Question

A spherical shell of radius R is uniformly charged to a surface charge density σ.

1. State the theorem which can be used to find the electric field outside the shell.

2. Using the theorem arrive at an expression for electric field at a distance r from the centre of the spherical shell.

3. It is safe to be inside a vehicle rather than outside, even when there is lightning and thunder. 

Answer 1

1. Gauss’s theorem states that the total electric flux over a closed surface is \(\frac{1}{\varepsilon_0}\) times the total charge enclosed by the surface.

2. Field due to A uniformly charged thin spherical shell:

Consider a uniformly changed hollow spherical conductor of radius R. Let ‘q’ be the total charge on the surface.

To find the electric field at P (at a distance r from the centre), we imagine a Gaussian spherical surface having radius r. Then, according to Gauss’s theorem we can write,

\(\int\overrightarrow E.d\overrightarrow s=\frac{1}{\varepsilon_0}q\)

The electric field is constant, at a distance ‘r’. So we can write,

\(E\int ds=\frac{1}{\varepsilon_0}q\)

\(E 4\pi r^2=\frac{1}{\varepsilon_0}q\)

E =\(\frac{1}{4\pi \varepsilon_0}\frac{q}{r^2}\)

Case -1: Electric field inside the shell is zero.

Case – II: At the surface of shell r = R

∴ E = \(\frac{1}{4\pi \varepsilon_0}\frac{q}{R^2}\)

3. Inside a spherical shell electrical field is zero. This is called electrostatic shielding. Hence it is safe to be inside a vehicle rather than outside.