2.21 Two charges –q and +q are located at points (0, 0, –a) and (0, 0, a), respectively
(c) How much work is done in moving a small test charge from the point (5,0,0) to (–7,0,0) along the x-axis? Does the answer change if the path of the test charge between the same points is not along the x-axis?
Since point (5,0,0) is equidistance from both charges, they both will cancel out each other potential and hence potential at this point is zero.
Similarly, point (–7,0,0) is also equidistance from both charges. and hence potential at this point is zero.
Since potential at both the point is zero, the work done in moving charge from one point to other is zero. Work done is independent of the path.