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The line AA ' is on a charged infinite conducting plane which is perpendicular to the plane of the paper. The plane has a surface density of charge σ and B is a ball of mass m with a like charge of magnitude q . B is connected by a string from a point on the line AA ' . The tangent of the angle θ formed between the line AA ' and the string is (provided, the charge q does not affect the distribution of charge on condu

Options

  1. Aqσ 2 ε 0 mg
  2. Bqσ 4 πε 0 mg
  3. Cqσ 2 πε 0 mg
  4. Dqσ ε 0 mg

Correct answer

D. qσ ε 0 mg

Step-by-step solution

The diagram is as follows, The electric filed due to charged infinite conducting sheet is E = σ ε 0 Now, force (electric force) on the charged ball is F = qE = σ · q ε 0 The resultant of electric force and mg balance the tension produced in the string. So, tanθ = F e mg = qσ ε 0 mg = qσ ε 0 mg

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