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Mathematics · University

A component of curl

The order of subtraction sets the orientation.

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Method and conditions

The order of subtraction sets the orientation.

(curl F)z = ∂Fᵧ/∂x − ∂Fₓ/∂y

Worked examples

For F = (7y², 7x², 0), calculate the z-component of curl F at (-1,0,0). Round the final result to 4 decimal places if needed.

Compute ∂Fᵧ/∂x = 14x and ∂Fₓ/∂y = 14y, then subtract.

-14

For F = (8y², 9x², 0), calculate the z-component of curl F at (8,-2,0). Round the final result to 4 decimal places if needed.

Compute ∂Fᵧ/∂x = 18x and ∂Fₓ/∂y = 16y, then subtract.

176

Try it

  1. For F = (1y², 9x², 0), calculate the z-component of curl F at (4,8,0). Round the final result to 4 decimal places if needed.

  2. For F = (1y², 11x², 0), calculate the z-component of curl F at (0,-4,0). Round the final result to 4 decimal places if needed.

Check your work

Answers and marking notes
  1. 56

    Compute ∂Fᵧ/∂x = 18x and ∂Fₓ/∂y = 2y, then subtract.

  2. 8

    Compute ∂Fᵧ/∂x = 22x and ∂Fₓ/∂y = 2y, then subtract.

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