Question

Figure shows a long U-shaped wire of width l placed in a perpendicular magnetic field B. A wire of length l is slid on the U-shaped wire with a constant velocity v towards right. The resistance of all the wires is r per unit length. At t = 0, the sliding wire is close to the left edge of the U-shaped wire. Draw an equivalent circuit diagram, showing the induced emf as a battery. Calculate the current in the circuit.

Answer 1

The induced emf is given by

e = Bvl

Total resistance, R = r × Total length of the wire

Because the length of the movable wire is l and the distance travelled by the movable wire in time t is vt, the total length of the loop is 2 (l + vt).

∴ e = i × 2r (l + vt)

Bvl = 2ri (l + vt)

\[\Rightarrow i = \frac{Bvl}{2r(l + vt)}\]