If a small sphere of mass \( m \) and charge \( q \) hangs from a s...

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If a small sphere of mass \( m \) and charge \( q \) hangs from a silk thread at angle \( \theta \) with a charged conducting plate, show that for equilibrium of the sphere, the surface charge density for the plate is \( \varepsilon_{0} \frac{m g}{q} \tan \theta \).
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