Two charges –q and +q are located at points (0, 0, -a) and (0, 0, a), respectively.
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?

 

Given,
Two charges -q and +q are located at (0,0,-a) and (0,0,a) respectively.

To find: the amount of work done to move a small test charge from point (5,0,0) to (-7,0,0) along x-axis.

Electrostatic potential at point (5, 0, 0) due to the dipole is given as


Electrostatic potential at point (–7, 0, 0) due to the dipole is given as

In moving small test charge q from the point (5, 0, 0) to (–7, 0, 0) the work done W = q(V₁– V₂) = q x 0 = 0.

The work done by the electrostatic field between two points is not dependant on path connecting two points. Therefore, work done by any charge along X axis, Y axis or on equitorial plane is zero as the potential does not change.