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JEE Main20199 Apr 2019Morning ShiftPhysicsElectrostaticsActual

A system of three charges are placed as shown in the figure: If D > > d , the potential energy of the system is best given by:

Options

  1. A1 4 π ϵ 0 - q 2 d - q Q d D 2
  2. B1 4 π ϵ 0 + q 2 d + q Q d D 2
  3. C1 4 π ϵ 0 - q 2 d - q Q d 2 D 2
  4. D1 4 π ϵ 0 - q 2 d + 2 q Q d D 2

Correct answer

A. 1 4 π ϵ 0 - q 2 d - q Q d D 2

Step-by-step solution

U = k - q q d + k - q Q d 2 - D + k q Q D + d 2 = - k q 2 d - k Q q D - d 2 + K Q q D + d 2 = - k q 2 d + k Q q - D - d 2 + D - d 2 D 2 - d 2 4 = - k q 2 d - k Q q d D 2 - d 2 4 Since, D>>d U = - k q 2 d - k Q q d D 2 = 1 4 π ϵ 0 - q 2 d - q Q d D 2

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