Question

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 $–Q$. The surface charge density on the inner and outer surfaces of the spherical shell will respectively be

• A. $-\frac{2Q}{4\pi b^2},\frac{Q}{4\pi c^2}$
• B. $-\frac{Q}{4\pi b^2},\frac{Q}{4\pi c^2}$
• C. $0,\frac{Q}{4\pi c^2}$
• D. None of the above

Answer 1

The correct option is A $-\frac{2Q}{4\pi b^2},\frac{Q}{4\pi c^2}$

Surface charge density $\left(\sigma \right)=\frac{\text{charge}}{\text{surface area}}$

So ${\sigma }_{\text{inner}}=\frac{-2Q}{4\pi b^2}$ and ${\sigma }_{\text{outer}}=\frac{Q}{4\pi c^2}$