in the figure two tiny conducting balls of identical mass

In the figure, two tiny conducting balls of identical mass m and identical charge q hang from nonconducting threads of length L. Assume that θ is so small that tan θ can be replaced by its approximate equal, sin θ. (a) Show that:

x = (q^2*L / (2πεmg))^(1/3)

gives the equilibrium separation x of the balls. (b) If L = 120 cm, m = 10 g, and x = 5.0 cm, what is q?

[rene]

Thanks man! You are a godsend for all physics students.

[j.yingling]

I am just learning this and it has been very helpful. One question however. What was the significance of reducing the fraction from "k" around 7:48 if k was going to be put back in the equation in the next step? I understand it would be correct to simplify if that was the final answer, but I found it confusing because step-by-step on paper it leads one to leave out the "2" in the numerator and put the constant "k" back in. Unless there is something I am completely missing.

[FreeSkillsStyle]

Thanks for the help, I just don't understand why the epsilon initial disappears 7:42