QUESTION #382

# I know for a fact that a moving charge can produce a magnetic field. But I'm curious if a moving magnetic field produce a charge?

'Moving magnetic field' is sort of wrong expression. Magnetic field does not move, but propagate (with the speed of light in vacuum). It can be defined as a function of space and time. When it is only a function of space, it's pronounced as 'constant field.'

I assume that you meant 'dynamic', which changes magnitude and/or direction in time, magnetic field.

The answer is no. Even dynamic magnetic fields can not produce charge (I'll refer electric charge as 'charge' only). Furthermore, nothing known to our knowledge can produce charge. It is absolutely a conserved quantity under ANY circumstances. If charge in a small volume changes in time, it means flow of charge in or out through the surface of this volume, but nothing else! And it is strictly defined by continuity equation in both classical electrodynamics, and relativistic electrodynamics. This equation is a companion to the four well known Maxwell's equations and these 5 equations (can be written in many different ways, and can be found in any text books) are the fundamentals of electrodynamics theory.

A good discussion about charge invariance can be found in 'Classical Electrodynamics by J.D. Jackson, section 11.9 (2nd Ed.)'

Besides being invariant, charge is a discrete quantity, it's always integral multiples of a well measured quantity, which is one third of the charge of electron. And this discreteness is tested very precisely, and there has been no observation which proves otherwise (Numerical figures can be found from the same section given above, although it may be rather old, it's still impressive). At some sense, this observation alone helps the explanation of invariance of charge. If one could produce charge by some kind of phenomena, he could produce -any- amount of charge, by changing the amount of action.
Answered by: Taylan Akdogan, Physics Ph.D. Candidate, M.I.T.

It cannot produce a charge, but it can move an already existing charge.

An electric charge has an associated electric field that is responsible for the force repulsing like charges and attracting opposite ones. If a charge is moved the electric field is moving with it, but this means that the electric field is changing in strength and direction at any given point in space. (Far away from the charge the field tends to zero, that means the changes are negligible as well.) Maxwell's equations (4th) now tell us that electric fields changing in time generate magnetic fields.

Another of the Maxwell equations (the 2nd) tells you that a changing magnetic field induces a electric field that exerts a force on an electric charge which consequently moves.

Electric power generators are based on that principle, only that the turbine usually moves the charges (the electrons in the metal) and the magnetic field is stationary. But from the electrons' point of view the magnetic field is moving and thus creating the electrical field that drives them through the wire.
Answered by: Andreas Engel, Ph.D. Student, Victoria University of Wellington