Physics I / Gradient, Divergence, and Curl
Practice question · Put in order

Order the steps to compute ∇×F\nabla \times F for F=(P,Q,R)F = (P, Q, R) in Cartesian coordinates.

Hints
  1. Set up the determinant with the unit vectors in the first row.
  2. Each component pairs two partial derivatives with a subtraction.
Show the answer
  1. Identify components P, Q, R of F
  2. Compute ∂R/∂y\partial R/\partial y − ∂Q/∂z\partial Q/\partial z (x-component)
  3. Compute ∂P/∂z\partial P/\partial z − ∂R/∂x\partial R/\partial x (y-component)
  4. Compute ∂Q/∂x\partial Q/\partial x − ∂P/∂y\partial P/\partial y (z-component)
  5. Assemble the curl vector
Why

The curl is computed component by component using partial derivatives.

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