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A rectangular loop has a sliding connector of length 1.0 m. The loop is situated in a uniform magnetic field $B = 4 T$ perpendicular and into the plane of loop. The resistance of connector is $2 Ω .$ Find the external force $(i n N)$ required to keep the connector moving with a constant velocity $v = 2 m / \sec$

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Detailed Solution

Motional emf $e = B v L = (4) (2) (1) = 8 V$

Current through connector $i = \frac{8}{2 + 2} = 2 A$

Magnetic force on connector $F_{m} = i L B = (2) (1) (4) = 8 N$

To keep the connector with constant velocity, a force of 8 N will be applied towards right.

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