Question

A force field is described by `<F_x,F_y,F_z> = < x +y , 2z, 2y -z >`. Is this force field conservative?

Answer 1

The force field is not conservative bacause `vec grad xx vec F ne vec 0`

Explanation:

Calculating the force field curl we have

# ((hat i, hat j, hat k), (partial/(partial x),partial/(partial y), partial/(partial z)), (x+y,2z,2y-z)) = (0,0,-hat k) #

which is different from `vec 0`