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Concepts Of Physics MCQ Edition [Volume 2]PhysicsElectric Field and Potential

Two particles A and B possessing charges q and 2q respectively are located on a smooth table with a separation d . A third particle C is to be clamped on the table such that particles A and B remain stationary under electrical forces. Determine the charge on C and its clamping position.

Options

  1. A-(6 - 4 2 )q , outside A and B at a distance of ( 2 + 1)d from A
  2. B-(6 + 4 2 )q , between A and B at a distance of ( 2 - 1)d from A
  3. C-(6 - 4 2 )q , between A and B at a distance of ( 2 - 1)d from A
  4. D-(3 - 2 2 )q , between A and B at a distance of ( 2 - 1)d from A

Correct answer

C. -(6 - 4 2 )q , between A and B at a distance of ( 2 - 1)d from A

Step-by-step solution

Let the charge of C be Q and its distance from A be x . Since A and B have like charges, they repel each other. For them to remain stationary, C must attract both, meaning C must have a negative charge and be placed between A and B . For the equilibrium of particle A , the net force on it must be zero: 1 4 ₀ q(2q) d^2 = 1 4 ₀ q|Q| x^2 |Q| = 2qx^2 d^2 For the equilibrium of particle B , the net force on it must be zero: 1 4 ₀ q(2q) d^2 = 1 4 ₀ 2q|Q| (d-x)^2 |Q| = q(d-x)^2 d^2 Equating the two expressions for |Q| : 2

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