One end of a \( 10 \mathrm{~cm} \) long silk thread is fixed to a l...

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One end of a \( 10 \mathrm{~cm} \) long silk thread is fixed to a large vertical surface of a charged nonconducting plate and the other end is fastened to a small ball having a mass of \( 10 \mathrm{~g} \) and a charge of \( 4.0 \times 10^{-6} \mathrm{C} \). In equilibrium, the thread makes an angle of \( 60^{\circ} \) with the vertical. Find the surface charge density on the plate.
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