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JEE MainPhysicsElectrostatics

Consider two infinitely large parallel conducting plates A and B placed facing each other. Plate A has a uniform surface charge density of +3 . Plate B has an unknown uniform surface charge density _B . A point charge -q placed in the region between the plates experiences a net electric force of magnitude 5 q 2 ₀ directed towards Plate A. The surface charge density _B of Plate B is :

Options

  1. A+8
  2. B-2
  3. C+ 2
  4. D+2

Correct answer

B. -2

Step-by-step solution

Let Plate A be on the left and Plate B be on the right. The electric force on the negative charge -q is directed towards Plate A (left). Since the charge is negative, the net electric field E must be directed opposite to the force, which is towards Plate B (right). The magnitude of the net electric field is: E = F q = 5 2 ₀ The net electric field between the plates (taking the direction from A to B as positive) is the vector sum of the fields produced by each plate: E_ net = E_A + E_B = _A 2 ₀ - _B 2 ₀ Substituting

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