VC5.44

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\iint _{S}{\frac  {\partial \phi }{\partial n}}dS=\iint _{S}[{\frac  {\partial \phi }{\partial n}}n]\cdot ndS\,

=\iint _{S}{\mathrm  {grad}}\phi ndS\, [Since {\mathrm  {grad}}\phi ={\frac  {\partial \phi }{\partial n}}n\,]

=\iiint _{V}{\mathrm  {div}}{\mathrm  {grad}}\phi dV\,,by divergence theorm.

=\iiint _{V}\nabla ^{2}\phi dV\, [Since{\mathrm  {div}}{\mathrm  {grad}}\phi =\nabla \cdot \nabla \phi =\nabla ^{2}\phi \,]


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