Question

A solid sphere of radius R₁ and volume charge density r = $\frac{\rho_{0}}{r}$ is enclosed by a hollow sphere of radius R₂ with negative surface charge density s, such that the total charge in the system is zero, r₀ is a positive constant and r is the distance from the centre of the sphere. The ratio $\frac{R_{2}}{R_{1}}$ is –

• A. $\frac{\sigma}{\rho_{0}}$
• B. $\sqrt{2\sigma/\rho_{0}}$
• C. $\sqrt{\rho_{0}/(2\sigma)}$
• D. $\frac{\rho_{0}}{\sigma}$

Answer 1

Answer: (C)

$\sqrt{\rho_{0}/(2\sigma)}$

Answer 2

For solid sphere

q₁ = Q r =

= 4pr₀ $\int _ { 0 } ^ { \mathrm { R } _ { 1 } } \mathrm { rdr }$

= …(1)

q₂ = –4ps

Q q₁ + q₂ = 0 \ $\frac { \mathrm { R } _ { 2 } } { \mathrm { R } _ { 1 } } = \sqrt { \frac { \rho _ { 0 } } { 2 \sigma } }$