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 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

Answer: (A)

$- \frac{2Q}{4\pi b^{2}},\frac{Q}{4\pi c^{2}}$

Answer 2

Surface charge density (σ) $= \frac{\text{Charge}}{\text{Surface area}}$

So $\sigma_{inner} = \frac{- 2Q}{4\pi b^{2}}$ and $\sigma_{Outer} = \frac{Q}{4\pi c^{2}}$