Expressing sol. of Poisson eqn. in terms of vol. and sur. integrals.

Hi,

Referring to Jackson's Electrodynamics 3ed, page 197, line 5.

He assumes that the magnetization can be divided into volume part and surface part, thus generating eqn 5.100. This is fine.

In a straightforward way, I wanted to do the same but for electrostatics, eqn 4.32:


∅= (1/4πε) ∫dv [ρ-∇.P]/[|r-r'|] (integral is over all space).

So is this correct:

∅= (1/4πε) ∫dv [ρ-∇.P]/[|r-r'|] + (1/4πε) ∫da [ρ-P.n]/[|r-r'|]
(1st is a vol. integral, 2nd is a sur. integral)

Note that the first term in the second eqn. is not the same as 4.32, in 4.32 integration is over all spave (which includes vol. and sur), while the first term in the second eqn. is over vol only.

Thanks in advance.