Stationary Electron in changing magnetic field

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Discussion Overview

The discussion centers on the behavior of a stationary electron in a changing magnetic field, particularly whether it experiences a force when the magnetic field varies with time. The scope includes theoretical considerations of electromagnetic induction and the effects of both time-varying and spatially varying magnetic fields.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant notes that a stationary electron in a uniform magnetic field experiences no force but questions the effect of a time-varying magnetic field.
  • Another participant asserts that Faraday's Law of induction creates an electric field in the vicinity of a changing magnetic field, which can accelerate free electrons.
  • A different participant provides the equation relating the induced electric field to the changing magnetic field, suggesting that both electric and magnetic forces can act on the electron.
  • One participant seeks clarification on the mathematical expressions used and questions how to calculate induced electromotive force (emf) for a single charged particle.
  • Another participant describes a specific scenario involving magnetic flux and induced electric fields, emphasizing the necessity of both time and spatial variation of the magnetic field for the force to act on the electron.
  • Clarification is provided regarding the term 'rot E', indicating it refers to the rotation in vector analysis.

Areas of Agreement / Disagreement

Participants express varying views on the conditions under which a stationary electron experiences force in a changing magnetic field. There is no consensus on the specific calculations or interpretations of the effects of time and spatial variations of the magnetic field.

Contextual Notes

Participants highlight the need for clarity in mathematical expressions and the implications of different types of magnetic field variations. The discussion includes unresolved questions about the calculation of induced emf for individual charged particles.

perryizgr8
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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.
 
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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
 
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.
 
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:
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
 

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