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The quantity that Laplace's equation determines, given the boundary values, is

  • A.the permittivity of the medium in the region
  • B.the total energy stored in the region
  • C.the potential throughout the region
  • D.the charge density throughout the region

Answer: C

Once the potential is known everywhere the field follows by differentiation, the surface charge on each conductor by applying the boundary condition, and the capacitance by dividing that charge by the potential difference. Everything else in an electrostatic problem flows from that one function.

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