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Q.

An insulating long cylinder is uniformly charged on its lateral surface with surface charge density $σ$ . On its flat surface, a circular and conducting loop of radius r is placed coaxially as shown in the figure. There is no friction between the cylinder and the loop. The cylinder is being rotated with a uniform angular acceleration $α$ about its axis. The relationship between the compressive force F in the loop with time t or the compressive force F with surface charged density or the compressive force F with radius of the loop is best represented by

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a

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b

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c

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d

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answer is B.

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Detailed Solution

Let $R_{s}$ is resistance of the loop field through loop
$B = (μ_{0} R σ ω) / 2 = (μ_{0} σ R α t) / 2$
Induced emf in the loop $e = (π r^{2} μ_{0} σ R α / 2)$
Current In the loop $i = \frac{e}{R_{s}} = \frac{π r^{2} μ_{0} σ R α}{2 R_{s}}$
$F = i B r = \frac{π r^{2} μ_{0} σ R α}{4 R_{s}} μ_{0} σ R α t r F = (\frac{π μ_{0}^{2} σ^{2} α^{2} R^{2} r^{3}}{4 R_{s}}) t$

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An insulating long cylinder is uniformly charged on its lateral surface with surface charge density σ. On its flat surface, a circular and conducting loop of radius r is placed coaxially as shown in the figure. There is no friction between the cylinder and the loop. The cylinder is being rotated with a uniform angular acceleration α about its axis. The relationship between the compressive force F in the loop with time t or the compressive force F with surface charged density or the compressive force F with radius of the loop is best represented by