Question
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?
Solution
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 (–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.
