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Curl

Curl

The curl is the cross product of the del operator with a vector function F. This operation leads to a new vector. It tells us how big a rotation (spin) is of a swirling vector field.

  Definition

  Example

Find the curl of

Put in the variables into the last row. Replace the F.

You can use the rules of the evaluation of a determinant.

First step

Strike out the column of the vector i.

Multiply the opposite components.

Then subtract the product. Begin with the left partial derivative. At last do the derivatives.

Second step

Strike out the column of the vector j.

Write the negative sign in front of the determinant. Multiply the opposite components.

Then subtract the product. Begin with the left partial derivative. At last do the derivatives.

Third step

Strike out the column of the vector k.

Multiply the opposite components.

Then subtract the product. Begin with the left partial derivative. At last do the derivatives.

Sum up the components.