Question

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

Answer 1

Not conservative

Explanation:

For a field to be a conservative field, a necessary condition is that its curl is zero. So:

`nabla times vec F = det ((hat i, hat j , hat k),(del_x, del_y, del_z),(xy+z, xy-x, xz))`

`= hat i (0) - hat j (z-1) + hat k (y-x) ne 0`

Not conservative