# Torque on a charged ring

I have been studying electromagnetic induction. As I understand, a magnetic field will exert a force on a moving charge. What I would like to know is whether a changing magnetic field will exert a force on a stationary charge?

For example, consider a charged ring that is placed in a magnetic field. I know that if a current was flowing through this ring, the torque exerted by a magnetic field would be given by $I(\hat{A} \times \hat B)$. Where I is the current flowing in the circuit, $A$ is the area of the coil and $B$ is the magnetic field.

As I understand, a current is just a flow of charge, or in other words, changing charge. Thus, a changing magnetic field should exert a torque on a stationary charge. Is this right?

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• That's how an induction motor works, isn't it? – CuriousOne May 12 '16 at 7:57
• @CuriousOne Isn't the torque in an induction motor developed due to a changing CURRENT rather than a changing magnetic field? – Gummy bears May 12 '16 at 8:34
• You can't get a current without a changing magnetic field, unless you have a superconductor. – CuriousOne May 12 '16 at 9:18

I mean, the force $F_L$ of a magnetic field on a moving charge, and the force from a changing magnetic field on a static charge. Both lead to the rule, that the emf is equal to the derivative of the magnetic flux. But it seems, there are two distinct reasons for this rule, not obviously derivable one from the other.
• well, not one formula, you need to know the properties of the field $B(t)$ and your charges (the positions). Then, yes, en.wikipedia.org/wiki/Maxwell's_equations ;) - just calculate the resulting E-field, and the force is straightforward $E\cdot q$ – Ilja May 12 '16 at 12:06