Physics Book - User contributions [en]

Non-Coulomb Electric Field

2015-12-06T03:25:25Z

Gmckelvey3:

Claimed by Geoffrey McKelvey

The non-Coulomb electric field, often represented by the variable <math> \vec{E}_{NC}</math>, is an electric field, which does not result from a stationary point charge.

==Magnetic Field- Induced Electric Field==

The concept of the non-Coulomb electric field arises from the discovery of electric fields, which cannot be created as a result of Coulomb's law. Due to the involvement of motion, the resulting potential difference is often referred to as motional emf. The non-Coulomb electric field is also know as the curly electric field, due to it's directionality of curling around the conductor, which in turn will induce voltage, which in turn will induce the current to flow.

===Lenz-Faraday Law===

[[File:Direction_of_E_NC_with_Changing_B.png|thumb|alt=dB/dt with ENC relationship |Relationship of <math> -\frac{dB}{dt}</math> and the non-Coulomb electric field]] While Faradays law tells us the magnitude of motional emf, which is equivalent to the change in magnetic flux over time, Lenz's law gives us the direction, and states that the direction of the motional emf can be found by <math> emf =- \frac{dB}{dt}</math>, and the resultant induced electric field can be found by using the associated right-hand rule. This rule states that with the thumb of the right hand pointing in the direction of <math> -\frac{dB}{dt}</math>, then the fingers will curl in the direction of the non-Coulomb electrical field. The combination of these two laws is known as the Lenz-Faraday law, and in its entirety appears as such <math> |emf| = \oint \vec{E}_{NC} \cdot \Delta \vec{l} = |\frac{d\Phi_{mag}}{dt}|</math>. These tell us that the flux of the time-varying magnetic field is what creates the non-Coulomb electric field, which is the source of voltage (emf) and ultimately, the induced current which follows.

===A Mathematical Model===

Along a closed path, the general equation, from which the magnitude of the non-Coulomb electric field can be obtained, is <math> |emf| = \oint \vec{E}_{NC} \cdot \Delta \vec{l} = |\frac{d\Phi_{mag}}{dt}|</math>. The direction of this can be found by using <math> emf =- \frac{dB}{dt}</math>, followed by the used of the above integral in order to determine the direction of the field.

===A Computational Model===

In this [http://www.glowscript.org/#/user/matterandinteractions/folder/matterandinteractions/program/22-Faraday-magnet vpython simulation], the effects of the motion of the magnet on a conductor can be observed, with the curly electric field shown in orange, while the induced magnetic field is shown in blue

In this [http://www.glowscript.org/#/user/matterandinteractions/folder/matterandinteractions/program/22-Faraday-coil vpython simulation], the curly magnetic field associated with the alternating magnetic field of a coil of wire can be seen, along with the measured induced current.

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
Problem:
On a circular path of radius 8 cm in air around a solenoid with increasing magnetic field, the emf is 32 volts. What is the magnitude of the non-Coulomb electric field on this path?

Solution:
1) We will use the equation <math> |emf| = |\oint \vec{E}_{NC} \cdot \Delta \vec{l}|</math>. As the electric field is constant, we are able to used <math> |emf| = \vec{E}_{NC} \cdot \Delta \vec{l}</math>

2) Now we plug in the variables which we have. The magnitude of the emf is known to be 32 V, and the radius of the coil is 0.08 m. Thus, the length of the path can be found by finding the circumference of the coil, which can be found by the equation 2πr, which gives a circumference of 0.5026 m.

3) Now that we have 2 of the 3 variables in our equation, we can then solve for the electric field by dividing the emf by the path length, which gives 63.66 V/m

===A Little Harder===
A wire of resistance 12 ohms and length 2.7 m is bent into a circle and is concentric with a solenoid in which the magnetic flux changes from 8 T·m2 to 5 T·m2 in 0.3 seconds. Find the emf, non-Coulomb electric field, and the induced current in the wire.

1) We will use the equations <math> |emf| = \oint \vec{E}_{NC} \cdot \Delta \vec{l} = |\frac{d\Phi_{mag}}{dt}|</math> along with <math> V = IR</math>

2)We know the path length is 2.7 m, the resistance is 12 Ω, and that the flux changes from 8 T·m2 to 5 T·m2 in 0.3 seconds, so <math> |\frac{(5-8)T·m^2 }{3 s}|</math>which via gives an emf of of 10 V

3) Knowing that the emf is 10 V, we can divide this by the length of the path, 2.7 m, for the magnitude of the NC electric field, which is 3.7 V/m.

4) Lastly, we are able to use the equation <math> V = IR</math> to solve for I. By dividing the voltage by the resistance, we find that the induced current measures 0.83 A

==Connectedness==

1. How is this topic connected to something that you are interested in?

Non-Coulomb electrical fields are a possible complication involved in magnetic resonance imaging (MRI), as they are what creates the induced voltage and ultimately, current, known as Eddy currents, , from the alternating magnetic fields that oppose the magnetic force that created them, which may cause such complications as heating tissue or creating an artifact within the image.

2. How is it connected to your major?

MRI and functional MRI (fMRI) are two very useful imaging techniques, being on of the highest resolution imaging techniques available, with none of the accompanying radiative dangers, which accompany computerized tomography (CT) scans. Eddy currents, product of the non-Coulomb fields, which accompany the induced, opposing magnetic field, present a significant complication to the use of MRI, via the creation of artifact within the image, heat within current loops induced in tissue, among others.

A step-by-step explanation of Eddy current can be found [https://www.youtube.com/watch?v=zJ23gmS3KHY here]

==History==
[[File:Heinrich Friedrich Emil Lenz.jpg|thumb|alt=Picture of Heinrich Lenz|Heinrich Lenz]]In 1831, Heinrich Lenz, an Estonian physicist, for whom the symbol "L" of inductance is named, discovered the right-hand-rule relationship between a changing magnetic field and the direction of induced electric field, the non-Coulomb field.

This occurrence, however, was preceded by the discovery of the motional electromotive force (emf), resulting from interactions between a non-constant magnetic field and conductor, earlier in same year of 1931 by Michael Faraday, an English physicist and chemist. It is worth noting that this was discovered independently in 1932 by Joseph Henry, an American scientist, however Faraday published first, and is therefore credited with the discovery and contribution to science.

== See also ==

[[Transformers (Circuits)]]: This page investigates the use of these concepts in the transmission of electricity from power plants to the home.

===External links===

This [https://youtu.be/2DH7ufrkeHM video] provides a video walkthrough of the process of motional emf form a time-varying magnetic field

==References==

Vpython Code Simulations, Written by Ruth Chabay and Bruce Sherwood, licensed under Creative Commons 4.0.

Non-Coulomb Electric Field

2015-12-06T03:24:58Z

Gmckelvey3: /* Examples */

Claimed by Geoffrey McKelvey, Work in Progress

The non-Coulomb electric field, often represented by the variable <math> \vec{E}_{NC}</math>, is an electric field, which does not result from a stationary point charge.

==Magnetic Field- Induced Electric Field==

The concept of the non-Coulomb electric field arises from the discovery of electric fields, which cannot be created as a result of Coulomb's law. Due to the involvement of motion, the resulting potential difference is often referred to as motional emf. The non-Coulomb electric field is also know as the curly electric field, due to it's directionality of curling around the conductor, which in turn will induce voltage, which in turn will induce the current to flow.

===Lenz-Faraday Law===

[[File:Direction_of_E_NC_with_Changing_B.png|thumb|alt=dB/dt with ENC relationship |Relationship of <math> -\frac{dB}{dt}</math> and the non-Coulomb electric field]] While Faradays law tells us the magnitude of motional emf, which is equivalent to the change in magnetic flux over time, Lenz's law gives us the direction, and states that the direction of the motional emf can be found by <math> emf =- \frac{dB}{dt}</math>, and the resultant induced electric field can be found by using the associated right-hand rule. This rule states that with the thumb of the right hand pointing in the direction of <math> -\frac{dB}{dt}</math>, then the fingers will curl in the direction of the non-Coulomb electrical field. The combination of these two laws is known as the Lenz-Faraday law, and in its entirety appears as such <math> |emf| = \oint \vec{E}_{NC} \cdot \Delta \vec{l} = |\frac{d\Phi_{mag}}{dt}|</math>. These tell us that the flux of the time-varying magnetic field is what creates the non-Coulomb electric field, which is the source of voltage (emf) and ultimately, the induced current which follows.

===A Mathematical Model===

Along a closed path, the general equation, from which the magnitude of the non-Coulomb electric field can be obtained, is <math> |emf| = \oint \vec{E}_{NC} \cdot \Delta \vec{l} = |\frac{d\Phi_{mag}}{dt}|</math>. The direction of this can be found by using <math> emf =- \frac{dB}{dt}</math>, followed by the used of the above integral in order to determine the direction of the field.

===A Computational Model===

In this [http://www.glowscript.org/#/user/matterandinteractions/folder/matterandinteractions/program/22-Faraday-magnet vpython simulation], the effects of the motion of the magnet on a conductor can be observed, with the curly electric field shown in orange, while the induced magnetic field is shown in blue

In this [http://www.glowscript.org/#/user/matterandinteractions/folder/matterandinteractions/program/22-Faraday-coil vpython simulation], the curly magnetic field associated with the alternating magnetic field of a coil of wire can be seen, along with the measured induced current.

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
Problem:
On a circular path of radius 8 cm in air around a solenoid with increasing magnetic field, the emf is 32 volts. What is the magnitude of the non-Coulomb electric field on this path?

Solution:
1) We will use the equation <math> |emf| = |\oint \vec{E}_{NC} \cdot \Delta \vec{l}|</math>. As the electric field is constant, we are able to used <math> |emf| = \vec{E}_{NC} \cdot \Delta \vec{l}</math>

2) Now we plug in the variables which we have. The magnitude of the emf is known to be 32 V, and the radius of the coil is 0.08 m. Thus, the length of the path can be found by finding the circumference of the coil, which can be found by the equation 2πr, which gives a circumference of 0.5026 m.

3) Now that we have 2 of the 3 variables in our equation, we can then solve for the electric field by dividing the emf by the path length, which gives 63.66 V/m

===A Little Harder===
A wire of resistance 12 ohms and length 2.7 m is bent into a circle and is concentric with a solenoid in which the magnetic flux changes from 8 T·m2 to 5 T·m2 in 0.3 seconds. Find the emf, non-Coulomb electric field, and the induced current in the wire.

1) We will use the equations <math> |emf| = \oint \vec{E}_{NC} \cdot \Delta \vec{l} = |\frac{d\Phi_{mag}}{dt}|</math> along with <math> V = IR</math>

2)We know the path length is 2.7 m, the resistance is 12 Ω, and that the flux changes from 8 T·m2 to 5 T·m2 in 0.3 seconds, so <math> |\frac{(5-8)T·m^2 }{3 s}|</math>which via gives an emf of of 10 V

3) Knowing that the emf is 10 V, we can divide this by the length of the path, 2.7 m, for the magnitude of the NC electric field, which is 3.7 V/m.

4) Lastly, we are able to use the equation <math> V = IR</math> to solve for I. By dividing the voltage by the resistance, we find that the induced current measures 0.83 A

==Connectedness==

1. How is this topic connected to something that you are interested in?

Non-Coulomb electrical fields are a possible complication involved in magnetic resonance imaging (MRI), as they are what creates the induced voltage and ultimately, current, known as Eddy currents, , from the alternating magnetic fields that oppose the magnetic force that created them, which may cause such complications as heating tissue or creating an artifact within the image.

2. How is it connected to your major?

MRI and functional MRI (fMRI) are two very useful imaging techniques, being on of the highest resolution imaging techniques available, with none of the accompanying radiative dangers, which accompany computerized tomography (CT) scans. Eddy currents, product of the non-Coulomb fields, which accompany the induced, opposing magnetic field, present a significant complication to the use of MRI, via the creation of artifact within the image, heat within current loops induced in tissue, among others.

A step-by-step explanation of Eddy current can be found [https://www.youtube.com/watch?v=zJ23gmS3KHY here]

==History==
[[File:Heinrich Friedrich Emil Lenz.jpg|thumb|alt=Picture of Heinrich Lenz|Heinrich Lenz]]In 1831, Heinrich Lenz, an Estonian physicist, for whom the symbol "L" of inductance is named, discovered the right-hand-rule relationship between a changing magnetic field and the direction of induced electric field, the non-Coulomb field.

This occurrence, however, was preceded by the discovery of the motional electromotive force (emf), resulting from interactions between a non-constant magnetic field and conductor, earlier in same year of 1931 by Michael Faraday, an English physicist and chemist. It is worth noting that this was discovered independently in 1932 by Joseph Henry, an American scientist, however Faraday published first, and is therefore credited with the discovery and contribution to science.

== See also ==

[[Transformers (Circuits)]]: This page investigates the use of these concepts in the transmission of electricity from power plants to the home.

===External links===

This [https://youtu.be/2DH7ufrkeHM video] provides a video walkthrough of the process of motional emf form a time-varying magnetic field

==References==

Vpython Code Simulations, Written by Ruth Chabay and Bruce Sherwood, licensed under Creative Commons 4.0.

Non-Coulomb Electric Field

2015-12-06T02:49:50Z

Gmckelvey3: /* Connectedness */

Claimed by Geoffrey McKelvey, Work in Progress

The non-Coulomb electric field, often represented by the variable <math> \vec{E}_{NC}</math>, is an electric field, which does not result from a stationary point charge.

==Magnetic Field- Induced Electric Field==

The concept of the non-Coulomb electric field arises from the discovery of electric fields, which cannot be created as a result of Coulomb's law. Due to the involvement of motion, the resulting potential difference is often referred to as motional emf. The non-Coulomb electric field is also know as the curly electric field, due to it's directionality of curling around the conductor, which in turn will induce voltage, which in turn will induce the current to flow.

===Lenz-Faraday Law===

[[File:Direction_of_E_NC_with_Changing_B.png|thumb|alt=dB/dt with ENC relationship |Relationship of <math> -\frac{dB}{dt}</math> and the non-Coulomb electric field]] While Faradays law tells us the magnitude of motional emf, which is equivalent to the change in magnetic flux over time, Lenz's law gives us the direction, and states that the direction of the motional emf can be found by <math> emf =- \frac{dB}{dt}</math>, and the resultant induced electric field can be found by using the associated right-hand rule. This rule states that with the thumb of the right hand pointing in the direction of <math> -\frac{dB}{dt}</math>, then the fingers will curl in the direction of the non-Coulomb electrical field. The combination of these two laws is known as the Lenz-Faraday law, and in its entirety appears as such <math> |emf| = \oint \vec{E}_{NC} \cdot \Delta \vec{l} = |\frac{d\Phi_{mag}}{dt}|</math>. These tell us that the flux of the time-varying magnetic field is what creates the non-Coulomb electric field, which is the source of voltage (emf) and ultimately, the induced current which follows.

===A Mathematical Model===

Along a closed path, the general equation, from which the magnitude of the non-Coulomb electric field can be obtained, is <math> |emf| = \oint \vec{E}_{NC} \cdot \Delta \vec{l} = |\frac{d\Phi_{mag}}{dt}|</math>. The direction of this can be found by using <math> emf =- \frac{dB}{dt}</math>, followed by the used of the above integral in order to determine the direction of the field.

===A Computational Model===

In this [http://www.glowscript.org/#/user/matterandinteractions/folder/matterandinteractions/program/22-Faraday-magnet vpython simulation], the effects of the motion of the magnet on a conductor can be observed, with the curly electric field shown in orange, while the induced magnetic field is shown in blue

In this [http://www.glowscript.org/#/user/matterandinteractions/folder/matterandinteractions/program/22-Faraday-coil vpython simulation], the curly magnetic field associated with the alternating magnetic field of a coil of wire can be seen, along with the measured induced current.

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
===Middling===
===Difficult===

==Connectedness==

1. How is this topic connected to something that you are interested in?

Non-Coulomb electrical fields are a possible complication involved in magnetic resonance imaging (MRI), as they are what creates the induced voltage and ultimately, current, known as Eddy currents, , from the alternating magnetic fields that oppose the magnetic force that created them, which may cause such complications as heating tissue or creating an artifact within the image.

2. How is it connected to your major?

MRI and functional MRI (fMRI) are two very useful imaging techniques, being on of the highest resolution imaging techniques available, with none of the accompanying radiative dangers, which accompany computerized tomography (CT) scans. Eddy currents, product of the non-Coulomb fields, which accompany the induced, opposing magnetic field, present a significant complication to the use of MRI, via the creation of artifact within the image, heat within current loops induced in tissue, among others.

A step-by-step explanation of Eddy current can be found [https://www.youtube.com/watch?v=zJ23gmS3KHY here]

==History==
[[File:Heinrich Friedrich Emil Lenz.jpg|thumb|alt=Picture of Heinrich Lenz|Heinrich Lenz]]In 1831, Heinrich Lenz, an Estonian physicist, for whom the symbol "L" of inductance is named, discovered the right-hand-rule relationship between a changing magnetic field and the direction of induced electric field, the non-Coulomb field.

This occurrence, however, was preceded by the discovery of the motional electromotive force (emf), resulting from interactions between a non-constant magnetic field and conductor, earlier in same year of 1931 by Michael Faraday, an English physicist and chemist. It is worth noting that this was discovered independently in 1932 by Joseph Henry, an American scientist, however Faraday published first, and is therefore credited with the discovery and contribution to science.

== See also ==

[[Transformers (Circuits)]]: This page investigates the use of these concepts in the transmission of electricity from power plants to the home.

===External links===

This [https://youtu.be/2DH7ufrkeHM video] provides a video walkthrough of the process of motional emf form a time-varying magnetic field

==References==

Vpython Code Simulations, Written by Ruth Chabay and Bruce Sherwood, licensed under Creative Commons 4.0.

Non-Coulomb Electric Field

2015-12-06T02:47:12Z

Gmckelvey3: /* A Mathematical Model */

Claimed by Geoffrey McKelvey, Work in Progress

The non-Coulomb electric field, often represented by the variable <math> \vec{E}_{NC}</math>, is an electric field, which does not result from a stationary point charge.

==Magnetic Field- Induced Electric Field==

The concept of the non-Coulomb electric field arises from the discovery of electric fields, which cannot be created as a result of Coulomb's law. Due to the involvement of motion, the resulting potential difference is often referred to as motional emf. The non-Coulomb electric field is also know as the curly electric field, due to it's directionality of curling around the conductor, which in turn will induce voltage, which in turn will induce the current to flow.

===Lenz-Faraday Law===

[[File:Direction_of_E_NC_with_Changing_B.png|thumb|alt=dB/dt with ENC relationship |Relationship of <math> -\frac{dB}{dt}</math> and the non-Coulomb electric field]] While Faradays law tells us the magnitude of motional emf, which is equivalent to the change in magnetic flux over time, Lenz's law gives us the direction, and states that the direction of the motional emf can be found by <math> emf =- \frac{dB}{dt}</math>, and the resultant induced electric field can be found by using the associated right-hand rule. This rule states that with the thumb of the right hand pointing in the direction of <math> -\frac{dB}{dt}</math>, then the fingers will curl in the direction of the non-Coulomb electrical field. The combination of these two laws is known as the Lenz-Faraday law, and in its entirety appears as such <math> |emf| = \oint \vec{E}_{NC} \cdot \Delta \vec{l} = |\frac{d\Phi_{mag}}{dt}|</math>. These tell us that the flux of the time-varying magnetic field is what creates the non-Coulomb electric field, which is the source of voltage (emf) and ultimately, the induced current which follows.

===A Mathematical Model===

Along a closed path, the general equation, from which the magnitude of the non-Coulomb electric field can be obtained, is <math> |emf| = \oint \vec{E}_{NC} \cdot \Delta \vec{l} = |\frac{d\Phi_{mag}}{dt}|</math>. The direction of this can be found by using <math> emf =- \frac{dB}{dt}</math>, followed by the used of the above integral in order to determine the direction of the field.

===A Computational Model===

In this [http://www.glowscript.org/#/user/matterandinteractions/folder/matterandinteractions/program/22-Faraday-magnet vpython simulation], the effects of the motion of the magnet on a conductor can be observed, with the curly electric field shown in orange, while the induced magnetic field is shown in blue

In this [http://www.glowscript.org/#/user/matterandinteractions/folder/matterandinteractions/program/22-Faraday-coil vpython simulation], the curly magnetic field associated with the alternating magnetic field of a coil of wire can be seen, along with the measured induced current.

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
===Middling===
===Difficult===

==Connectedness==

1. How is this topic connected to something that you are interested in?

Non-Coulomb electrical fields are a possible complication involved in magnetic resonance imaging (MRI), as they are what creates the induced voltage and ultimately, current, known as Eddy currents, , from the alternating magnetic fields that oppose the magnetic force that created them, which may cause such complications as heating tissue or creating an artifact within the image.

2. How is it connected to your major?

MRI and functional MRI (fMRI) are two very useful imaging techniques, being on of the highest resolution imaging techniques available, with none of the accompanying radiative dangers, which accompany computerized tomography (CT) scans. Eddy currents, product of the non-Coulomb fields, which accompany the induced, opposing magnetic field, present a significant complication to the use of MRI, via the creation of artifact within the image, heat within current loops induced in tissue, among others.

==History==
[[File:Heinrich Friedrich Emil Lenz.jpg|thumb|alt=Picture of Heinrich Lenz|Heinrich Lenz]]In 1831, Heinrich Lenz, an Estonian physicist, for whom the symbol "L" of inductance is named, discovered the right-hand-rule relationship between a changing magnetic field and the direction of induced electric field, the non-Coulomb field.

This occurrence, however, was preceded by the discovery of the motional electromotive force (emf), resulting from interactions between a non-constant magnetic field and conductor, earlier in same year of 1931 by Michael Faraday, an English physicist and chemist. It is worth noting that this was discovered independently in 1932 by Joseph Henry, an American scientist, however Faraday published first, and is therefore credited with the discovery and contribution to science.

== See also ==

[[Transformers (Circuits)]]: This page investigates the use of these concepts in the transmission of electricity from power plants to the home.

===External links===

This [https://youtu.be/2DH7ufrkeHM video] provides a video walkthrough of the process of motional emf form a time-varying magnetic field

==References==

Vpython Code Simulations, Written by Ruth Chabay and Bruce Sherwood, licensed under Creative Commons 4.0.

Non-Coulomb Electric Field

2015-12-06T02:46:30Z

Gmckelvey3: /* References */

Claimed by Geoffrey McKelvey, Work in Progress

The non-Coulomb electric field, often represented by the variable <math> \vec{E}_{NC}</math>, is an electric field, which does not result from a stationary point charge.

==Magnetic Field- Induced Electric Field==

The concept of the non-Coulomb electric field arises from the discovery of electric fields, which cannot be created as a result of Coulomb's law. Due to the involvement of motion, the resulting potential difference is often referred to as motional emf. The non-Coulomb electric field is also know as the curly electric field, due to it's directionality of curling around the conductor, which in turn will induce voltage, which in turn will induce the current to flow.

===Lenz-Faraday Law===

[[File:Direction_of_E_NC_with_Changing_B.png|thumb|alt=dB/dt with ENC relationship |Relationship of <math> -\frac{dB}{dt}</math> and the non-Coulomb electric field]] While Faradays law tells us the magnitude of motional emf, which is equivalent to the change in magnetic flux over time, Lenz's law gives us the direction, and states that the direction of the motional emf can be found by <math> emf =- \frac{dB}{dt}</math>, and the resultant induced electric field can be found by using the associated right-hand rule. This rule states that with the thumb of the right hand pointing in the direction of <math> -\frac{dB}{dt}</math>, then the fingers will curl in the direction of the non-Coulomb electrical field. The combination of these two laws is known as the Lenz-Faraday law, and in its entirety appears as such <math> |emf| = \oint \vec{E}_{NC} \cdot \Delta \vec{l} = |\frac{d\Phi_{mag}}{dt}|</math>. These tell us that the flux of the time-varying magnetic field is what creates the non-Coulomb electric field, which is the source of voltage (emf) and ultimately, the induced current which follows.

===A Mathematical Model===

Along a closed path, the general equation, from which the magnitude of the non-Coulomb electric field can be obtained, is <math> |emf| = \oint \vec{E}_{NC} \cdot \Delta \vec{l} = |\frac{d\Phi_{mag}}{dt}|</math>. The direction of this can be found by using <math> emf =- \frac{dB}{dt}</math>.

===A Computational Model===

In this [http://www.glowscript.org/#/user/matterandinteractions/folder/matterandinteractions/program/22-Faraday-magnet vpython simulation], the effects of the motion of the magnet on a conductor can be observed, with the curly electric field shown in orange, while the induced magnetic field is shown in blue

In this [http://www.glowscript.org/#/user/matterandinteractions/folder/matterandinteractions/program/22-Faraday-coil vpython simulation], the curly magnetic field associated with the alternating magnetic field of a coil of wire can be seen, along with the measured induced current.

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
===Middling===
===Difficult===

==Connectedness==

1. How is this topic connected to something that you are interested in?

Non-Coulomb electrical fields are a possible complication involved in magnetic resonance imaging (MRI), as they are what creates the induced voltage and ultimately, current, known as Eddy currents, , from the alternating magnetic fields that oppose the magnetic force that created them, which may cause such complications as heating tissue or creating an artifact within the image.

2. How is it connected to your major?

MRI and functional MRI (fMRI) are two very useful imaging techniques, being on of the highest resolution imaging techniques available, with none of the accompanying radiative dangers, which accompany computerized tomography (CT) scans. Eddy currents, product of the non-Coulomb fields, which accompany the induced, opposing magnetic field, present a significant complication to the use of MRI, via the creation of artifact within the image, heat within current loops induced in tissue, among others.

==History==
[[File:Heinrich Friedrich Emil Lenz.jpg|thumb|alt=Picture of Heinrich Lenz|Heinrich Lenz]]In 1831, Heinrich Lenz, an Estonian physicist, for whom the symbol "L" of inductance is named, discovered the right-hand-rule relationship between a changing magnetic field and the direction of induced electric field, the non-Coulomb field.

This occurrence, however, was preceded by the discovery of the motional electromotive force (emf), resulting from interactions between a non-constant magnetic field and conductor, earlier in same year of 1931 by Michael Faraday, an English physicist and chemist. It is worth noting that this was discovered independently in 1932 by Joseph Henry, an American scientist, however Faraday published first, and is therefore credited with the discovery and contribution to science.

== See also ==

[[Transformers (Circuits)]]: This page investigates the use of these concepts in the transmission of electricity from power plants to the home.

===External links===

This [https://youtu.be/2DH7ufrkeHM video] provides a video walkthrough of the process of motional emf form a time-varying magnetic field

==References==

Vpython Code Simulations, Written by Ruth Chabay and Bruce Sherwood, licensed under Creative Commons 4.0.

Non-Coulomb Electric Field

2015-12-06T02:43:27Z

Gmckelvey3: /* A Computational Model */

Claimed by Geoffrey McKelvey, Work in Progress

The non-Coulomb electric field, often represented by the variable <math> \vec{E}_{NC}</math>, is an electric field, which does not result from a stationary point charge.

==Magnetic Field- Induced Electric Field==

The concept of the non-Coulomb electric field arises from the discovery of electric fields, which cannot be created as a result of Coulomb's law. Due to the involvement of motion, the resulting potential difference is often referred to as motional emf. The non-Coulomb electric field is also know as the curly electric field, due to it's directionality of curling around the conductor, which in turn will induce voltage, which in turn will induce the current to flow.

===Lenz-Faraday Law===

[[File:Direction_of_E_NC_with_Changing_B.png|thumb|alt=dB/dt with ENC relationship |Relationship of <math> -\frac{dB}{dt}</math> and the non-Coulomb electric field]] While Faradays law tells us the magnitude of motional emf, which is equivalent to the change in magnetic flux over time, Lenz's law gives us the direction, and states that the direction of the motional emf can be found by <math> emf =- \frac{dB}{dt}</math>, and the resultant induced electric field can be found by using the associated right-hand rule. This rule states that with the thumb of the right hand pointing in the direction of <math> -\frac{dB}{dt}</math>, then the fingers will curl in the direction of the non-Coulomb electrical field. The combination of these two laws is known as the Lenz-Faraday law, and in its entirety appears as such <math> |emf| = \oint \vec{E}_{NC} \cdot \Delta \vec{l} = |\frac{d\Phi_{mag}}{dt}|</math>. These tell us that the flux of the time-varying magnetic field is what creates the non-Coulomb electric field, which is the source of voltage (emf) and ultimately, the induced current which follows.

===A Mathematical Model===

Along a closed path, the general equation, from which the magnitude of the non-Coulomb electric field can be obtained, is <math> |emf| = \oint \vec{E}_{NC} \cdot \Delta \vec{l} = |\frac{d\Phi_{mag}}{dt}|</math>. The direction of this can be found by using <math> emf =- \frac{dB}{dt}</math>.

===A Computational Model===

In this [http://www.glowscript.org/#/user/matterandinteractions/folder/matterandinteractions/program/22-Faraday-magnet vpython simulation], the effects of the motion of the magnet on a conductor can be observed, with the curly electric field shown in orange, while the induced magnetic field is shown in blue

In this [http://www.glowscript.org/#/user/matterandinteractions/folder/matterandinteractions/program/22-Faraday-coil vpython simulation], the curly magnetic field associated with the alternating magnetic field of a coil of wire can be seen, along with the measured induced current.

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
===Middling===
===Difficult===

==Connectedness==

1. How is this topic connected to something that you are interested in?

Non-Coulomb electrical fields are a possible complication involved in magnetic resonance imaging (MRI), as they are what creates the induced voltage and ultimately, current, known as Eddy currents, , from the alternating magnetic fields that oppose the magnetic force that created them, which may cause such complications as heating tissue or creating an artifact within the image.

2. How is it connected to your major?

MRI and functional MRI (fMRI) are two very useful imaging techniques, being on of the highest resolution imaging techniques available, with none of the accompanying radiative dangers, which accompany computerized tomography (CT) scans. Eddy currents, product of the non-Coulomb fields, which accompany the induced, opposing magnetic field, present a significant complication to the use of MRI, via the creation of artifact within the image, heat within current loops induced in tissue, among others.

==History==
[[File:Heinrich Friedrich Emil Lenz.jpg|thumb|alt=Picture of Heinrich Lenz|Heinrich Lenz]]In 1831, Heinrich Lenz, an Estonian physicist, for whom the symbol "L" of inductance is named, discovered the right-hand-rule relationship between a changing magnetic field and the direction of induced electric field, the non-Coulomb field.

This occurrence, however, was preceded by the discovery of the motional electromotive force (emf), resulting from interactions between a non-constant magnetic field and conductor, earlier in same year of 1931 by Michael Faraday, an English physicist and chemist. It is worth noting that this was discovered independently in 1932 by Joseph Henry, an American scientist, however Faraday published first, and is therefore credited with the discovery and contribution to science.

== See also ==

[[Transformers (Circuits)]]: This page investigates the use of these concepts in the transmission of electricity from power plants to the home.

===External links===

This [https://youtu.be/2DH7ufrkeHM video] provides a video walkthrough of the process of motional emf form a time-varying magnetic field

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Non-Coulomb Electric Field

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Non-Coulomb Electric Field

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Gmckelvey3: /* Lenz's Law */

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Non-Coulomb Electric Field

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Non-Coulomb Electric Field

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Non-Coulomb Electric Field

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Gmckelvey3: /* Magnetic Field- Induced Electric Field */

Non-Coulomb Electric Field

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Non-Coulomb Electric Field

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Non-Coulomb Electric Field

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File:Direction of E NC with Changing B.png

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Gmckelvey3: Relationship of <math> -\frac{dB}{dt}</math> and the non-Coulomb electric field

Relationship of <math> -\frac{dB}{dt}</math> and the non-Coulomb electric field

Non-Coulomb Electric Field

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File:Heinrich Friedrich Emil Lenz.jpg

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Gmckelvey3: https://upload.wikimedia.org/wikipedia/commons/c/cc/Heinrich_Friedrich_Emil_Lenz.jpg

https://upload.wikimedia.org/wikipedia/commons/c/cc/Heinrich_Friedrich_Emil_Lenz.jpg

Non-Coulomb Electric Field

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Non-Coulomb Electric Field

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Non-Coulomb Electric Field

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Non-Coulomb Electric Field

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Gmckelvey3: /* Polarized Metal Bar and Steady State */

Non-Coulomb Electric Field

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Non-Coulomb Electric Field

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Non-Coulomb Electric Field

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Gmckelvey3: Created page with "Claimed by Geoffrey McKelvey Short Description of Topic ==The Main Idea== State, in your own words, the main idea for this topic Electric Field of Capacitor ===A Mathemati..."

Claimed by Geoffrey McKelvey

Short Description of Topic

==The Main Idea==

State, in your own words, the main idea for this topic
Electric Field of Capacitor

===A Mathematical Model===

What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

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===Simple===
===Middling===
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==Connectedness==
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==History==

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== See also ==

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Main Page

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Gmckelvey3: /* Fields */

__NOTOC__
Welcome to the Georgia Tech Wiki for Intro Physics. This resources 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!

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<div class="toccolours mw-collapsible mw-collapsed">
===Interactions===
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===Momentum===
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===Fields===
<div class="mw-collapsible-content">
* [[Electric Field]] of a
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===Sound===
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== Resources ==
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* A page to keep track of all the physics [[Constants]]
* An overview of [[VPython]]