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The capacitance of an isolated conducting sphere of radius \( a \) is

  • A.\( \epsilon a \)
  • B.\( 4\pi\epsilon/a \)
  • C.\( 4\pi\epsilon a \)
  • D.\( 4\pi\epsilon a^2 \)

Answer: C

It follows from the potential of a sphere by rearrangement, and it may be read as the limit of two concentric spheres as the outer one recedes to infinity. A sphere of one metre radius has about 111 picofarads, which shows how small an isolated capacitance is.

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