Four point charges, each of magnitude q, are located at the corners of a square with sides of length a. Two of the charges are +q, and two are -q. The charges are arranged in one of the following two ways: (1) The charges alternate in sign (+q, -q, +q, -q) as you go around the square; (2) The top two corners of the square have positive charges (+q, +q), and the bottom two corners have negative charges (-q, -q).

(a) In which case will the electric field at the center of the square have the greatest magnitude? Explain.

(b) Calculate the electric field at the center of the square for each of these two cases.