XPQY is a vertical smooth long loop having a total resistance R where PX is parallel to QY and the separation between them is . [2026]

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Solution

Q.
XPQY is a vertical smooth long loop having a total resistance R where PX is parallel to QY and the separation between them is $l$ . A constant magnetic field B perpendicular to the plane of the loop exists in the entire space. A rod CD of length L $(L > l)$ and mass m is made to slide down from rest under gravity as shown in the figure. The terminal speed acquired by the rod is _______ m/s. (g = acceleration due to gravity) [2026]

1 $\frac{2 m g R}{B^{2} L^{2}}$

2 $\frac{m g R}{B^{2} l^{2}}$

3 $\frac{8 m g R}{B^{2} l^{2}}$

4 $\frac{2 m g R}{B^{2} l^{2}}$

Ans.
(2)

$At equilibrium (or for terminal velocity)$

$m g = I B ℓ \Rightarrow m g = (\frac{B v ℓ}{R}) B ℓ$

$V = \frac{m g R}{B^{2} ℓ^{2}}$

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