Question

Consider the force $F$ on a charge ${}^{\prime }{q}^{\prime }$ due to a uniformly charged spherical shell of radius $R$ carrying charge $Q$ distributed uniformly over it. Which one of the following statements is true for $F$, if ${}^{\prime }{q}^{\prime }$ is placed at distance $r$ from the centre of the shell ?

• A. $F=\frac{1}{4\pi {\epsilon }_0}\frac{Qq}{r^2}$ for $r>R$
• B. $\frac{1}{4\pi {\epsilon }_0}\frac{qQ}{R^2}>F>0$ for $r<R$
• C. $F=\frac{1}{4\pi {\epsilon }_0}\frac{Qq}{r^2}$ for all $r$
• D. $F=\frac{1}{4\pi {\epsilon }_0}\frac{Qq}{R^2}$ for $r<R$

Answer 1

Answer: (A)

Inside the shell
$E=0$
hence $F=0$
Oustside the sheell
$E=\frac{1}{4\pi {\epsilon }_0}\frac{Q}{r^2}$
hence $F=\frac{1}{4\pi {\epsilon }_0}\frac{Qq}{r^2}$ for $r>R$