Question

A thin metallic spherical shell of radius R carries a charge Q on its surface. A point charge Q/2 is placed at its centre C and an other charge +2 outside the shell at a distance x from the centre as shown in the figure. Find the force on the charge at the centre of shell and at the point A.

Answer 1

The electric field inside a spherical shell is zero thus, the force experienced by the charge at the centre of the shell $C$ will also be zero.

$\therefore \overrightarrow{F_C}=q\overrightarrow{E}$

$\therefore \overrightarrow{F_C}=0$

At Point A,

$|\overrightarrow{F_A}|=2Q\left(\frac{1}{4\pi {ϵ}_0}\frac{\frac{3Q}{2}}{x^2}\right)$

$|\overrightarrow{F_A}|=\frac{3Q^2}{4\pi {ϵ}_0{x}^2}$