Time varying magnetic field and electron

[pedro-filipe]

I am a bit depressed, I have just finished my PhD as a physicist and cannot work out this simple question.

I am trying to find out what happens to a static electron in a time varying magnetic field.

This is my understanding:

There are two laws, the Lorentz's force, for moving charges, and the Faraday's Law for time varying magnetic fields.

The electron is not moving, therefore v=0, and Lorentz force = 0

From the Faraday's law, a time varying magnetic field creates a flow of electrons on a closed circuit. But I am not sure what happens to a lonely charge.

Any help and or corrections is appreciated.

Thanks.

 

[phyzguy]

If there is a time-varying magnetic field, then there is an electric field, so the Lorentz force is not zero.

 

[pedro-filipe]

I see. Thanks, I was in fact looking at an incomplete formula for the Lorentz formula, without the q E component.

I will try and workout what the E field looks like.

Thanks for your help phyzguy.

 

[Bob S]

There is no Lorentz force on a static electron.

There is an electric field force on a static electron from the Faraday Law. The transformer and the betatron electron accelerator are good examples. See

http://teachers.web.cern.ch/teachers/archiv/HST2001/accelerators/teachers notes/betatron.htm

Bob S

 

[K^2]

$$\nabla\times{E} = -\frac{\partial{B}}{\partial{t}}$$

 

[Antiphon]

Extra credit: if B=-t along the positive Z axis, what is the resulting force on an electron located at the origin?