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Two point charges 8 C and -2 C are placed at (10,0,0) cm and (-10,0,0) cm respectively in an external electric field E = A r^2 r . Considering the potential at infinity to be zero, the total electrostatic energy of the configuration is exactly zero. The value of the constant A (in N m^2 / C ) is

Options

  1. A0
  2. B7200
  3. C24000
  4. D12000

Correct answer

D. 12000

Step-by-step solution

The total electrostatic energy U of the system is the sum of the potential energy of each charge in the external field and the interaction energy between the two charges. The external electric field is E = A r^2 r . The potential V(r) is found by integrating the field: V(r) = - _ ^ r E d r = - _ ^ r A r^2 dr = A r The distances of the charges from the origin are: r₁ = 10 cm = 0.1 m for q₁ = 8 C r₂ = |-10| cm = 0.1 m for q₂ = -2 C The distance between the two charges is r₁₂ = 10 - (-10) = 20 cm = 0.2 m . The interac

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