Find the Conservative vector field for the potential function by finding its gradient.

Question

Find the <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Conservative vector field for the potential function by finding its gradient.

Answer 1

Step 1:

The potential function is .

Gradient field :

If is scalar function of two variables, then the gradient vector and it is denoted by is .

The gradient of the function is .

is the partial derivative of with respect to .

Then .

is the partial derivative of with respect to .

Then .

The conservative vector field is .

Solution :

The gradient of is .

The conservative vector field is .