Does a time varying magnetic field in vacuum produce electric field or not?

[yashraj]

TL;DR

Will a charged particle at rest experience a force on it due to the electric field produced by a time varying magnetic field in vacuum.

Suppose there is very long current carrying wire. A charged particle is present somewhere around it. The current in the wire varies with time, thus by biot-savart's law there should be time varying magnetic field. I want to know that will this time varying magnetic field produce electric field or not ? If it produces electric field then the charged particle initially present at rest will experience a electric force on it.

 

[kuruman]

TL;DR Summary: Will a charged particle at rest experience a force on it due to the electric field produced by a time varying magnetic field in vacuum.

Suppose there is very long current carrying wire. A charged particle is present somewhere around it. The current in the wire varies with time, thus by biot-savart's law there should be time varying magnetic field. I want to know that will this time varying magnetic field produce electric field or not ? If it produces electric field then the charged particle initially present at rest will experience an electric force on it.

Yes.

 

[yashraj]

Yes.

How ? I mean initially charge was at rest. So whatever be the magnetic field either changing or constant, the force on charge due to this magnetic field according to this relation F = q*(VxB) should be zero, so this charge at rest shouldn't experience force due to magnetic field at this instant. What doubt right now i am having is that how could changing magnetic field can produce electric field in vacuum ?

 

[Ibix]

How ?

Because, as you noted, a time-varying magnetic field implies the presence of an electric field. So the particle moves under the influence of the electric field.

What doubt right now i am having is that how could changing magnetic field can produce electric field in vacuum ?

I guess the question is why you think it shouldn't.

 

[yashraj]

Because, as you noted, a time-varying magnetic field implies the presence of an electric field. So the particle moves under the influence of the electric field.
I guess the question is why you think it shouldn't.

Thank you for the clarification. But I don't understand that if at a point "A" there is only one field that is magnetic field "B" and this magnetic field is changing with time then would there be electric field produced at point "A" or not ?

 

[kuruman]

Thank you for the clarification. But I don't understand that if at a point "A" there is only one field that is magnetic field "B" and this magnetic field is changing with time then would there be electric field produced at point "A" or not ?

Not quite. Roughly speaking, magnetic field lines varying in time are sources of circulating electric field lines about them. If free charges happen to be around, they will be accelerated by them. This is the Maxwell-Faraday equation, one of the 4 Maxwell's equations. read about it here.

 

[Ibix]

Thank you for the clarification. But I don't understand that if at a point "A" there is only one field that is magnetic field "B" and this magnetic field is changing with time then would there be electric field produced at point "A" or not ?

You can't have "only a magnetic field that is changing" - there will always be an electric field if there is a changing magnetic field. You can have an unchanging magnetic field and no electric field, and then you can start the magnetic field changing and an electric field will appear, if that's what you mean.

I think that it's probably better to think of the electromagnetic field, some components of which we call the electric field and some we call the magnetic field, rather than thinking of the electric and magnetic fields as separate things.

 

[yashraj]

You can't have "only a magnetic field that is changing" - there will always be an electric field if there is a changing magnetic field. You can have an unchanging magnetic field and no electric field, and then you can start the magnetic field changing and an electric field will appear, if that's what you mean.

I think that it's probably better to think of the electromagnetic field, some components of which we call the electric field and some we call the magnetic field, rather than thinking of the electric and magnetic fields as separate things.

Your answer now gave me some better clarity. Thank you for helping me.