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Two point charges +q and -q are fixed on the x-axis at positions (-d, 0) and (d, 0) respectively. A test charge +Q is moved slowly from an initial position A(0, d) on the y-axis to a final position B(3d, 0) on the x-axis. The work done by an external agent in this process is:

Options

  1. AqQ 16 ₀ d
  2. B3qQ 16 ₀ d
  3. C- qQ 16 ₀ d
  4. D0

Correct answer

C. - qQ 16 ₀ d

Step-by-step solution

The work done by an external agent in moving a charge Q from point A to point B is given by: W_ ext = Q(V_B - V_A) First, calculate the electric potential at the initial position A(0, d) . Since A lies on the equatorial line of the dipole setup, the distances to both charges are equal ( r = d^2 + d^2 = d 2 ). V_A = 1 4 ₀ q d 2 + 1 4 ₀ (-q) d 2 = 0 Next, calculate the electric potential at the final position B(3d, 0) . The distance from +q at (-d, 0) is 3d - (-d) = 4d , and from -q at (d, 0) is 3d - d = 2d . V_B = 1

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