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Between coaxial cylinders the solution of Laplace's equation gives a potential varying

  • A.as the logarithm of the radius
  • B.linearly with the radius
  • C.as the inverse of the radius
  • D.as the square of the radius

Answer: A

The cylindrical Laplacian in the radial variable alone integrates twice to give a logarithm plus a constant. Differentiating it returns the inverse first power field of a line charge, which Gauss's law gives by a much shorter route.

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