A semi-circular ring of mass \( m \) and radius \( R \) with linear charge density \( \lambda \)...

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A semi-circular ring of mass \( m \) and radius \( R \) with linear charge density \( \lambda \), hinged at its centre is placed in a uniform electric field as shown in the figure-1.451. If the ring is slightly rotated about \( O \) and released find the time period (in sec) of oscillation. Take \( m=8 \mathrm{~kg}, \lambda=2 \mathrm{C} / \mathrm{m} \) and \( E=2 \mathrm{~N} / \mathrm{c} \). Assume that coil is rotated in its own plane :
Figure \( 1.451 \)
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