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If a small sphere of mass m and charge q is hanged from a silk thread at an angle θ with the surface of a vertical charged conducting plate, then for equilibrium of sphere the surface charge density of the plate -

Options

  1. Aε 0 m g t a n θ q
  2. B2ε 0 m g t a n θ q
  3. Cε 0 m g q t a n θ
  4. Dε 0 m g t a n θ 3 q

Correct answer

B. 2ε 0 m g t a n θ q

Step-by-step solution

T s i n θ = q E … ( 1 ) T c o s θ = m g … ( 2 ) t a n θ = q E m g = q σ 2 ε 0 m g σ = 2 ε 0 m g t a n θ q

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