Question

Two Styrofoam balls of mass 10.0 g are suspended by threads of length 25cm. The balls are charged, after which they hang apart, each at to the vertical. Find the net charge on each ball assuming that the charges are equal.

Answer 1

Write all forces by axes:

$$Ox: k\frac{q^2}{r^2}=T\text{ sin}\theta,\\ Oy: mg=T\text{ cos}\theta.\\ \space\\ \frac{kq^2}{mgr^2}=\text{tan}\theta,\\ \space\\ q=r\sqrt{\frac{mg\text{ tan}\theta}{k}}=2r\sqrt{\pi\epsilon_0mg\text{ tan}\theta}=\\ \space\\ =2\cdot0.25\sqrt{\pi\cdot8.85\cdot10^{-12}\cdot0.01\cdot9.8\cdot\text{ tan}\theta}=\\ \space\\ =8.26\cdot10^{-7}\cdot\sqrt{\text{tan}\theta}.$$