Consider a coil of wire rotating in a uniform magnetic field, of flux density, B, as shown below.

When the coil is in the position shown in the diagram, side 2 is moving down and side 1 is moving up. We can use Fleming’s right hand rule to decide that end q will (at that instant) be the positive terminal of the generator.

When the coil has rotated through half a turn, end p will be the positive terminal.

Therefore, a coil of wire rotating in a magnetic field has an alternating emf induced in it.

To connect the coil to a light bulb (or any other component) brushes made of carbon make contact with slip rings made of brass, as shown in the next diagram.

Consider a coil having N turns, rotating in a magnetic field of uniform flux density, B. The area of the coil is A and the angle between the normal to the plane of the coil and the field is a.

If the angular velocity is w, then a = wt, so the flux linkage at any time, t, is given by

Therefore, the induced emf at any instant is given by

Now,

represents the slope of a graph of cos wt against t.

It can easily be shown that the slope of a graph of cos wt against t is equal to –wsin wt so the induced emf is given by

Graph of induced emf against time

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