A solid conducting sphere of radius a has a net positive charge 2Q. A conducting spherical shell of inner radius b and outer radius c is concentric with the solid sphere and has a net charge -Q. Surface charge density on the inner and outer surfaces of the spherical shell will be respectively

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$0, \frac{Q}{4 π c^{2}}$

$- \frac{Q}{4 {πb}^{2}}, \frac{Q}{4 π c^{2}}$

$- \frac{2 Q}{4 {πb}^{2}}, \frac{Q}{4 π c^{2}}$

$\frac{Q}{4 π c^{2}}, 0$

answer is A.

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Detailed Solution

Surface charge density $(σ) = \frac{C h a r g e}{S u r f a c e a r e a}$

Due to the sphere the shell will have a charge of $- 2 Q$ on the inner surface of the shell, As the total charge on the shell is $- Q$ , there will be a charge of $+ Q$ on the outer surface of the shell

So, $σ_{inner} = - \frac{2 Q}{4 {πb}^{2}}$

and $σ_{Outer} = \frac{Q}{4 {πc}^{2}}$

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