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JEE Main 2005 (AIEEE) · Motion of Charges in an Electric Field

Motion of Charges in an Electric Field question from JEE Main 2005 (AIEEE)

Q43JEE Main 2005 · AIEEEMedium

Motion of Charges in an Electric Field

A charged ball BB hangs from a silk thread S,S, which makes angle θ\theta with a large charged conducting sheet P,P, as shown in the figure. The surface charge density σ\sigma of the sheet is proportional to

Figure

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Answer: (c)

  1. Ball in equilibrium under TT, mgmg and horizontal force qEqE: tan⁡θ=qEmg\tan\theta = \frac{qE}{mg}.
  2. Near a charged conducting sheet E=σε0E = \frac{\sigma}{\varepsilon_0}.
  3. σ=ε0mgqtan⁡θ⇒σ∝tan⁡θ\sigma = \frac{\varepsilon_0 mg}{q}\tan\theta \Rightarrow \sigma \propto \tan\theta
  4. So the answer is (c) tan⁡θ\tan\theta.
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