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Two infinitely large parallel conducting plates A and B are separated by a distance d . They have uniform surface charge densities of +4 and -2 respectively. A point charge +q of mass m is released from rest at the surface of Plate A. The kinetic energy of the charge +q just before it reaches Plate B is :

Options

  1. Aq d ₀
  2. B6 q d ₀
  3. C3 q d ₀
  4. D3 q d 2 ₀

Correct answer

C. 3 q d ₀

Step-by-step solution

The net electric field in the region between the plates is the vector sum of the fields due to Plate A and Plate B. Since Plate A has a positive charge density and Plate B has a negative charge density, both fields point in the same direction (from A to B). Magnitude of the net electric field E is: E = _A 2 ₀ - _B 2 ₀ = 4 2 ₀ - (-2 ) 2 ₀ E = 4 + 2 2 ₀ = 6 2 ₀ = 3 ₀ The force experienced by the charge +q is: F = qE = 3 q ₀ The work done by the electric field as the charge moves a distance d from Plate A to Plate B i

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