Problem 72-8    Source:  Problem elaborated by the author of the site.

Consider two points, A and B, distant d_A = 8 cm and d _B = 25 cm, respectively, of a charge loaded with 120 µC. How much work must the electric field do to move a charge of -12 µC from point B to point A?

Solution of the Problem 72-8   

Initially we must calculate the potential at each point due to the charge of 120 µC. For this, we will use the eq. 72-10, shown below for clarity.

For the point A, we have

Carrying out the calculation, we find

For the point B, we have

Carrying out the calculation, we find

Note that the potential at point A is greater than the potential at point B. Now, we need to calculate the potential difference ΔV between the two points, remembering that we are going to shift a negative charge from a lower potential to a higher one. So, we define the potential difference as below:

Carrying out the calculation, we find

To calculate the work, we will use the eq. 72-07, or

Carrying out the calculation, we find

Note that the work is positive because the charges attract each other and the force of attraction is in the same direction as the displacement.