Two identical point charges +Q are fixed at points A and B separated by a distance d. A point P lies on the perpendicular bisector of AB at a distance 2d from the midpoint O of AB.
(a) Derive an expression for the electric potential at P due to the two charges.
(b) Another point Q lies on the line AB, on the side of B such that BQ=d. Find the potential difference VQ−VP.
(c) A test charge qt is moved from P to Q along an arbitrary curved path in the electric field of the two fixed charges. Prove that the work done depends only on the potential difference obtained in part (b) and is independent of the actual path chosen.