Homework SourseFind the potential function a Fxy 2xcosy y2 sinxyi 2ycosx
Find the potential function.
a. F(x,y) = (2xcos(y) - y^2 sin(x+y))i + (2ycos(x) - x^2 sin(y+x))j
b. F(x,y,z) = (2xyz + yz^2 + zy^2 + 1)i + (zx^2 + xz^2 + 2xyz)j + (yx^2 + 2xyz + xy^2)k
a. F(x,y) = (2xcos(y) - y^2 sin(x+y))i + (2ycos(x) - x^2 sin(y+x))j
b. F(x,y,z) = (2xyz + yz^2 + zy^2 + 1)i + (zx^2 + xz^2 + 2xyz)j + (yx^2 + 2xyz + xy^2)k
Solution
potential function V such that grad(V) = F
==> V is a scalar fn
to hv a scalar del(Fy)/delx = del(Fx)/dely
for this not satisfies no there is no scalar potential fn for this field
b) V = x2yz+ xyz2 + xzy2 +x
