These have been driving me crazy. The book is terrible at explaining this stuff, so I was hoping someone here could help me out.(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

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.

2. Relevant 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}

3. 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!

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# Homework Help: Electric Field Problems

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