Question

An electric dipole is placed at the centre of a sphere. Mark the correct options.
(a) The flux of the electric field through the sphere is zero.
(b) The electric field is zero at every point of the sphere.
(c) The electric field is not zero anywhere on the sphere.
(d) The electric field is zero on a circle on the sphere.

Answer 1

(a) The flux of the electric field through the sphere is zero.
(c) The electric field is not zero anywhere on the sphere.

The sphere encloses a dipole, i.e. two equal and opposite charges. In other words, net charge enclosed in the sphere is zero. Hence, the flux is zero through the sphere.
But the electric field at any point p on the sphere,

$E=\frac{1}{4\pi {\in }_0}\frac{p}{r^3}\sqrt{3{\cos }^2\theta +1}$ , where $\theta$ is the angle made by the point p with the centre of the dipole.
Hence, we can see that the field is not zero anywhere on the sphere.