Question

Four point charges each having charge Q are located at the corners of a square having sides of length a.

(a) Find an expression for the total electric potential at the center of the square due to the four charges. (Use any variable or symbol stated above along with the following as necessary: k_e.)
V =  

(b) Find an expression for the work required to bring a fifth charge q from infinity to the center of the square. (Use any variable or symbol stated above along with the following as necessary: k_e.)
W =  

please explain.

Answer 1

PART (a)

If four point charges have charge Q are placed at the corners of sides of a square of length a.

Then the distance to center from each charge is r = a / √2

Then the electric potential at the center of the square is

                 V = 4(keQ / r)

                    = 4√2 (keQ / a)

In part (a) we found what V was, and the charge we are trying to add is just p. So to find work, all you have to do is take the answer from part (a) and times it by p.

PART (b)

Amount of workdone to bring a fifth charge p from infinity to the center of the square is

              W = qV

                  = p4√2 (keQ / a)

                  = 4√2 (kepQ / a)

any way
I figured out a by finding out the length firsts. So you know the diagonal of the square will be sqrt(a^2 + a^2). So now you can say that the length from the corner to the center is sqrt(2a^2)/2. Then just plug into the formula that you have for V. V=keq/r and multiply by 4 because there are four charges.