Question

Find (a) the curl and (b) the divergence of the vector field.

Answer 1

Step 1 :

If  is a vector field on  and the partial derivatives of P , Q  and R  all are

exists, then the curl of F is , or

And the divergence of F is .

Step 2 :

(a)

The vector field is .

Compare with .

and .

Find the curl of the vector field F.

The curl of the vector field F is

Step 3 :

(b)

Consider .

Apply partial derivative on each side with respect to x.

Consider .

Apply partial derivative on each side with respect to y.

Consider .

Apply partial derivative on each side with respect to z.

Step 4 :

Find the divergence of vector field F.

Substitute corresponding values.

The divergence of the vector field F is

Solution :

(a) The curl of the vector field F is .

(b) The divergence of the vector field F is