Question
Two identical pith balls, each carrying a charge q, are suspended from a common point by two strings of equal length l. Find the mass of each ball if the angle between the strings is $2\theta$ in equilibrium.
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Answer
Electric force $=\frac{\text{kq}^2}{(\ell\sin\text{Q}+\ell\sin\text{Q})^2}$
$=\frac{\text{kq}^2}{4\ell^2\sin^2}$
So, $\text{T}\cos\theta=\text{ms}$ (For equilibrium) $\text{T}\sin\theta=\text{Ef},$
$\text{tan}\theta=\frac{\text{Ef}}{\text{mg}}$
$\Rightarrow\text{mg}=\text{Ef}\cot\theta$
$=\frac{\text{kq}^2}{4\ell^2\sin^2\theta}\cot\theta$
$=\frac{\text{q}^2\cot\theta}{\ell^2\sin^2\theta16\pi\text{E}_0}$
$\text{m}=\frac{\text{q}^2\cot\theta}{16\pi\text{E}_0\ell^2\sin^2\theta\text{g}}\text{unit}$
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