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The Laplacian of a scalar in cylindrical coordinates begins with the term

  • A.\( (1/\rho^2)\,\partial^2 V/\partial\rho^2 \)
  • B.\( (1/\rho)\,\partial(\rho \, \partial V/\partial\rho)/\partial\rho \)
  • C.\( \partial^2 V/\partial\rho^2 \) alone
  • D.\( \rho \, \partial^2 V/\partial\rho^2 \)

Answer: B

The metric factor appears both inside and outside the differentiation, which is what distinguishes the curvilinear form from the Cartesian one. Expanding it gives the second derivative plus a first derivative divided by the radius.

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