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In Cartesian coordinates the divergence of \( \mathbf{A} \) is

  • A.\( \partial A_z/\partial y - \partial A_y/\partial z \) and its cyclic partners
  • B.\( \partial^2 A_x/\partial x^2 + \partial^2 A_y/\partial y^2 + \partial^2 A_z/\partial z^2 \)
  • C.\( \partial A_x/\partial x + \partial A_y/\partial y + \partial A_z/\partial z \)
  • D.\( \partial A_x/\partial x \cdot \partial A_y/\partial y \cdot \partial A_z/\partial z \)

Answer: C

Correct answer: \( \partial A_x/\partial x + \partial A_y/\partial y + \partial A_z/\partial z \)

Each component is differentiated with respect to its own coordinate and the three are added, giving a scalar. The first option is one component of the curl, which is built from the cross derivatives, and the second is the Laplacian of a vector.

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