Stationary Electron in changing magnetic field

[perryizgr8]

I know that a stationary electron kept in uniform magnetic field experiences no force. But will it experience force if the field suddenly starts varying with time?
Any help will be appreciated.

 

[Bob S]

Certainly. Faraday's Law of induction produces an electric field near (as well as in) a rapidly changing magnetic field. The secondary winding of a transformer is an example. In vacuum, a changing magnetic field can accelerate free electrons. The betatron electron (particle) accelerator accelerates electrons by the electric (Faraday induction) field due to a changing magnetic field.
Bob S

 

[sweet springs]

Hi.

rot E = -∂B/∂ｔ. Electric field E induced by time-varying magnetic field B works on the electron.

F = m・grad B. In case of space-varying magnetic field, magnetic force also works on electron with spin magnetic momentum m.
　
Regards.

 

[perryizgr8]

Hi. Thanks for the replys. Sweet spring, I'm viewing with my phone and don't have access to a computer right now and I can't see the formulas that you wrote. Can you rewrite them without using special characters?
Usually to calculate induced emf I multiply dB/dt with the area of a loop. But when there is only a single charged particle what do I do to get the emf and subsequentally the force on the particle?
Also what does 'rot E' mean?

 

[sweet springs]

Hi. Let me explain in some specific case. Magnetic flux Φ is bundled in the rod shape and change in time. Outside of the bundle, B = 0 and induced electric field E appears in tangent direction of a circle around the bundle. E works force on an electron there. Not only time but also space variation of B is required in this case. I assume it is so in general case.

rot is the abbreviation of ”rotation” in vector analysis.

Regards