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A thin wire ring having resistance $r$ is located inside a long solenoid so that their axes coincide. The coefficient of self induction of the solenoid is L and the inductance of the ring is neglected. The solenoid is closed at time $t = 0$ . The total resistance of the circuit is $R$ . The radial force acting per unit length of the ring is maximum at time $t$ given by

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$\frac{L}{R}$

$\frac{2 L}{R}$

$\frac{L}{2 R}$

$\frac{L l n 2}{R}$

answer is D.

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Detailed Solution

$I = \frac{v}{R} (1 - e^{- \frac{R t}{L}}) B = μ_{0} η I$

Current through ring $α \frac{d I}{d t}$

$∴ \frac{d F}{d l} α (1 - e^{- \frac{R t}{L}}) (e^{- \frac{R t}{L}})$ which is maximum when $t = \frac{L l n 2}{R}$

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