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A charged ball B hangs from a silk thread S, which makes an angle θ with a large charged conducting sheet P, as shown in the figure [the sheet P is vertical, the thread is tied to the top of the sheet and the ball B hangs away from it]. The surface charge density σ of the sheet is proportional to

Asked in JEE Main 2005 · Infinite sheet and sheet combinations

• (1) sin θ
• (2) tan θ
• (3) cos θ
• (4) cot θ

Step-by-step solution

Why the other options are wrong

• (1) Takes the tension itself as mg rather than T cos θ=mg, so the horizontal balance reads qE=mg sin θ.
• (3) Needs two slips at once, the tension taken as mg and its horizontal component written T cos θ, giving qE=mg cos θ; the balance done properly can only give tan θ or its inverse cot θ.
• (4) Inverts the ratio, dividing the vertical balance by the horizontal one rather than the other way round.

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