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