Rotating Coil in a Magnetic Field

If we have a rectangle of wire that has an area of A and we place it in a magnetic field of flux density B, we have seen that the amount of flux flowing through the wire depends on the angle between it and the flux lines.

The flux linkage at an angle θ from the perpendicular to the magnetic field is given by:

From our lessons on circular motion we established that the angular speed is given by which can be rearranged to and substituted into the equation above to transform it into:

When t = 0 the wire is perpendicular to the field so there is a maximum amount of flux.

At 1 the flux linkage is a maximum in one direction. There is the lowest rate of change at this point.

At 2 the flux linkage is zero. There is the biggest rate of change at this point

At 3 the flux linkage is maximum but in the opposite direction. The lowest rate of change occurs here too.

At 4 the flux linkage is zero. There is the biggest rate of change at the point too but in the opposite direction.

Next lesson we will be looking at inducing an e.m.f. using a wire and a magnetic field. The size of the e.m.f. depends on the rate of change of flux linkage.