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So at school we have this teacher who said something along the lines of the following:
Assume there exists a charge in a field free environment (no electric or magnetic field) initially, say a room in which the charge is placed.
He said that if he were to switch on a source of uniform magnetic field, the charge would experience a force (to our surprise actually, since the charge isn't moving) and start moving. Every single one of us in the class said the charge wouldn't move.

Is he wrong? Or are we missing something?

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Your teacher is correct. Recall Faraday's law:

$\nabla\times\vec{E} = -\frac{\partial\vec{B}}{\partial t}$

When the field is switched on, the changing $\vec{B}$ field induces an electric field, which is enough to accelerate the particle. The magnetic field does not make the particle move ($\vec{B}$ never does any work!), but the induced electric field does (which is quite sneaky). If instead your teacher turned on the magnetic field and THEN placed a particle at rest in the room, there would be no motion.

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