Answer to Question #182872 in Field Theory for Esmail

Question

Two small conducting balls of identical mass m and charge q hang from non-conducting rope of length L Assume that Ɵ is very small tanƟ = sinƟ. Find an expression for the equilibrium separation x of the balls.

Answer 1

Answer

Tension in rope

By vertical equilibrium

$T=\frac{mg}{cos\theta}$

By equilibrium

$\frac{kq^2}{L^2sin^2\theta}=Tsin{\theta}$

And

$\frac{kq^2}{L^2sin^2\theta}=\frac{mg}{cos\theta}sin{\theta}$

$\frac{kq^2}{4(L^2sin^2\theta)}=mgtan{\theta}$