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A small bob of mass 100 mg and charge +10 C is connected to an insulating string of length 1 m. It is brought near to an infinitely long nonconducting sheet of charge density ' ' as shown in figure. If string subtends an angle of 45^ with the sheet at equilibrium the charge density of sheet will be : (Given, ₀=8.85 10⁻¹² ~F ~m and acceleration due to gravity, g=10 ~m / s ^2 )

Options

  1. A0.885 nC / m ^2
  2. B17.7 nC / m ^2
  3. C885 nC / m ^2
  4. D1.77 nC / m ^2

Correct answer

D. 1.77 nC / m ^2

Step-by-step solution

aligned & qE = mg & q [ 2 ₀ ]= mg & = 2 ₀ mg q & = 2 8.85 10⁻¹² 100 10⁻⁶ 10 10 10⁻⁶ & =17.7 10⁻¹⁰ C / m ^2 & =1.77 nC / m ^2 aligned

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