VC5.28

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Let S denote the surface of the given sphere and V be the volume enclosed by S.Now,by definition,

{\mathrm  {div}}F={\frac  {\partial }{\partial x}}(x)+{\frac  {\partial }{\partial y}}(-y)+{\frac  {\partial }{\partial z}}(2z)=1-1+2=2\, --(1)

Hence,by the divergence theorm,we have

\iint _{S}F\cdot ndS=\iiint _{V}{\mathrm  {div}}FdV\,

=\iiint _{V}2dV\, by (1)

=2V=2({\frac  {4}{3}}\pi )={\frac  {8\pi }{3}}\,

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