Question 37 of 311

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$F=\dfrac{1}{4\pi {\in }_{0}}\dfrac{Qq}{{R}^{2}}$ for $r\lt R$B$\dfrac{1}{4\pi {\in }_{0}}\dfrac{qQ}{{R}^{2}}\gt F\gt 0$ for $r\lt R$C$F=\dfrac{1}{4\pi {\in }_{0}}\dfrac{Qq}{{r}^{2}}$ for $r\gt R$D$F=\dfrac{1}{4\pi {\in }_{0}}\dfrac{Qq}{{r}^{2}}$ for all $r$

Show answer and solution▾

Answer: (C) $F=\dfrac{1}{4\pi {\in }_{0}}\dfrac{Qq}{{r}^{2}}$ for $r\gt R$

$E=O, r\lt R$
$=\dfrac{qQ}{{r}^{2}}, r\geq R$
Inside $F=0$ and outside sphare
$F=\dfrac{2Qq}{4\pi {\in }_{0}{r}^{2}}$