The diagram shows a semicircular ring carrying uniformly distributed charge +2μC on it. The radius of the ring is 4cm. A point charge +2μC is taken slowly from the point (0, 0, 8cm) to (0, 8cm, 0). The magnitude of work done is equal to 4J. After fixing the charge at its new position, the ring is rotated in anticlockwise sense about the X-axis as seen from (16cm, 0, 0) by an angle π/2. What is the magnitude of work done by electric field during the rotation of the ring?

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Question

The diagram shows a semicircular ring carrying uniformly distributed charge +2μC on it. The radius of the ring is 4cm. A point charge +2μC is taken slowly from the point (0, 0, 8cm) to (0, 8cm, 0). The magnitude of work done is equal to 4J. After fixing the charge at its new position, the ring is rotated in anticlockwise sense about the X-axis as seen from (16cm, 0, 0) by an angle π/2. What is the magnitude of work done by electric field during the rotation of the ring?

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$W_{A \to B}^{ex .} = W = U_{B} - U_{A}$

$W = U_{B} - \frac{Q^{2}}{4 {πε}_{0} \sqrt{5} R} . . . . . (1)$
At new position
$U'_{B} = \frac{Q^{2}}{4 {πε}_{0} \sqrt{5} R}$
Work done = U'_B = U_B = –W = – 4J