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

Answer 1

The correct option is C $F=\frac{1}{4\pi {\epsilon }_0}\frac{Qq}{r^2}\text{for}r>R$

For uniformly distributed spherical shell,

$E=\frac{1}{4\pi {\epsilon }_0}\frac{Q}{r^2}(\text{if}r\ge R)$

$E=0$ $(\text{if}r<R)$

So, force on charge in electried field,
$F=qE$

$F=0(\text{For}r<R)$
And,
$F=\frac{1}{4\pi {\epsilon }_0}\frac{Qq}{r^2}(\text{For}r>R)$

Hence, option $\left(\text{C}\right)$ is correct.