# Electromagnetic induction by a coil

Moving magnet produces current in a coil and the galvanometer shows deflection because of the change in magnetic flux. What if the coil is moved why won't it produce an induced current?

• Are you sure it won't? – probably_someone Nov 28 '18 at 11:11
• "moving magnet": moving relative to what? Answer: moving relative to the coil. – Andrew Steane Nov 28 '18 at 11:31

Moving a coil towards (or away from) a magnet will produce an emf in the coil, as will moving the magnet towards (or away from) the coil.

After all, whether it is the magnet that moves, or the coil, depends only on our frame of reference, and that can't alter the phenomenon of induction of an emf.

Oddly, or so it seemed to Einstein, the classical laws of electromagnetism account for the phenomenon differently according to whether you are in the reference frame in which the magnet is stationary, or the frame in which the coil is stationary. In both cases the emf arises from the so-called Lorentz force on the electrons in the coil:$$\mathbf {F}=(-e)(\mathbf{E}+\mathbf{v} \times \mathbf{B}).$$

In the frame in which the coil is stationary and the magnet moving (the frame you seem to be comfortable with) the electrons experience a force due to the electric field, E set up by the moving magnet, that is due to the first term on the right in the Lorentz force equation. [The electric field is linked to the changing magnetic field by the Maxwell-Faraday equation,$$\text{curl}\ \mathbf{E}=-\frac{\partial \mathbf{B}}{dt}$$].

In the frame in which the coil is moving and the magnet stationary, the coil is cutting lines of flux due to the magnet, and the electrons in the coil experience a force due to the second term on the right in the Lorentz force equation.

In practical cases, we needn't worry too much about frame of reference, because there's a mathematical description of e-m induction that fits both frames of reference, namely$$\mathscr{E}=-(n)\frac{d \Phi}{dt}.$$ $$\Phi$$ is the magnetic flux linked with the coil, and it changes by the same amount whether we move the magnet towards the coil or the coil towards the magnet (so $$\frac{d \Phi}{dt}$$ will be the same as long as we're not dealing with speeds of movement comparable with the speed of light!).

You will find that this topic is explored fairly fully on the Physics Stack Exchange.