Question

An electric dipole is placed at the centre of a hollow sphere. The electric field intensity at a point outside the sphere at a distance $x$ metres from the centre will be:
(charge of dipole is $q$ and radius of sphere is $R$)

• A. $\frac{kq}{x^3}$
• B. $\frac{kqx}{R^3}$
• C. $\frac{kq}{R^2}$
• D. Zero

Answer 1

The correct option is D Zero

The electric dipole is made of opposite charges $q$ and $–q$ separated by a distance $d$. Let us assume that $d$ is very small compared to the radius of the hollow sphere.


Draw a Gaussian surface at a distance $x$ from the centre of hollow sphere.
Charge enclosed in Gaussian surface, $q_{en}=q+(-q)=0$

Let $\overrightarrow{E}$ be the electric field and $\overrightarrow{dA}$ be an elemental Gaussian surface area.
Applying Gauss's law,
${\varphi }_{net}=\overrightarrow{E}.\overrightarrow{dA}=\frac{q_{en}}{{ϵ}_0}=0$
$\therefore E=0$

Thus, the electric field outside the sphere containing the dipole is zero.

Hence, option (d) is correct.