0

Suppose there is a space with constant magnetic field, and a charged particle is moving in that space with a constant velocity, ofcourse it experiences a magnetic force and gets deflected.
But the particle it not necessarily moving wrt all frames. There may be some frame for which the particle doesn't move at all but still gets deflected. How is this possible, there must be some velocity for the particle to experience any deflection under influence of a magnetic field?
Also a still particle in the same space doesn't experience any deflection. True, but the same particle may be moving wrt to some other frame without experiencing a magnetic force, so here we have a velocity but no magnetic force case.

I remember I have used the relation $|F| = qv|B|$ a lot before, but I am afraid to use it any more, these things are really confusing.

Abhishek Verma
  • 388

2 Answers2

1

The answer has to do with relativity. You are correct in saying that in the particle's rest frame its velocity is zero and so there's no magnetic force, but the particle should still move. Special Relativity tells us that the electric and magnetic fields are really two aspects of the same thing instead of being distinct entities. When we change our reference frame, they transform into each other so as to make sure the overall effect is still the same.

In this example, what will happen is that an electric field will appear, and it will have the correct magnitude and direction so the charge will move exactly like it would if you looked at it from a frame in which it's moving. The Lorentz force law, $\mathbf{F} = q(\mathbf{E}+\mathbf{v}\times\mathbf{B})$, is still correct, but $\mathbf{E}$ and $\mathbf{B}$ will change from one frame to another, and that's what you need to take into account.

If you want to read in more detail about this, you should check out Feynman's Lectures on Physics, Vol II, among others.

Javier
  • 28,106
0

In the rest frame of the electron it experiences only an electric force even though there may also be a magnetic field there. These two forces transform generally into another pair of electric and magnetic forces where the electron is now moving, and therefore experiences both, although either could be zero for some unique frame depending on what they are in the rest frame of the electron.

Larry Harson
  • 5,278