A conducting square loop of side l and resistance R moves in its plane with a uniform velocity v perpendicular to one of its sides. A uniform and constant magnetic field B exists along the perpendicular to the plane of the loop as shown in figure. The current induced in the loop is
(a) Blv/R clockwise
(b) Blv/R anticlockwise
(c) 2Blv/R anticlockwise
(d) zero.

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Solution

(d) zero

Figure (a) shows the square loop moving in its plane with a uniform velocity v.

Figure (b) shows the equivalent circuit.

The induced emf across ends AB and CD is given by
$E = B v l$

On applying KVL in the equivalent circuit, we get

$E - E + i R = 0 \Rightarrow i = 0$

No current will be induced in the circuit due to zero potential difference between the closed ends.

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