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
$E=\frac{1}{4 \pi \varepsilon_{0}} \frac{Q}{x^{2}}$
If the radius of the sphere is
$R, Q=\sigma 4 \pi R^{2}$
$\therefore E=\frac{1}{4 \pi \varepsilon_{0}} \frac{\sigma 4 \pi R^{2}}{x^{2}}=\frac{\sigma R^{2}}{\varepsilon_{0} x^{2}}$
This is inversely proportional to square of the distance from the centre. It is as if the whole charge is concentrated at the centre.