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Question

A rectangular loop with a slide wire of length l is kept in a uniform magnetic field as shown in the figure the resistance of slider is R. Neglecting self-inductance of the loop find the current in the connector during its motion with a velocity v.

A

\frac{B l v}{R_{1} + R_{2} + R}

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B

\frac{B l v (R_{1} + R_{2})}{R + (R_{1} + R_{2})}

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C

\frac{B l v (R_{1} + R_{2})}{R R_{1} + R R_{2} + R_{1} R_{2}}

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D

B l v [\frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{3}}]

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Solution

The correct option is C $\frac{B l v (R_{1} + R_{2})}{R R_{1} + R R_{2} + R_{1} R_{2}}$

$I = \frac{B l v}{R + \frac{R_{1} R_{2}}{R_{1} + R_{2}}} = \frac{B l v (R_{1} + R_{2})}{R R_{1} + R R_{2} + R_{1} R_{2}}$

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