Question

A spherical conductor of radius $R$ is charged with $Q$ units of negative charge. The escape velocity of a particle of mass $m$ and charge $q$ from the surface of this conductor is

• A. $\sqrt{\frac{Qq}{2\pi {ϵ}_{0}mR}}$
• B. $\sqrt{\frac{Qq}{4\pi {ϵ}_{0}R}}$
• C. $\sqrt{\frac{Qq}{4\pi {ϵ}_{0}m{R}^2}}$
• D. Escape is not possible.

Answer 1

The correct option is A $\sqrt{\frac{Qq}{2\pi {ϵ}_{0}mR}}$

From conservation of energy,
Total energy at surface is equal to total energy as particle escapes to $\infty$
$T{E}_S=T{E}_F$
$K{E}_S+P{E}_S=K{E}_F+P{E}_F$
$\frac{1}{2}m{v}^2-\frac{1}{4\pi {ϵ}_0}\frac{Qq}{R}=0+0$
$v^2=\frac{Qq}{2\pi {ϵ}_{0}mR}$
$v=\sqrt{\frac{Qq}{2\pi {ϵ}_{0}mR}}$