Aspherical conductor of radius a is placed in a uniform electric field $$\overrightarrow {\bf{E}} = {E_0}\,{\bf{\hat k}}.$$   The potential at a point P(r, θ) for r > a, is given by $$\phi \left( {r,\,\theta } \right) = {\text{constant}} - {E_0}r\cos \theta + \frac{{{E_0}{a^3}}}{{{r^2}}}\cos \theta $$
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