Question

Consider the force $F$ on a charge $'q'$ 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 $'q'$ is placed at distance $r$ from the centre of the shell ?

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

Answer 1

Answer: (A)

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