Let T be the part of the paraboloid surface
z = (x + 1)² + y² -5
that lies between the cylinders
x² + y² = 1 and x² + y² = 3.
Assume Tis oriented with downward unit normal. Let
F(x, y, z) = i + (z+eˣ) j + 2y(eˣ - 4)k
be a magnetic field.
(a) Determine whether or not F is a conservative vector field.