Electric field at the surface, of a conducting shell of radius 'r' is measured as X. Electric field at a distance 3r from the centre of the shell is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( \displaystyle\frac{X}{9} \)
By Gauss's law, the field outside a charged conducting shell is the same as if the whole charge \( Q \) were at its centre, so it falls as the inverse square of the distance from the centre.
\( \displaystyle E = \frac{1}{4\pi\varepsilon_0}\,\frac{Q}{d^{2}} \;\Rightarrow\; E \propto \frac{1}{d^{2}} \)
At the surface \( d = r \) and \( E = X \). At \( d = 3r \):
\( \displaystyle \frac{E}{X} = \frac{r^{2}}{(3r)^{2}} = \frac{1}{9} \)
\( \displaystyle E = \frac{X}{9} \)