Physics
posted by Jerry on .
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.

THere are a number of ways to do this, some more difficult than others.
If you note the E due to q2 is upward, and the E due to q1 is horizontal, then the E due to q3 must add to zero. That is, the E due to q3 in the horizontal direction must be equal and opposite to q1, and The E due to q3 in the vertical must be equal and opposite to Q2
So dealing with q3 first.
letting o be the distance of the horizontal (o^2=d^2+4d^2=5d^2; or o=dsqrt5)
Ehorizontal=k q/o^2*2d/o=2kqd/o^3
Evertical= kq/o^2*d/o=kqd/o^3
So now setting the vertical of q3 equal to the vertical of q2
k*q2/d^2=kqd/o^3
q2=q (d/o)^3=q(d/dsqrt5)^3=q/5sqrt5
now, setting the horizontal of q3 equal to the horizontal of q1
kq1/4d^2=2kqd/o^3
q1=8q (d/o)^3 and you can finish the algebra.
Check all this math, I did it in my head keying it in.