Question

A thin metallic spherical shell contains a charge $Q$ on it. A point charge $q$ is placed at the center of the shell and another charge $q_1$ is placed outside it. All three charges are positive. What is the force on the charge at the center?

Answer 1

Step 1: Force on charge

1. The metallic spherical shell acts as a shield and does not allow the electric field caused by outside charges to pass through it due to electrostatic shielding.
2. As a result, the electric field inside the shell caused by $Q$ and $q_1$ is zero.

Mathematical representation:

$\mathrm{F}=\mathrm{qE}$

Here,

$\mathrm{F}$ is the force experienced.

$\mathrm{q}$ is the charge.

$\mathrm{E}$ is the electric field intensity.

Step 2: Electrostatic shielding

1. Electrostatic shielding operates in the case of closed metallic surfaces with cavities where the external field has no effect on the internal contents and the internal field has no effect on the external contents.
2. All the charges lie on the surface of the charged sphere. If a gaussian surface is drawn within the sphere, there will not be any charge within the surface. Therefore, the electric field strength inside a sphere is zero.
3. Since $E=0$ inside the sphere, the force acting on the charge $q$ is $F=0$

Hence, no force will act on the charge $q$ at the center.