A rectangle has a length of 2d and a height of d. Each of the following three charges is located at a corner of the rectangle: +q1 (upper left corner), +q2 (lower right corner), and -q (lower left corner). The net electric field at the (empty) upper right corner is zero. Find the magnitudes of q1 and q2. Express your answers in terms of q.

Question

I'm really lost at how to do tackle this problem. I know that an electric field is zero at infinity for positive charges but I don't know how to show it.

Answer 1

The horizontal E-field component at the empty corner is due to q1 and q only. For it to be zero,
q1/4d^2 = [q/(5d^2)]*(2/sqrt5)

The last term in parentheses is the cosine of the angle that the diagonal makes with the horizontal axis.

q1 = (4/5)(2/sqrt5) = 0.7155 q

The vertical E-field component at the empty corner is due to q2 and q only. For it to be zero,
q2/d^2 = [q/(5d^2)]*(1/sqrt5)
q2 = (1/5)(1/sqrt5) q = 0.0894 q