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  4. A solid spherical conductor of radius R has a spherical cavity of radius a (a < R) at its centre. A charge + Q is kept at the centre. The charge at the inner surface, outer surface and at a position r (a < r < R) are respectively

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Q. A solid spherical conductor of radius $R$ has a spherical cavity of radius $a\, (a < R)$ at its centre. A charge $+ Q$ is kept at the centre. The charge at the inner surface, outer surface and at a position $ r\, (a < r < R)$ are respectively

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Solution:

The solid conductor with a cavity is shown in figure.
image
The inner surface of cavity will be $-Q$ due to induction. At outer surface, the charge will be $+Q$ and at a point between $P$ at a position $r(a < r < R)$ will be zero.