An electric dipole is positioned at the centre of a sphere. Choose...

The electric field due to a short dipole at a distance $r$ from its centre is given by $E = \dfrac{p}{4\pi\epsilon_0 r^3} \sqrt{1 + 3\cos^2\theta}$, where $\theta$ is the angle made by the position vector with the dipole moment.

For any point on the sphere of radius $r$, the magnitude of the electric field is minimum at the equatorial plane ($\theta = \dfrac{\pi}{2}$), where $E = \dfrac{p}{4\pi\epsilon_0 r^3}$, which is non-zero. Thus, the electric field is non-zero at all points on the sphere.

An electric dipole consists of two equal and opposite charges, $+q$ and $-q$. The net charge enclosed by the sphere is $q_{enclosed} = +q - q = 0$.

According to Gauss's law, the net electric flux through the sphere is $\Phi = \dfrac{q_{enclosed}}{\epsilon_0} = 0$.