JEE MAIN - Physics (2005 - No. 48)
A charged ball $$B$$ hangs from a silk thread $$S,$$ which makes angle $$\theta $$ with a large charged conducting sheet $$P,$$ as shown in the figure. The surface charge density $$\sigma $$ of the sheet is proportional to
f
f$$\cot \,\theta $$
$$\cos \,\theta $$
$$\tan \,\theta $$
$$\sin \,\theta $$
Explanation
$$T\sin \theta = {\sigma \over {{\varepsilon _0}K}}.q\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,...\left( i \right)$$
$$T\cos \theta = mg\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,...\left( {ii} \right)$$
Dividing $$(i)$$ by $$(ii),$$
$$\tan \theta = {{\sigma q} \over {{\varepsilon _0}K.mg}}$$
$$\therefore$$ $$\sigma \propto \,\tan \theta $$
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