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      Question

      A conducting sphere of radius R carries a charge Q. If

      half of the charge is transferred to an identical uncharged sphere brought into contact and removed, the electrostatic energy of the system becomes:
      A Half of original Correct Answer Incorrect Answer
      B One-fourth of original Correct Answer Incorrect Answer
      C Three-fourths of original Correct Answer Incorrect Answer
      D Greater than original Correct Answer Incorrect Answer

      Solution

      The electrostatic energy (U) of a charged conducting sphere is given by: When the charged sphere (with charge Q) is brought into contact with an identical uncharged sphere, the charge will be equally distributed between them due to their identical nature and conducting property.

      • Each sphere will have a charge of Q/2.
      Now we have two identical conducting spheres, each with a charge of Q/2 and radius R. The electrostatic energy of each sphere is: So, the final electrostatic energy of the system is half of the original electrostatic energy. Therefore, the correct answer is (a) Half of original.

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