There is a uniform electrostatic field in a region. The potential at various points on a small sphere centred at P, in the region, is found to vary between the limits 589.0 V to 589.8 V. What is the potential at a point on the sphere whose radius vector makes an angle of 60° with the direction of the field?

ΔV = E.d = Edcosθ
The potential varies between 589.0 V and 589.8 V. This means the maximum potential difference across the sphere is 0.8 V (589.8 V - 589.0 V = 0.8 V).
Assuming the diameter of the sphere is 'd', the maximum potential difference is given by ΔV = Ed, where E is the electric field strength. Therefore, Ed = 0.8 V.
We are asked to find the potential at a point on the sphere where the radius vector makes an angle of 60° with the direction of the field. The potential difference at this point is given by ΔV = Edcosθ, where θ = 60°.
ΔV = 0.8 V * cos(60°) = 0.8 V * 0.5 = 0.4 V
Hence the new potential at the point on the sphere is 589.0 V + 0.4 V = 589.4 V