Question

Consider a thin spherical shell of radius $R$ consisting of uniform surface charge density $\sigma$ The electric field at a point of distance $x$ from its centre and outside the shell is

• A. inversely proportional to $\sigma$
• B. directly proportional to $x^2$
• C. directly proportional to $\sigma$
• D. inversely proportional to $x^2$

Answer 1

Answer: (D)

For a thin uniformly charged spherical shell, the field points outside the shell at a distance $x$ from the centre is
$E=\frac{1}{4\pi {\epsilon }_0}\frac{Q}{x^2}$
If the radius of the sphere is
$R,Q=\sigma 4\pi R^2$
$\therefore E=\frac{1}{4\pi {\epsilon }_0}\frac{\sigma 4\pi R^2}{x^2}=\frac{\sigma R^2}{{\epsilon }_0{x}^2}$
This is inversely proportional to square of the distance from the centre. It is as if the whole charge is concentrated at the centre.