Aspherical conductor of radius a is placed in a uniform electric field E = E_0\, k. The potential at a point P(r, θ) for r > a, is given by ( r,\, ) = constant - E_0r + E_0a^3r^2 where, r is the distance of P from the centre O of the sphere and θ is the angle, OP makes with the Z-axis. The charge density on the sphere at θ = 30° is

Aspherical conductor of radius a is placed in a uniform electric field $$\overrightarrow{\mathbf{E}}=E_0\hat{\mathbf{k}}.$$   The potential at a point P(r, θ) for r > a, is given by $$\varphi \left(r,\theta \right)=\text{constant}-E_{0}r\cos \theta +\frac{E_0{a}^3}{r^2}\cos \theta$$
where, r is the distance of P from the centre O of the sphere and θ is the angle, OP makes with the Z-axis.

The charge density on the sphere at θ = 30° is

Answer: Option A