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Does a magnetic field moving relative to a stationary charge act on it?

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  • $\begingroup$ Yes, but when I saw the comment I got confused, So I asked. $\endgroup$
    – RaMathuzen
    Jun 23, 2020 at 8:06

2 Answers 2

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Yes.

Two ways of thinking about this.

(Let’s assume for simplicity the magnetic field is generated by a magnet).

  1. Move to a frame of reference comoving with the magnet. Now the field is stationary and the charge is moving. So there will be a Lorentz force $q\mathbf{v}\times\mathbf{B}$.

  2. Maxwell’s equations tell you that a time varying magnetic field generates an electric field, $\partial_t \mathbf{B} \propto \nabla \times \mathbf{E}$. That will in turn exert a force on the charge $q\mathbf{E}$.

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You can always change the frame of reference such that it is the other way around, since no frame is special. So you are to expect a force acting on the charge. However, in the rest frame of the charge, the magnetic field becomes an electric field in some sense, so you still get a force on the charge, but now it is an electric force. This is one of the reasons why special relativity was postulated.

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