# Inducing emf in a circular coil

Magnetic field lines from a moving magnet induces emf in a circular coil.What does the velocity of the magnet have to do with the emf induced?Increasing the velocity of the magnet doesn't increase the amount of field lines entering the coil right?

• Emf induced is directly proportional to rate of change of flux, not field. – AlphaLife Nov 18 '17 at 15:17

According to Faraday's Law (ignoring Lenz's law, which isn't relevant here):

$$\epsilon = \frac{\Delta N\phi}{\Delta t}$$

Therefore, the EMF ($\epsilon$) is proportional to the rate of change of magnetic flux linkage ($N\phi)$. Magnetic flux ($\phi$) is just the number of field lines (imaginary lines denoting the strength and direction of a magnetic field) through the coil and $N$ is the number of turns there are in your coil.

Anyway, this is what the flux around a bar magnet looks like: If you move this bar magnet towards the coil of wire, the number of field lines passing through the coil will change. In other words, the total magnetic flux (and therefore magnetic flux linkage) through the coil is changing. This change is what induces an EMF.

Note: the field lines are stronger closer to the magnet and extend away from it. So when the magnet is far away only a few outer field lines are passing through the coil, but as the magnet comes closer more of the closer field lines pass through the coil as well, resulting in a change in flux linkage through the coil.

A change in flux may induce an EMF across each turn in the coil, but what determines the size of this induced EMF is the rate of change of flux linkage.

So now think logically: If the magnet moves towards the coil with a fast velocity, the rate at which the flux through the coil is changing will be very fast, right? That's why the velocity of the magnet is important. An EMF will be produced whether the magnet is moving quickly or slowly, but it's the magnitude of the EMF that depends on the rate of change of flux, which is dependant on many things, including the speed of the magnet (or the speed of coil moving towards the magnet - same difference).

If you want to know more about whether the EMF induced is positive or negative (remember, electromagnetic induction produces an AC current), then look up Lenz's law.