Find ratio of two charges

jamiewilliams

1. The problem statement, all variables and given/known data
The drawing shows two positive charges q1 and q2 fixed to a circle. At the center of the circle they produce a net electric field that makes an angle 28.6° with the vertical axis, measured counterclockwise. Determine the ratio q2/q1.

[the drawing shows a circle with two charges: q1 measures 30° from the vert and q2 (on the other side of the vertical axis) measures 60° from the vert]


2. Relevant equations

Coulomb's Law
?

3. The attempt at a solution

First I sketched the situation and drew 2 vectors coming from the origin for the energy fields E1 and E2 (from q1 and q2, respectively). I drew the x and y components of each vector using trig functions. I think I am on the right track but I am stuck! No matter how I move around the equations and/or algebra I can't seem to get the right answer.

[correct answer is 1.64]

gneill

Your description is a bit vague about where the angles are being measured from (with respect to the positive or negative y-axis???), but I think I've managed to come up with a diagram that fits the bill:



You might want to take note of the fact that the two lines that converge on the circle center from the charges happen to meet at a 90° angle, thus the electric field vectors from the charges will also be at right angles to each other at the center. You should be able to use that fact and your given angle for the resultant to determine the angle that the resultant makes with one or the other of those lines. That angle will then be related to the magnitudes of the field vectors...

Attached Thumbnails