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

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Answer 1 · 2016-10-16T08:35:48

Not conservative

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

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