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Does a stationary electron in magnetic field experience Lorentz force?

  1. Apr 21, 2012 #1
    1. The problem statement, all variables and given/known data

    If an electron is stationary in a magnetic field, will it experience a Lorentz force?


    2. Relevant equations

    3. The attempt at a solution

    The total vector force (Lorentz force - F) is
    F = Fe + Fm = Q(E + u X B)


    The Lorentz force can also be written in terms of Newton’s law such that
    F = ma = m (du/dt) = Q(E + u X B)

    ∴ Since the electron is stationary, acceleration equals zero and the so the electron does not experience a Lorentz Force.
     
  2. jcsd
  3. Apr 21, 2012 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Well, I not sure I like "acceleration equal zero and so the electron does not experience a Lorentz Force". If an electron is constrained to be stationary, then both velocity and acceleration are 0 so the net force is 0. Just saying that something is stationary is not enough to show that a particular force, rather than the net force, is 0.

    However, in this problem, since there is no electrical field, E, and the velocity vector, u, is 0, it follows that F= Q(0+0x B)= 0 and, for that reason, there is no Lortentz force.
     
  4. Apr 21, 2012 #3
    Thank you HallsofIvy!
     
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