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(D) According to the property of a conducting shell,if a point charge $q_A$ is placed at the center of a cavity of radius $a$,an equal and opposite ch

Vedclass · Accepted Answer

$A$ and $C$ both.

Vedclass · Answer

(D) According to the property of a conducting shell,if a point charge $q_A$ is placed at the center of a cavity of radius $a$,an equal and opposite charge $-q_A$ is induced on the inner surface of the shell.Given that the inner surface has a uniform charge density $-\sigma$,the total charge on the inner surface is $Q_{inner} = -\sigma 	imes (4\pi a^2)$.Since the induced charge must be equal to $-q_A$,we have $-q_A = -\sigma(4\pi a^2)$,which implies $q_A = 4\pi \sigma a^2$.Since $\sigma$,$a$,and $\pi$ are positive,$q_A$ must be positive.Thus,both the statement that the charge is positive and the statement that its magnitude is $4\pi \sigma a^2$ are correct.Therefore,the correct option is $D$.

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