
</div><br />
<br />
===Week 7===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====The Hydrogen Atom====<br />
<div class="mw-collapsible-content"><br />
*[[Quantum Theory]]<br />
*[[Atomic Theory]]<br />
</div><br />
</div><br />
<br />
===Week 8===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Many-Electron Atoms====<br />
<div class="mw-collapsible-content"><br />
*[[Quantum Theory]]<br />
*[[Atomic Theory]]<br />
*[[Pauli exclusion principle]]<br />
</div><br />
</div><br />
<br />
===Week 9===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Molecules====<br />
<div class="mw-collapsible-content"><br />
</div><br />
</div><br />
<br />
===Week 10===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Statistical Physics====<br />
<div class="mw-collapsible-content"><br />
</div><br />
</div><br />
<br />
===Week 11===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Condensed Matter Physics====<br />
<div class="mw-collapsible-content"><br />
</div><br />
</div><br />
<br />
===Week 12===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====The Nucleus====<br />
<div class="mw-collapsible-content"><br />
*[[Nucleus]]<br />
</div><br />
</div><br />
<br />
===Week 13===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Nuclear Physics====<br />
<div class="mw-collapsible-content"><br />
*[[Nuclear Fission]]<br />
*[[Nuclear Energy from Fission and Fusion]]<br />
</div><br />
</div><br />
<br />
===Week 14===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Particle Physics====<br />
<div class="mw-collapsible-content"><br />
*[[Elementary Particles and Particle Physics Theory]]<br />
*[[String Theory]]<br />
</div><br />
</div><br />
</div></div>Vramanan3http://www.physicsbook.gatech.edu/index.php?title=Main_Page&diff=32211Main Page2018-10-10T02:28:14Z<p>Vramanan3: /* 3D Vectors */</p>
<hr />
<div>__NOTOC__<br />
= '''Georgia Tech Student Wiki for Introductory Physics.''' =<br />
<br />
This resource was created so that students can contribute and curate content to help those with limited or no access to a textbook. When reading this website, please correct any errors you may come across. If you read something that isn't clear, please consider revising it for future students!<br />
<br />
Looking to make a contribution?<br />
#Pick one of the topics from intro physics listed below<br />
#Add content to that topic or improve the quality of what is already there.<br />
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Please remember that this is not a textbook and you are not limited to expressing your ideas with only text and equations. Whenever possible embed: pictures, videos, diagrams, simulations, computational models (e.g. Glowscript), and whatever content you think makes learning physics easier for other students.<br />
<br />
== Source Material ==<br />
All of the content added to this resource must be in the public domain or similar free resource. If you are unsure about a source, contact the original author for permission. That said, there is a surprisingly large amount of introductory physics content scattered across the web. Here is an incomplete list of intro physics resources (please update as needed).<br />
* A physics resource written by experts for an expert audience [https://en.wikipedia.org/wiki/Portal:Physics Physics Portal]<br />
* A wiki written for students by a physics expert [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes MSU Physics Wiki]<br />
* A wiki book on modern physics [https://en.wikibooks.org/wiki/Modern_Physics Modern Physics Wiki]<br />
* The MIT open courseware for intro physics [http://ocw.mit.edu/resources/res-8-002-a-wikitextbook-for-introductory-mechanics-fall-2009/index.htm MITOCW Wiki]<br />
* An online concept map of intro physics [http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics]<br />
* Interactive physics simulations [https://phet.colorado.edu/en/simulations/category/physics PhET]<br />
* OpenStax intro physics textbooks: [https://openstax.org/details/books/university-physics-volume-1 Vol1], [https://openstax.org/details/books/university-physics-volume-2 Vol2], [https://openstax.org/details/books/university-physics-volume-3 Vol3]<br />
* The Open Source Physics project is a collection of online physics resources [http://www.opensourcephysics.org/ OSP]<br />
* A resource guide compiled by the [http://www.aapt.org/ AAPT] for educators [http://www.compadre.org/ ComPADRE]<br />
* The Feynman lectures on physics are free to read [http://www.feynmanlectures.caltech.edu/ Feynman]<br />
* Final Study Guide for Modern Physics II created by a lab TA [https://docs.google.com/document/d/1_6GktDPq5tiNFFYs_ZjgjxBAWVQYaXp_2Imha4_nSyc/edit?usp=sharing Modern Physics II Final Study Guide]<br />
<br />
== Resources ==<br />
* Commonly used wiki commands [https://en.wikipedia.org/wiki/Help:Cheatsheet Wiki Cheatsheet]<br />
* A guide to representing equations in math mode [https://en.wikipedia.org/wiki/Help:Displaying_a_formula Wiki Math Mode]<br />
* A page to keep track of all the physics [[Constants]]<br />
* A page for review of [[Vectors]] and vector operations<br />
* A listing of [[Notable Scientist]] with links to their individual pages <br />
<br />
<br />
<div style="float:left; width:30%; padding:1%;"><br />
==Physics 1==<br />
===Week 1===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Help with VPython====<br />
<div class="mw-collapsible-content"><br />
*[[Python Syntax]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Vectors and Units====<br />
<br />
<br />
<br />
<br />
<div class="mw-collapsible-content"><br />
*[[Vectors]]<br />
*[[SI Units]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====VPython====<br />
<br />
<div class="mw-collapsible-content"><br />
*[[VPython]]<br />
*[[VPython basics]]<br />
*[[VPython Common Errors and Troubleshooting]]<br />
*[[VPython Functions]]<br />
*[[VPython Lists]]<br />
*[[VPython Loops]]<br />
*[[VPython Multithreading]]<br />
*[[VPython Animation]]<br />
*[[VPython Objects]]<br />
*[[VPython 3D Objects]]<br />
*[[VPython Reference]]<br />
*[[VPython MapReduceFilter]]<br />
*[[VPython GUIs]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Vectors and Units====<br />
<div class="mw-collapsible-content"><br />
*[[Vectors]]<br />
*[[SI Units]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Interactions====<br />
<div class="mw-collapsible-content"><br />
*[[Types of Interactions and How to Detect Them]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Velocity and Momentum====<br />
<div class="mw-collapsible-content"><br />
*[[Newton's First Law of Motion]]<br />
*[[Velocity]]<br />
*[[Mass]]<br />
*[[Speed and Velocity]]<br />
*[[Relative Velocity]]<br />
*[[Derivation of Average Velocity]]<br />
*[[2-Dimensional Motion]]<br />
*[[3-Dimensional Position and Motion]]<br />
</div><br />
</div><br />
<br />
===Week 2===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Momentum and the Momentum Principle====<br />
<div class="mw-collapsible-content"><br />
*[[Momentum Principle]]<br />
*[[Inertia]]<br />
*[[Net Force]]<br />
*[[Derivation of the Momentum Principle]]<br />
*[[Impulse Momentum]]<br />
*[[Acceleration]]<br />
*[[Momentum with respect to external Forces]]<br />
*[[Relativistic Momentum]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Iterative Prediction with a Constant Force====<br />
<div class="mw-collapsible-content"><br />
*[[Newton’s Second Law of Motion]]<br />
*[[Iterative Prediction]]<br />
*[[Kinematics]]<br />
*[[Newton’s Laws and Linear Momentum]]<br />
*[[Projectile Motion]]<br />
</div><br />
</div><br />
<br />
===Week 3===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Analytic Prediction with a Constant Force====<br />
<div class="mw-collapsible-content"><br />
*[[Analytical Prediction]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Iterative Prediction with a Varying Force====<br />
<div class="mw-collapsible-content"><br />
*[[Predicting Change in multiple dimensions]]<br />
*[[Spring Force]]<br />
*[[Hooke's Law]]<br />
*[[Simple Harmonic Motion]]<br />
*[[Iterative Prediction of Spring-Mass System]]<br />
*[[Terminal Speed]]<br />
*[[Determinism]]<br />
</div><br />
</div><br />
<br />
===Week 4===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Fundamental Interactions====<br />
<div class="mw-collapsible-content"><br />
<br />
==Main Idea==<br />
<br />
*[[Gravitational Force]]<br />
*[[Fluid Mechanics]]<br />
*[[An Application of Gravitational Potential]]<br />
*[[Electric Force]]<br />
*[[Reciprocity]]<br />
</div><br />
</div><br />
<br />
===Week 5===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Conservation of Momentum====<br />
<div class="mw-collapsible-content"><br />
*[[Conservation of Momentum]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Properties of Matter====<br />
<div class="mw-collapsible-content"><br />
*[[Kinds of Matter]]<br />
*[[Ball and Spring Model of Matter]]<br />
*[[Density]]<br />
*[[Length and Stiffness of an Interatomic Bond]]<br />
*[[Young's Modulus]]<br />
*[[Speed of Sound in Solids]]<br />
*[[Malleability]]<br />
*[[Ductility]]<br />
*[[Weight]]<br />
*[[Hardness]]<br />
*[[Boiling Point]]<br />
*[[Melting Point]]<br />
*[[Change of State]]<br />
</div><br />
</div><br />
<br />
===Week 6===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Identifying Forces====<br />
<div class="mw-collapsible-content"><br />
*[[Free Body Diagram]]<br />
*[[Inclined Plane]]<br />
*[[Compression or Normal Force]]<br />
*[[Tension]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Curving Motion====<br />
<div class="mw-collapsible-content"><br />
*[[Curving Motion]]<br />
*[[Centripetal Force and Curving Motion]]<br />
*[[Perpetual Freefall (Orbit)]]<br />
</div><br />
</div><br />
<br />
===Week 7===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Energy Principle====<br />
<div class="mw-collapsible-content"><br />
*[[The Energy Principle]]<br />
*[[Conservation of Energy]]<br />
*[[Kinetic Energy]]<br />
*[[Work]]<br />
*[[Power (Mechanical)]]<br />
</div><br />
</div><br />
<br />
===Week 8===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Work by Non-Constant Forces====<br />
<div class="mw-collapsible-content"><br />
*[[Work Done By A Nonconstant Force]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Potential Energy====<br />
<div class="mw-collapsible-content"><br />
*[[Potential Energy]]<br />
*[[Potential Energy of Macroscopic Springs]]<br />
*[[Spring Potential Energy]]<br />
*[[Ball and Spring Model]]<br />
*[[Gravitational Potential Energy]]<br />
*[[Energy Graphs]]<br />
*[[Escape Velocity]]<br />
</div><br />
</div><br />
<br />
===Week 9===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Multiparticle Systems====<br />
<div class="mw-collapsible-content"><br />
*[[Center of Mass]]<br />
*[[Multi-particle analysis of Momentum]]<br />
*[[Momentum with respect to external Forces]]<br />
*[[Potential Energy of a Multiparticle System]]<br />
*[[Work and Energy for an Extended System]]<br />
*[[Internal Energy]]<br />
**[[Potential Energy of a Pair of Neutral Atoms]]<br />
</div><br />
</div><br />
<br />
===Week 10===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Choice of System====<br />
<div class="mw-collapsible-content"><br />
*[[System & Surroundings]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Thermal Energy, Dissipation, and Transfer of Energy====<br />
<div class="mw-collapsible-content"><br />
*[[Thermal Energy]]<br />
*[[Specific Heat]]<br />
*[[Heat Capacity]]<br />
*[[Calorific Value(Heat of combustion)]]<br />
*[[Specific Heat Capacity]]<br />
*[[First Law of Thermodynamics]]<br />
*[[Second Law of Thermodynamics and Entropy]]<br />
*[[Temperature]]<br />
*[[Predicting Change]]<br />
*[[Energy Transfer due to a Temperature Difference]]<br />
*[[Transformation of Energy]]<br />
*[[The Maxwell-Boltzmann Distribution]]<br />
*[[Air Resistance]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Rotational and Vibrational Energy====<br />
<div class="mw-collapsible-content"><br />
*[[Translational, Rotational and Vibrational Energy]]<br />
</div><br />
</div><br />
<br />
===Week 11===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Different Models of a System====<br />
<div class="mw-collapsible-content"><br />
*[[Point Particle Systems]]<br />
*[[Real Systems]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Models of Friction====<br />
<div class="mw-collapsible-content"><br />
*[[Friction]]<br />
*[[Static Friction]]<br />
</div><br />
</div><br />
<br />
===Week 12===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Collisions====<br />
<div class="mw-collapsible-content"><br />
*[[Newton's Third Law of Motion]]<br />
*[[Collisions]]<br />
*[[Elastic Collisions]]<br />
*[[Inelastic Collisions]]<br />
*[[Maximally Inelastic Collision]]<br />
*[[Head-on Collision of Equal Masses]]<br />
*[[Head-on Collision of Unequal Masses]]<br />
*[[Scattering: Collisions in 2D and 3D]]<br />
*[[Rutherford Experiment and Atomic Collisions]]<br />
*[[Coefficient of Restitution]]<br />
</div><br />
</div><br />
<br />
===Week 13===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Rotations====<br />
<div class="mw-collapsible-content"><br />
*[[Rotation]]<br />
*[[Angular Velocity]]<br />
*[[Eulerian Angles]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Angular Momentum====<br />
<div class="mw-collapsible-content"><br />
*[[Total Angular Momentum]]<br />
*[[Translational Angular Momentum]]<br />
*[[Rotational Angular Momentum]]<br />
*[[The Angular Momentum Principle]]<br />
*[[Angular Momentum Compared to Linear Momentum]]<br />
*[[Angular Impulse]]<br />
*[[Predicting the Position of a Rotating System]]<br />
*[[Angular Momentum of Multiparticle Systems]]<br />
*[[The Moments of Inertia]]<br />
*[[Moment of Inertia for a cylinder]]<br />
*[[Right Hand Rule]]<br />
</div><br />
</div><br />
<br />
===Week 14===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Analyzing Motion with and without Torque====<br />
<div class="mw-collapsible-content"><br />
*[[Torque]]<br />
*[[Torque 2]]<br />
*[[Systems with Zero Torque]]<br />
*[[Systems with Nonzero Torque]]<br />
*[[Torque vs Work]]<br />
*[[Gyroscopes]]<br />
</div><br />
</div><br />
<br />
===Week 15===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Introduction to Quantum Concepts====<br />
<div class="mw-collapsible-content"><br />
*[[Bohr Model]]<br />
*[[Energy graphs and the Bohr model]]<br />
*[[Quantized energy levels]]<br />
*[[Quantized energy levels part II]]<br />
*[[Entropy]]<br />
</div><br />
</div><br />
</div><br />
<br />
<div style="float:left; width:30%; padding:1%;"><br />
<br />
==Physics 2==<br />
===Week 1===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====3D Vectors====<br />
<br />
'''VAISHNAVI RAMANAN - FALL 2018'''<br />
<br />
<div class="mw-collapsible-content"><br />
*[[Vectors]]<br />
*[[Right-Hand Rule]]<br />
*[[Right Hand Rule]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Electric field====<br />
<div class="mw-collapsible-content"><br />
*[[Electric Field]]<br />
*[[Electric Field and Electric Potential]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Electric force====<br />
<div class="mw-collapsible-content"><br />
*[[Electric Force]]<br />
*[[Lorentz Force]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Electric field of a point particle====<br />
<div class="mw-collapsible-content"><br />
*[[Point Charge]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Superposition====<br />
<div class="mw-collapsible-content"><br />
*[[Superposition Principle]]<br />
*[[Superposition principle]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Dipoles====<br />
<div class="mw-collapsible-content"><br />
*[[Electric Dipole]]<br />
*[[Magnetic Dipole]]<br />
</div><br />
</div><br />
<br />
===Week 2===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Interactions of charged objects====<br />
<div class="mw-collapsible-content"><br />
*[[Electric Field]]<br />
*[[Electric Potential]]<br />
*[[Electric Force]]<br />
*[[Lorentz Force]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Tape experiments====<br />
<div class="mw-collapsible-content"><br />
*[[Polarization]]<br />
*[[Electric Polarization]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Polarization====<br />
<div class="mw-collapsible-content"><br />
*[[Polarization]]<br />
*[[Electric Polarization]]<br />
*[[Polarization of an Atom]]<br />
</div><br />
</div><br />
<br />
===Week 3===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Insulators====<br />
<div class="mw-collapsible-content"><br />
*[[Insulators]]<br />
*[[Potential Difference in an Insulator]]<br />
*[[Charged Conductor and Charged Insulator]]<br />
*[[Charged conductor and charged insulator]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Conductors====<br />
<div class="mw-collapsible-content"><br />
*[[Conductivity]]<br />
*[[Charge Transfer]]<br />
*[[Resistivity]]<br />
*[[Polarization of a conductor]]<br />
*[[Charged Conductor and Charged Insulator]]<br />
*[[Charged conductor and charged insulator]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Charging and Discharging====<br />
<div class="mw-collapsible-content"><br />
*[[Charge Transfer]]<br />
*[[Electrostatic Discharge]]<br />
*[[Charged Conductor and Charged Insulator]]<br />
*[[Charged conductor and charged insulator]]<br />
</div><br />
</div><br />
<br />
===Week 4===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Field of a charged rod====<br />
<div class="mw-collapsible-content"><br />
*[[Charged Rod]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Field of a charged ring/disk/capacitor====<br />
<div class="mw-collapsible-content"><br />
*[[Charged Ring]]<br />
*[[Charged Disk]]<br />
*[[Charged Capacitor]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Field of a charged sphere====<br />
<div class="mw-collapsible-content"><br />
*[[Charged Spherical Shell]]<br />
*[[Field of a Charged Ball]]<br />
</div><br />
</div><br />
<br />
===Week 5===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Potential energy====<br />
<div class="mw-collapsible-content"><br />
*[[Potential Energy]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Electric potential====<br />
<div class="mw-collapsible-content"><br />
*[[Electric Potential]]<br />
*[[Path Independence of Electric Potential]]<br />
*[[Potential Difference Path Independence, claimed by Aditya Mohile]] <br />
*[[Potential Difference in a Uniform Field]]<br />
*[[Potential Difference of Point Charge in a Non-Uniform Field]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Sign of a potential difference====<br />
<div class="mw-collapsible-content"><br />
*[[Sign of a Potential Difference]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Potential at a single location====<br />
<div class="mw-collapsible-content"><br />
*[[Electric Potential]]<br />
*[[Potential Difference at One Location]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Path independence and round trip potential====<br />
<div class="mw-collapsible-content"><br />
*[[Path Independence of Electric Potential]]<br />
*[[Potential Difference Path Independence, claimed by Aditya Mohile]]<br />
</div><br />
</div><br />
<br />
===Week 6===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Electric field and potential in an insulator====<br />
<div class="mw-collapsible-content"><br />
*[[Potential Difference in an Insulator]]<br />
*[[Electric Field in an Insulator]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Moving charges in a magnetic field====<br />
<div class="mw-collapsible-content"><br />
*[[Magnetic Field]]<br />
*[[Magnetic Force]]<br />
*[[Lorentz Force]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Biot-Savart Law====<br />
<div class="mw-collapsible-content"><br />
*[[Biot-Savart Law]]<br />
*[[Biot-Savart Law for Currents]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Moving charges, electron current, and conventional current====<br />
<div class="mw-collapsible-content"><br />
*[[Moving Point Charge]]<br />
*[[Current]]<br />
</div><br />
</div><br />
<br />
===Week 7===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Magnetic field of a wire====<br />
<div class="mw-collapsible-content"><br />
*[[Magnetic Field of a Long Straight Wire]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Magnetic field of a current-carrying loop====<br />
<div class="mw-collapsible-content"><br />
*[[Magnetic Field of a Loop]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Magnetic field of a Charged Disk====<br />
<div class="mw-collapsible-content"><br />
*[[Magnetic Field of a Disk]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Magnetic dipoles====<br />
<div class="mw-collapsible-content"><br />
*[[Magnetic Dipole Moment]]<br />
*[[Bar Magnet]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Atomic structure of magnets====<br />
<div class="mw-collapsible-content"><br />
*[[Atomic Structure of Magnets]]<br />
</div><br />
</div><br />
<br />
===Week 8===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Steady state current====<br />
<div class="mw-collapsible-content"><br />
*[[Steady State]]<br />
*[[Non Steady State]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Kirchoff's Laws====<br />
<div class="mw-collapsible-content"><br />
*[[Kirchoff's Laws]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Electric fields and energy in circuits====<br />
<div class="mw-collapsible-content"><br />
*[[Series circuit]]<br />
*[[Node Rule]]<br />
*[[Loop Rule]]<br />
*[[Electric Potential Difference]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Macroscopic analysis of circuits====<br />
<div class="mw-collapsible-content"><br />
*[[Series Circuits]]<br />
*[[Parallel Circuits]]<br />
*[[Parallel Circuits vs. Series Circuits*]]<br />
*[[Loop Rule]]<br />
*[[Node Rule]]<br />
*[[Fundamentals of Resistance]]<br />
*[[Problem Solving]]<br />
</div><br />
</div><br />
<br />
===Week 9===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Electric field and potential in circuits with capacitors====<br />
<div class="mw-collapsible-content"><br />
*[[Charging and Discharging a Capacitor]]<br />
*[[RC Circuit]] <br />
*[[R Circuit]]<br />
*[[AC and DC]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Magnetic forces on charges and currents====<br />
<div class="mw-collapsible-content"><br />
*[[Magnetic Force]]<br />
*[[Lorentz Force]]<br />
*[[Motors and Generators]]<br />
*[[Applying Magnetic Force to Currents]]<br />
*[[Magnetic Force in a Moving Reference Frame]]<br />
*[[Right-Hand Rule]]<br />
*[[Analysis of Railgun vs Coil gun technologies]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Electric and magnetic forces====<br />
<div class="mw-collapsible-content"><br />
*[[Electric Force]]<br />
*[[Magnetic Force]]<br />
*[[Lorentz Force]]<br />
*[[VPython Modelling of Electric and Magnetic Forces]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Velocity selector====<br />
<div class="mw-collapsible-content"><br />
*[[Lorentz Force]]<br />
*[[Combining Electric and Magnetic Forces]]<br />
</div><br />
</div><br />
<br />
===Week 10===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Hall Effect====<br />
<div class="mw-collapsible-content"><br />
*[[Hall Effect]]<br />
*[[Right-Hand Rule]]<br />
*[[Motional Emf]]<br />
*[[Magnetic Force]]<br />
*[[Magnetic Torque]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Motional EMF====<br />
<div class="mw-collapsible-content"><br />
*[[Motional Emf]]<br />
*[[Motional Emf using Faraday's Law]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Magnetic force====<br />
<div class="mw-collapsible-content"><br />
*[[Magnetic Force]]<br />
*[[Lorentz Force]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Magnetic torque====<br />
<div class="mw-collapsible-content"><br />
*[[Magnetic Torque]]<br />
*[[Right-Hand Rule]]<br />
</div><br />
</div><br />
<br />
===Week 12===<br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Gauss's Law====<br />
<div class="mw-collapsible-content"><br />
*[[Gauss's Flux Theorem]]<br />
*[[Gauss's Law]]<br />
*[[Magnetic Flux]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Ampere's Law====<br />
<div class="mw-collapsible-content"><br />
*[[Ampere's Law]]<br />
*[[Ampere-Maxwell Law]]<br />
*[[Magnetic Field of Coaxial Cable Using Ampere's Law]]<br />
*[[Magnetic Field of a Long Thick Wire Using Ampere's Law]]<br />
*[[Magnetic Field of a Toroid Using Ampere's Law]]<br />
*[[Magnetic Field of a Solenoid Using Ampere's Law]]<br />
*[[The Differential Form of Ampere's Law]]<br />
</div><br />
</div><br />
<br />
===Week 13===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Semiconductors====<br />
<div class="mw-collapsible-content"><br />
*[[Semiconductor Devices]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Faraday's Law====<br />
<div class="mw-collapsible-content"><br />
*[[Faraday's Law]]<br />
*[[Motional Emf using Faraday's Law]]<br />
*[[Lenz's Law]]<br />
<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Maxwell's equations====<br />
<div class="mw-collapsible-content"><br />
*[[Gauss's Law]]<br />
*[[Magnetic Flux]]<br />
*[[Ampere's Law]]<br />
*[[Faraday's Law]]<br />
*[[Maxwell's Electromagnetic Theory]]<br />
</div><br />
</div><br />
<br />
===Week 14===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Circuits revisited====<br />
<div class="mw-collapsible-content"><br />
<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Inductors====<br />
<div class="mw-collapsible-content"><br />
*[[Inductors]]<br />
*[[Current in an LC Circuit]]<br />
*[[Current in an RL Circuit]]<br />
</div><br />
</div><br />
<br />
===Week 15===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
==== Electromagnetic Radiation ====<br />
<div class="mw-collapsible-content"><br />
*[[Electromagnetic Radiation]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Sparks in the air====<br />
<div class="mw-collapsible-content"><br />
*[[Sparks in Air]]<br />
*[[Spark Plugs]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Superconductors====<br />
<div class="mw-collapsible-content"><br />
*[[Superconducters]]<br />
*[[Superconductors]]<br />
*[[Meissner effect]]<br />
</div><br />
</div><br />
</div><br />
<br />
<div style="float:left; width:30%; padding:1%;"><br />
<br />
==Physics 3==<br />
<br />
===Week 1===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Classical Physics====<br />
<div class="mw-collapsible-content"><br />
</div><br />
</div><br />
<br />
===Week 2===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Special Relativity====<br />
<div class="mw-collapsible-content"><br />
*[[Frame of Reference]]<br />
*[[Einstein's Theory of Special Relativity]]<br />
*[[Time Dilation]]<br />
*[[Einstein's Theory of General Relativity]]<br />
*[[Albert A. Micheleson & Edward W. Morley]]<br />
*[[Magnetic Force in a Moving Reference Frame]]<br />
</div><br />
</div><br />
<br />
===Week 3===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Photons====<br />
<div class="mw-collapsible-content"><br />
*[[Spontaneous Photon Emission]]<br />
*[[Light Scattering: Why is the Sky Blue]]<br />
*[[Lasers]]<br />
*[[Electronic Energy Levels and Photons]]<br />
*[[Quantum Properties of Light]]<br />
</div><br />
</div><br />
<br />
===Week 4===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Matter Waves====<br />
<div class="mw-collapsible-content"><br />
*[[Wave-Particle Duality]]<br />
</div><br />
</div><br />
<br />
===Week 5===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Wave Mechanics====<br />
<div class="mw-collapsible-content"><br />
*[[Standing Waves]]<br />
*[[Wavelength]]<br />
*[[Wavelength and Frequency]]<br />
*[[Mechanical Waves]]<br />
*[[Transverse and Longitudinal Waves]]<br />
</div><br />
</div><br />
<br />
===Week 6===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Rutherford-Bohr Model====<br />
<div class="mw-collapsible-content"><br />
*[[Rutherford Experiment and Atomic Collisions]]<br />
*[[Bohr Model]]<br />
*[[Quantized energy levels]]<br />
*[[Energy graphs and the Bohr model]]<br />
</div><br />
</div><br />
<br />
===Week 7===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====The Hydrogen Atom====<br />
<div class="mw-collapsible-content"><br />
*[[Quantum Theory]]<br />
*[[Atomic Theory]]<br />
</div><br />
</div><br />
<br />
===Week 8===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Many-Electron Atoms====<br />
<div class="mw-collapsible-content"><br />
*[[Quantum Theory]]<br />
*[[Atomic Theory]]<br />
*[[Pauli exclusion principle]]<br />
</div><br />
</div><br />
<br />
===Week 9===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Molecules====<br />
<div class="mw-collapsible-content"><br />
</div><br />
</div><br />
<br />
===Week 10===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Statistical Physics====<br />
<div class="mw-collapsible-content"><br />
</div><br />
</div><br />
<br />
===Week 11===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Condensed Matter Physics====<br />
<div class="mw-collapsible-content"><br />
</div><br />
</div><br />
<br />
===Week 12===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====The Nucleus====<br />
<div class="mw-collapsible-content"><br />
*[[Nucleus]]<br />
</div><br />
</div><br />
<br />
===Week 13===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Nuclear Physics====<br />
<div class="mw-collapsible-content"><br />
*[[Nuclear Fission]]<br />
*[[Nuclear Energy from Fission and Fusion]]<br />
</div><br />
</div><br />
<br />
===Week 14===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Particle Physics====<br />
<div class="mw-collapsible-content"><br />
*[[Elementary Particles and Particle Physics Theory]]<br />
*[[String Theory]]<br />
</div><br />
</div><br />
</div></div>Vramanan3