Point charges hanging on a string

AI Thread Summary
To determine the angle theta for two charged balls hanging from strings, the forces acting on each ball must be analyzed using the equations for horizontal and vertical forces. The gravitational force and the electrostatic force between the charges can be expressed through the equations Fx = Tsin(theta) - kq1q2/(2cos(theta))^2 = 0 and Fy = Tcos(theta) - mg = 0. By solving these equations, one can find the tension T and the angle theta, although it may involve complex trigonometric calculations. An alternative approach suggested is to solve the problem numerically by graphing the trigonometric functions. The discussion emphasizes the importance of correctly setting up the equations to find the solution.
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Homework Statement


What would be the angle theta as shown in the picture, if the 5 gram balls hangin off 1m strings have been charges to 100nC each


http://img178.imageshack.us/img178/5103/mooche.th.jpg


The Attempt at a Solution



I'm not really sure how to solve such a question, can i get a hint?
i know the force each one exerts on the other is kq1q2 / r^2 and i can find that the distance between them is 2sin(theta) so the force is kq1q2/(2sin(theta))^2
So for , say, the left ball, we have
Fx = Tsintheta - kq1q2/(2costheta)^2 = 0
Fy = tcostheta - mg = 0

but what can i do with those eqations really :S
I definitely am stuck and have no idea how to proceed for such a q
 
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Can't see the diagram - too small. Clicking on it doesn't work.
Check the Fx equation - looks like you copied the 2sin(theta) incorrectly.
Two equations, two unknowns (theta and T) - you should be all set. Solve the Fy equation for T and sub into the Fx one to get . . . a nasty bit of trigonometry. Well you could always solve it numerically - just graph the trig function on your calculator and trace to the value you want it to be, then read off the angle.
 

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