See attached file for full problem description.
8. (a) Three charges are situated at the corners of a square (side a) as shown in Figure 2.41:
(a) how much work does it take to bring in another charge, +q, from far away and place it in the fourth corner?
(b) How much work does it take to assemble the whole configuration of four charges?
6. One of these is an impossible electrostatic field, which on?
Here, k is a constant with appropriate units. For the possible one, find the potential, using the origin as your reference point. Check you answer by computing its gradient. [hint: you must select a specific path to integrate along, it doesn't matter what path you choose, since the answer is path-independent, but you simply cannot integrate unless you have a particular path in mind].
The solution shows detailed calculation of finding out the work done to bring the fourth charge to the square corner and to assemble the four charges together. It also explains how to determine if the given field vector is an electrostatic field or not.