How Do Suspended Charged Spheres Behave?

[Nevok]

Homework Statement

This is a long one...
Two small spheres with mass m are suspended with insulating threads of length L from a common point. Uncharged, the spheres hang so they touch each other. When given the same charge q they repel each other and hang d distance apart. Assume d is pretty small when compared to L but not the the diameter of the spheres.

a) Explain, using a net force diagram, why the magnitude of the electrostatic force F_e acting on the spheres must be equal to mgtan(theta)

b) Explain why in this situation we can approximate tan(theta) as d/2L and what the percent error if d=L/10

c)Combine the answers to part a and b with Coulombs law to show that abs(q)= sqrt((mgd^3)/(2kL))
L=70cm, d=4.0cm m=0.4g

Homework Equations

Coulombs law, F_e=(k(q_1*q_2))/r^2.

The Attempt at a Solution

Well, I have part a, but i have no clue about why you could do that approximation.

 

[graphene]

Hello nevok. For really small angles, \sin \theta \approx \tan \theta

 

[Nevok]

Thanks, with that and a little bit of thinking I solved it.