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Laplace's equation is the special case of Poisson's equation applying where

  • A.the field is uniform throughout the region
  • B.the charge density is zero
  • C.the potential is zero on all the boundaries
  • D.the permittivity of the medium is unity

Answer: B

With no charge in the region the right hand side vanishes and the equation becomes homogeneous. Charge may still exist on the boundaries, and usually does, which is what makes the boundary values non-trivial and the problem worth solving at all.

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