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JEE Main201910 Jan 2019Evening ShiftPhysicsElectrostaticsActual

Four equal point charges Q each are placed in the x y plane at 0 ,   2 , 4 ,   2 , 4 ,   - 2 and 0 ,   - 2 . The work required to put a fifth charge Q at the origin of the coordinate system will be:

Options

  1. AQ 2 4 π ϵ 0
  2. BQ 2 2 2 π ϵ 0
  3. CQ 2 4 π ϵ 0 1 + 1 5
  4. DQ 2 4 π ϵ 0 1 + 1 3

Correct answer

C. Q 2 4 π ϵ 0 1 + 1 5

Step-by-step solution

Work done in bringing the fifth charge at origin is equal to change in the potential energy of the system of charges. W e x t = Δ U = U f - U i if U i = 0 (assumed) W e x t = U f - 0 = K Q 2 2 + K Q 2 2 + K Q 2 2 5 + K Q 2 2 5 Hence, the work done in bringing the fifth charge at the origin is W e x t = Q 2 4 π ε 0 1 + 1 5 .

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