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(Solved): Use the identity grad\times gradf=0 and Stokes' Theorem to show that the circulations of the followi ...
Use the identity
grad\times gradf=0and Stokes' Theorem to show that the circulations of the following fields around the boundary of any smooth orientable surface in space are zero. a.
F=5\xi +5yj+5zkb.
F=grad(2xy^(2)z^(3))c.
F=grad\times (\xi +yj+zk)d.
F=gradfdirection counterclockwise with respect to the surface's unit normal vector
nequals the integral of
grad\times F*nover S . The formula is shown below.
o\int_C F*dr=∬_(S)grad\times F*nd\sigma 