How Does Gauss' Theorem Transform Volume to Surface Integrals?

[dreamfly]

how －∫(v)laplace functor *J*dτ change into -∮(s) J(n) dS using Gauss formula?

 

[Galileo]

Do you mean

$$\int_V \vec \nabla \cdot \vec J d\tau = \oint_S \vec J \cdot d\vec S$$
under the appropriate conditions on J, S and V.

This is the divergence theorem (also called Gauss' or Ostrogradsky's theorem). You cannot use Gauss' Law (if that is what you meant) to prove this. the divergence theorem is stronger and can be used to prove Gauss' law.

 

[dreamfly]

ok thanks! it's just our teacher told us to prove this equation by Gauss' theorem.and now I've known the process.thanks!