provided x is outside AV. We now treat AV as (macroscopically) infinitesimal, put it equal to...

 

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provided x is outside AV. We now treat AV as (macroscopically) infinitesimal, put it equal to d³x', and integrate over all space to obtain the potential + P(x'). V' The second term is analogous to the dipole layer potential (1.25), but is for a volume distribution of dipoles. An integration by parts transforms the potential into Φ(x) √ d³x '[_P(x²) 4 TEO X-X' Φ(x) = 1/6 fd²x². 4πTEO [p(x')' P(x')] X This is just the customary expression for the potential caused by a charge distri- bution (pVP). With E= -VO, the first Maxwell equation therefore reads 1 provided x is outside AV. We now treat AV as (macroscopically) infinitesimal, put it equal to d³x', and integrate over all space to obtain the potential + P(x'). V' The second term is analogous to the dipole layer potential (1.25), but is for a volume distribution of dipoles. An integration by parts transforms the potential into Φ(x) √ d³x '[_P(x²) 4 TEO X-X' Φ(x) = 1/6 fd²x². 4πTEO [p(x')' P(x')] X This is just the customary expression for the potential caused by a charge distri- bution (pVP). With E= -VO, the first Maxwell equation therefore reads 1

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