By Green's theorem in space (divergence theorem).
Prove that
that
(V x A) - n ds for any closed surface S.
S
Prove that
10.66.
dS
ff n ds = 0. where n is the outward drawn normal to any closed surface S. (Hint: Let A = Oc,
SS
S
where c is an arbitrary vector constant.) Express the divergence theorem in this special case. Use the
arbitrary property of c.
10.67. If n is the unit outward drawn normal to any closed surface S bounding the region V, prove that
fff div n dv = S
V
Stokes's theorem
40.68.
Verify Stokes's theorem for A = 2yi + 3xj - z²k, where S is the upper half surface of the sphere x² + y² + ² =
9 and C is its boundary.
Ans. Common value = 9T
10.65.
, y = 0,
