Question

Two identical balls each carrying a charge Q are suspended from a common point by two strings of equal length l. Calculate the mass of each ball if the angle between “the strings is 2q in equilibrium.

Answer 1

$$\begin{gathered} LetthetensioninthestringduetotheweightandtheforceofrepulsionbeT. \\ Inequilibrium,followingaretheequations: \\ T\cos q=mg------\left(1\right) \\ andT\sin q=\frac{1}{4\pi {\epsilon }_0}\times \frac{Q^2}{l^2{\sin }^{2}q}-------\left(2\right) \\ Dividingeqn\left(2\right)byeqn\left(1\right),weget \\ \tan q=\frac{4\pi {\epsilon }_0\times l^{2}si{n}^{2}q\times mg}{Q^2} \\ orm=\frac{Q^2\tan q}{4\pi {\epsilon }_0\times l^{2}gsi{n}^{2}q}=\frac{Q^2}{2\pi {\epsilon }_0\times l^{2}gsin2q} \end{gathered}$$