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Two point charges +q and -q are placed on the x -axis at x = a and x = -a respectively. A third point charge +Q is moved by an external agent from x = 2a to x = 3a along the x -axis. The work done by the external agent in this process is:

Options

  1. A- 5Qq 72 ₀ a
  2. B5Qq 48 ₀ a
  3. C- 7Qq 48 ₀ a
  4. D- 5Qq 48 ₀ a

Correct answer

D. - 5Qq 48 ₀ a

Step-by-step solution

The electric potential at a point x on the axis of the dipole ( x > a ) is given by the exact expression: V(x) = 1 4 ₀ ( q x-a - q x+a ) = 1 4 ₀ 2qa x^2-a^2 The initial potential at x = 2a is: V_i = 1 4 ₀ 2qa (2a)^2 - a^2 = 1 4 ₀ 2qa 3a^2 = 2q 12 ₀ a The final potential at x = 3a is: V_f = 1 4 ₀ 2qa (3a)^2 - a^2 = 1 4 ₀ 2qa 8a^2 = 2q 32 ₀ a = q 16 ₀ a The work done by the external agent is: W = Q(V_f - V_i) = Q ( q 16 ₀ a - 2q 12 ₀ a ) Taking the common denominator as 48 ₀ a : W = Q ( 3q - 8q 48 ₀ a ) = - 5Qq 48 ₀

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