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## Homework Statement

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: +q

_{1}(upper left corner), +q

_{2}(lower right corner), and -q (lower left corner). The net electric field at the (empty) upper right corner is zero. Find the magnitudes of q

_{1}and q

_{2}. Express your answers in terms of q.

## Homework Equations

Coloumb's Law: k * (|q

_{1}| * |q

_{2}| / r

^{2})

Where k= a proportionality constant ~ 8.99 * 10

^{9}N * m

^{2}/C

^{2}

Electric Field Definition: E = F / q

_{0}

Where E is the net electric field at a point, and F is the force experienced by a small test charge represented by q

_{0}

## The Attempt at a Solution

I really got nowhere trying to find this solution, but here's what I tried:

--> I defined the upper right corner where the net electric field is zero as point T (for easy reference).

--> I represented the forces exerted on point T as three vectors, all with unknown magnitudes. The vector created by q

_{1}had a direction of 0º; the vector created by q

_{2}had a direction of arctan(2)~63.43º (reasoning below), and the vector created by -q had a direction of 270º.

--> I obtained the direction of the vector created by q

_{2}by drawing a right triangle with leg lengths 1 and 2 and solving for the angle opposite the side with length 2. The leg lengths were obtained from the given data that the sides of the rectangle are d and 2d.

--> At this point, I realized I was completely on the wrong track. I was planning on solving for the resultant of these three vectors, but I realized that it was already given in the problem that the resultant is, in effect, zero. Thus, in my line of thought, the resultant of the vectors produced by q

_{1}and q

_{2}(the positive charges) must be equal in magnitude and opposite in direction of the vector produced by -q. However, because the two vectors produced by these positive charges are at 0º and ~63.43º, they cannot produce a resultant at 90º, which would be needed in order to have the opposite direction of the vector created by then negative charge. Thus, to me, the problem appears impossible, unless q

_{1}or q

_{2}were allowed to be negative, which I don't believe they are.

Thanks a ton for any help you can provide!