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Two point charges q₁ = 4 C and q₂ = -2 C are initially fixed at (2, 0) m and (-2, 0) m respectively, in a 2D non-uniform external electric field given by E = (x i - y j ) , where = 5 10^4 V/m^2 . The charges are then moved by an external agent to new positions where q₁ is at (0, 2) m and q₂ is at (0, -2) m . Considering the potential at the origin to be zero, the total work done by the external agent to change the co

Options

  1. A0.4
  2. B-0.4
  3. C0.2
  4. D0.382

Correct answer

A. 0.4

Step-by-step solution

The work done by the external agent is equal to the change in the total electrostatic potential energy of the system: W = U = U_f - U_i . First, find the potential function V(x,y) from the given electric field: dV = - E d r = -( x i - y j ) (dx i + dy j ) = - x dx + y dy Integrating with the condition V(0,0) = 0 : V(x,y) = - x^2 2 + y^2 2 Calculate the initial potential energy of the charges in the external field: For q₁ at (2,0) : V(2,0) = - (2)^2 2 = -2 For q₂ at (-2,0) : V(-2,0) = - (-2)^2 2 = -2 U_ i,ext = q₁ V

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