Problem III:
A square in the xy-plane with center at the origin has sides
of length 2d. Analyze the two different situations below.
1. At the vertex at (d, d, 0) you place a charge +Q. At the vertex at (-d, d, 0) you
place a charge +Q. At the vertex at (-d, -d, 0) you place a charge +Q. At the
vertex at (d, -d, 0) you place a charge +Q.
Compute the electric field $E$ at the point (0,0,z). You may assume z > 0. Write
an approximate answer for $E$ with z >> d.
2. At the vertex at (d, d, 0) you place a charge +Q. At the vertex at (-d, d, 0) you
place a charge -Q. At the vertex at (-d, -d, 0) you place a charge +Q. At the
vertex at (d, -d, 0) you place a charge -Q.
Compute the electric field $E$ at the point (0,0,z). You may assume z > 0