Consider the force F on a charge ' q'

Question:

Consider the force $\mathrm{F}$ 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?

1. (1) $\mathrm{F}=\frac{1}{4 \pi \varepsilon_{0}} \frac{Q q}{R^{2}}$ for $r 2. (2)$\frac{1}{4 \pi \varepsilon_{0}} \frac{Q q}{R^{2}}>\mathrm{F}>0$for$r

3. (3) $\mathrm{F}=\frac{1}{4 \pi \varepsilon_{0}} \frac{Q q}{R^{2}}$ for $r>R$

4. (4) $\mathrm{F}=\frac{1}{4 \pi \varepsilon_{0}} \frac{Q q}{R^{2}}$ for all $r$

Correct Option: , 3

Solution:

(3) For spherical shell

$E=\frac{1}{4 \pi \varepsilon_{0}} \frac{Q}{r^{2}}$            (if $r \geq R$ )

$=0$                                                                                 (if $r Force on charge in electried field,$F=q E\therefore F=0 \quad($For$r

$F=\frac{1}{4 \pi \varepsilon_{0}} \frac{Q q}{r^{2}}$    (For $r>R$ )