Point charges hanging on a string

[theneedtoknow]

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

 

[Delphi51]

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.

 

[nlightner]

uestion. Any help is appreciated!

I would first start by identifying the variables and equations that are relevant to this problem. We have two charged balls, each with a charge of 100nC, hanging from strings that are 1m long. The force that each ball exerts on the other can be calculated using Coulomb's law: F = kq1q2/r^2, where k is the Coulomb's constant, q1 and q2 are the charges on the two balls, and r is the distance between them. We also have the force of gravity acting on each ball, which is equal to its weight, mg, where m is the mass of the ball and g is the acceleration due to gravity.

Using these equations, we can set up a system of equations to solve for the angle theta. For example, for the left ball, we have the horizontal force equation: Fx = Tsin(theta) - kq1q2/(2cos(theta))^2 = 0, where T is the tension in the string. We also have the vertical force equation: Fy = Tcos(theta) - mg = 0. These two equations can be solved simultaneously to find the value of theta.

Another approach would be to use the concept of equilibrium. In order for the balls to remain stationary, the net force on each ball must be equal to zero. This means that the horizontal and vertical components of the forces must balance out. By setting up and solving equations for the forces in the horizontal and vertical directions, we can again find the value of theta.

Overall, the key to solving this problem is to carefully identify the relevant variables and equations, and then use mathematical techniques to solve for the unknown angle theta. I hope this helps!