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Stationary Electron in changing magnetic field

  1. Dec 16, 2009 #1
    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.
  2. jcsd
  3. Dec 16, 2009 #2
    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
  4. Dec 17, 2009 #3

    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.
  5. Dec 17, 2009 #4
    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?
    Last edited: Dec 17, 2009
  6. Dec 17, 2009 #5
    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.

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