QinsldeV=-∮qNd.da-∫ppdV paired charge or equivalently polarization charge density Q--.da--v-dv-odV (Divergence Theorem) P=qNd V.P=-Pp B.Gauss'Law V,e。目=poa=putp=pu-V.p unpaired charge density;also called free charge density V(e。E+p=pu D=8。E+p Displacement Flux Density V.D=Pu C.Boundary Conditions Ea,Pa,Da ⊙ Osur Osp Eo,Po,Do b 6.641,Electromagnetic Fields,Forces,and Motion Lecture 7 Prof.Markus Zahn Page 3 of 276.641, Electromagnetic Fields, Forces, and Motion Lecture 7 Prof. Markus Zahn Page 3 of 27 − =ρ ∫ ∫ i inside V P v S V Q = qN d da dV − =− ∇ = ρ ∫∫ ∫ i i inside V P v SV V Q = P da P dV dV P = qNd (Divergence Theorem) ∇ = −ρ iP P B. Gauss’ Law ∇ =ρ =ρ +ρ =ρ −∇ i i ( ) εo total u P u E P ∇ + =ρ i( ) εo u E P D EP o = + ε Displacement Flux Density ∇ =ρ iD u C. Boundary Conditions paired charge or equivalently polarization charge density unpaired charge density; also called free charge density