# Why is induced electric field always circular?

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Whenever there is change in magnetic field, electric field is induced. The most common explanation that is found is: " If a closed loop circular conductor is placed in time varying magnetic field then current is induced as per the Faraday's Law and direction is given by Lenz's law. So, there must be electric field that cause charge carriers to move and this field is there even if there is no circular conductor. Furthermore, it's direction is always tangent to the loop of the conductor. Hence, circular electric field is induced due to changing magnetic field, field line being the circumference of the conducting loop."

Now that the position of the conductor is not unique, we can place conductor in one one position we get one field line and if we place same conductor in another position we get another field line following similar arguments. But as the position of the conductor is not unique, two field lines can be made to intersect, a contradiction.

Can this be explained in some other way?

If the electric field lines are concentric circles then what uniquely specifies their centres?

Thanks in advance.

[ Please try to explain this in the level of A-Level Physics i.e. with no knowledge of Maxwell's equations and vector calculus ]

Now that the position of the conductor is not unique, we can place conductor in one one position we get one field line and if we place same conductor in another position we get another field line following similar arguments. But as the position of the conductor is not unique, two field lines can be made to intersect, a contradiction.

Can this be explained in some other way?

If the electric field lines are concentric circles then what uniquely specifies their centres?

Thanks in advance.

[ Please try to explain this in the level of A-Level Physics i.e. with no knowledge of Maxwell's equations and vector calculus ]

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#2

That doesn't sound like a conventional explanation - there isn't a latent EMF that's still there when you take the conductor away, the EMF is generated by the interaction of charge carriers with a magnetic field... i.e. there is no EMF unless you are in some way dragging the charge carriers through the magnetic field.

maybe watch this series of four calculus free lectures and see if it makes any sense (in any case it shows you what you'll need to reproduce in A level exams so you might as well just learn it anyway)

https://www.youtube.com/watch?v=ejRJ...POUk5WIGVYBzDy

maybe watch this series of four calculus free lectures and see if it makes any sense (in any case it shows you what you'll need to reproduce in A level exams so you might as well just learn it anyway)

https://www.youtube.com/watch?v=ejRJ...POUk5WIGVYBzDy

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(Original post by

That doesn't sound like a conventional explanation - there isn't a latent EMF that's still there when you take the conductor away, the EMF is generated by the interaction of charge carriers with a magnetic field... i.e. there is no EMF unless you are in some way dragging the charge carriers through the magnetic field.

maybe watch this series of four calculus free lectures and see if it makes any sense (in any case it shows you what you'll need to reproduce in A level exams so you might as well just learn it anyway)

https://www.youtube.com/watch?v=ejRJ...POUk5WIGVYBzDy

**Joinedup**)That doesn't sound like a conventional explanation - there isn't a latent EMF that's still there when you take the conductor away, the EMF is generated by the interaction of charge carriers with a magnetic field... i.e. there is no EMF unless you are in some way dragging the charge carriers through the magnetic field.

maybe watch this series of four calculus free lectures and see if it makes any sense (in any case it shows you what you'll need to reproduce in A level exams so you might as well just learn it anyway)

https://www.youtube.com/watch?v=ejRJ...POUk5WIGVYBzDy

I am referring to https://www.youtube.com/watch?v=2DH7ufrkeHM 0.00 to 2:10.

What would happen if he had square shaped closed conducting loop instead of the ring?

What would be the situation if magnetic field were passing throughout the plane of paper, not just the part shown in the video.

Thank you.

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#4

(Original post by

Whenever there is change in magnetic field, electric field is induced. The most common explanation that is found is: " If a closed loop circular conductor is placed in time varying magnetic field then current is induced as per the Faraday's Law and direction is given by Lenz's law. So, there must be electric field that cause charge carriers to move and this field is there even if there is no circular conductor. Furthermore, it's direction is always tangent to the loop of the conductor. Hence, circular electric field is induced due to changing magnetic field, field line being the circumference of the conducting loop."

Now that the position of the conductor is not unique, we can place conductor in one one position we get one field line and if we place same conductor in another position we get another field line following similar arguments. But as the position of the conductor is not unique, two field lines can be made to intersect, a contradiction.

Can this be explained in some other way?

If the electric field lines are concentric circles then what uniquely specifies their centres?

Thanks in advance.

[ Please try to explain this in the level of A-Level Physics i.e. with no knowledge of Maxwell's equations and vector calculus ]

**tangotangopapa2**)Whenever there is change in magnetic field, electric field is induced. The most common explanation that is found is: " If a closed loop circular conductor is placed in time varying magnetic field then current is induced as per the Faraday's Law and direction is given by Lenz's law. So, there must be electric field that cause charge carriers to move and this field is there even if there is no circular conductor. Furthermore, it's direction is always tangent to the loop of the conductor. Hence, circular electric field is induced due to changing magnetic field, field line being the circumference of the conducting loop."

Now that the position of the conductor is not unique, we can place conductor in one one position we get one field line and if we place same conductor in another position we get another field line following similar arguments. But as the position of the conductor is not unique, two field lines can be made to intersect, a contradiction.

Can this be explained in some other way?

If the electric field lines are concentric circles then what uniquely specifies their centres?

Thanks in advance.

[ Please try to explain this in the level of A-Level Physics i.e. with no knowledge of Maxwell's equations and vector calculus ]

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I was looking for the explanation, if any, that does not involve curl of the vector field. Is there any purely intuitive explanation?

Thank you.

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#6

**tangotangopapa2**)

Whenever there is change in magnetic field, electric field is induced. The most common explanation that is found is: " If a closed loop circular conductor is placed in time varying magnetic field then current is induced as per the Faraday's Law and direction is given by Lenz's law. So, there must be electric field that cause charge carriers to move and this field is there even if there is no circular conductor. Furthermore, it's direction is always tangent to the loop of the conductor. Hence, circular electric field is induced due to changing magnetic field, field line being the circumference of the conducting loop."

Now that the position of the conductor is not unique, we can place conductor in one one position we get one field line and if we place same conductor in another position we get another field line following similar arguments. But as the position of the conductor is not unique, two field lines can be made to intersect, a contradiction.

Can this be explained in some other way?

If the electric field lines are concentric circles then what uniquely specifies their centres?

Thanks in advance.

[ Please try to explain this in the level of A-Level Physics i.e. with no knowledge of Maxwell's equations and vector calculus ]

---(1)

(An induced emf is the sum—via integration—of quantities around a closed path, where is the electric field induced by a changing magnetic flux and is a differential length vector along the path.)

and

---(2)

---(3)

When you look at equation (3), we know that the magnetic flux is computed using magnetic flux density dot cross-sectional area or and the closed loop that is chosen for the integration in the LHS must be based on the area that you have chosen on the RHS.

If the magnetic flux is computed using a circular area, then the integration is performed on the circumference of the circle.

OR

Compare equation (1) with Ampere law

---(4)

---(1)

Based on equation 4, the magnetic field of a thin infinite long conducting wire flowing with current

*I*, are the concentric circles - I hope you are not disputing it, so based on similar argument for the induced electric field associated with the induced emf should be also concentric circles.

I hope this two cents help.

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(Original post by

If you view Faraday's law in an integral form, you "may see the reason" of why it is a closed loop and a simple closed loop is a circle.

---(1)

(An induced emf is the sum—via integration—of quantities around a closed path, where is the electric field induced by a changing magnetic flux and is a differential length vector along the path.)

and

---(2)

---(3)

When you look at equation (3), we know that the magnetic flux is computed using magnetic flux density dot cross-sectional area or and the closed loop that is chosen for the integration in the LHS must be based on the area that you have chosen on the RHS.

If the magnetic flux is computed using a circular area, then the integration is performed on the circumference of the circle.

OR

Compare equation (1) with Ampere law

---(4)

---(1)

Based on equation 4, the magnetic field of a thin infinite long conducting wire flowing with current

I hope this two cents help.

**Eimmanuel**)If you view Faraday's law in an integral form, you "may see the reason" of why it is a closed loop and a simple closed loop is a circle.

---(1)

(An induced emf is the sum—via integration—of quantities around a closed path, where is the electric field induced by a changing magnetic flux and is a differential length vector along the path.)

and

---(2)

---(3)

When you look at equation (3), we know that the magnetic flux is computed using magnetic flux density dot cross-sectional area or and the closed loop that is chosen for the integration in the LHS must be based on the area that you have chosen on the RHS.

If the magnetic flux is computed using a circular area, then the integration is performed on the circumference of the circle.

OR

Compare equation (1) with Ampere law

---(4)

---(1)

Based on equation 4, the magnetic field of a thin infinite long conducting wire flowing with current

*I*, are the concentric circles - I hope you are not disputing it, so based on similar argument for the induced electric field associated with the induced emf should be also concentric circles.I hope this two cents help.

1) Electric field lines induced due to single magnetic field line (varying in strength) is concentric circles, i.e. exactly analogous to Ampere's Circuital law for long straight conductor. (The centre of all circles being the field line)

2) If there are few magnetic field lines (varying in strength) then the induced electric field lines are concentric circles with line of circle being the line of symmetry. (i.e. the centroid line of the magnetic field lines)

3) If there is time varying magnetic field with field lines going into infinitely large plane then there is no unique electric field line as there is no unique axis of symmetry. (Are electric field lines still circular in this case? What about their centres?)

Thank you

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#8

(Original post by

Thank you so much. Really appreciate it. Correct me if I am wrong:

1) Electric field lines induced due to single magnetic field line (varying in strength) is concentric circles, i.e. exactly analogous to Ampere's Circuital law for long straight conductor. (The centre of all circles being the field line)

2) If there are few magnetic field lines (varying in strength) then the induced electric field lines are concentric circles with line of circle being the line of symmetry. (i.e. the centroid line of the magnetic field lines)

3) If there is time varying magnetic field with field lines going into infinitely large plane then there is no unique electric field line as there is no unique axis of symmetry. (Are electric field lines still circular in this case? What about their centres?)

Thank you

**tangotangopapa2**)Thank you so much. Really appreciate it. Correct me if I am wrong:

1) Electric field lines induced due to single magnetic field line (varying in strength) is concentric circles, i.e. exactly analogous to Ampere's Circuital law for long straight conductor. (The centre of all circles being the field line)

2) If there are few magnetic field lines (varying in strength) then the induced electric field lines are concentric circles with line of circle being the line of symmetry. (i.e. the centroid line of the magnetic field lines)

3) If there is time varying magnetic field with field lines going into infinitely large plane then there is no unique electric field line as there is no unique axis of symmetry. (Are electric field lines still circular in this case? What about their centres?)

Thank you

Consider this:

you have a thin disk of radius a with a varying magnetic field passing through it with

so for r<a

and for r>a

so these are concentric circles in the plane of the disk dying off as 1/r

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#9

**Eimmanuel**)

If you view Faraday's law in an integral form, you "may see the reason" of why it is a closed loop and a simple closed loop is a circle.

---(1)

(An induced emf is the sum—via integration—of quantities around a closed path, where is the electric field induced by a changing magnetic flux and is a differential length vector along the path.)

and

---(2)

---(3)

When you look at equation (3), we know that the magnetic flux is computed using magnetic flux density dot cross-sectional area or and the closed loop that is chosen for the integration in the LHS must be based on the area that you have chosen on the RHS.

If the magnetic flux is computed using a circular area, then the integration is performed on the circumference of the circle.

OR

Compare equation (1) with Ampere law

---(4)

---(1)

Based on equation 4, the magnetic field of a thin infinite long conducting wire flowing with current

*I*, are the concentric circles - I hope you are not disputing it, so based on similar argument for the induced electric field associated with the induced emf should be also concentric circles.

I hope this two cents help.

Also, where is the centre of the circles of the electric field? you could put a circular conductor anywhere but surely if there's nothing there, where will be centre be?

tangotangopapa2

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#10

One possible source of confusion is that you're not considering physically-possible magnetic fields.

Remember that the magnetic field is a

When the magnetic field lines have closed loops, it is much easier to visualise why the electric field that is generated is in concentric circles around a well-defined axis.

By the way, that definition at the start of this thread is slightly ropey. Faraday's law connects the induced electric field to the change in magnetic field, and says nothing about current. If a conductor of any shape happens to exist inside that induced electric field, then you'll probably get currents flowing, but not necessarily in circular paths.

Remember that the magnetic field is a

__solenoidal__field, i.e. it has the form "curl(B) = something" (Ampere's law), and that it has no divergence (Gauss's law for magnetism). That means the magnetic field lines must form closed loops. Your thought experiments are leaving you confused because none of them use such a field (e.g. single field line, or infinite and parallel field lines). These fields would indeed cause some problems in electromagnetism!When the magnetic field lines have closed loops, it is much easier to visualise why the electric field that is generated is in concentric circles around a well-defined axis.

By the way, that definition at the start of this thread is slightly ropey. Faraday's law connects the induced electric field to the change in magnetic field, and says nothing about current. If a conductor of any shape happens to exist inside that induced electric field, then you'll probably get currents flowing, but not necessarily in circular paths.

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#11

**tangotangopapa2**)

Thank you so much. Really appreciate it. Correct me if I am wrong:

1) Electric field lines induced due to single magnetic field line (varying in strength) is concentric circles, i.e. exactly analogous to Ampere's Circuital law for long straight conductor. (The centre of all circles being the field line)

2) If there are few magnetic field lines (varying in strength) then the induced electric field lines are concentric circles with line of circle being the line of symmetry. (i.e. the centroid line of the magnetic field lines)

3) If there is time varying magnetic field with field lines going into infinitely large plane then there is no unique electric field line as there is no unique axis of symmetry. (Are electric field lines still circular in this case? What about their centres?)

Thank you

I would like to add a few points to your point 1 and 3.

When field (vector field to be more precise in this example) is considered in Physics, it means a region of space ..... Can we have a magnetic field confined to a mathematical line region? I am not sure.

If the time-varying magnetic field extends into an infinite plane, the symmetry should be where you place your origin. In this case, (to me) one need to choose a coordinate system to make sense of it. The induced electric field should be still in the direction if the time-varying magnetic field point in the direction. The induced electric field can be found using the differential form (given by langlitz) of Faraday's law .

https://www.youtube.com/watch?v=OL3uBX68-CY

OR

Look at magnetostatics in the differential form and Biot-Savart law:

and

The solution of the magnetic field is Biot-Savart law.

Draw the analog

and

The solution of electric field is

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#12

(Original post by

I thought we integrate around a closed loop because the electric field is circular, not the other way around (ie the electric field isn't circular, because that's how we chose to integrate it.)

tangotangopapa2

**lawlieto**)I thought we integrate around a closed loop because the electric field is circular, not the other way around (ie the electric field isn't circular, because that's how we chose to integrate it.)

tangotangopapa2

(Original post by

Also, where is the centre of the circles of the electric field? you could put a circular conductor anywhere but surely if there's nothing there, where will be centre be? tangotangopapa2

**lawlieto**)Also, where is the centre of the circles of the electric field? you could put a circular conductor anywhere but surely if there's nothing there, where will be centre be? tangotangopapa2

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