Poynting Theorem Derivation Pdf Download > shorl.com/brysifygrebrylu

Poynting Theorem Derivation Pdf Download

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Considering,,,,the,,,,statement,,,,in,,,,words,,,,above,,,,-,,,,there,,,,are,,,,three,,,,elements,,,,to,,,,the,,,,theorem,,,,,which,,,,involve,,,,writing,,,,energy,,,,transfer,,,,(per,,,,unit,,,,time),,,,as,,,,volume,,,,integrals:[3].,,,,Weisstein,,"Poynting,,Theorem",,From,,ScienceWorld,,,,A,,Wolfram,,Web,,Resource.,,∂,,,∂,,,t,,,(,,,u,,,e,,,+,,,u,,,m,,,),,,+,,,∇,,,⋅,,,(,,,S,,,e,,,+,,,S,,,m,,,),,,=,,,0,,,,,,,{displaystyle,,,{frac,,,{partial,,,}{partial,,,t}}left(u{e}+u{m}right)+nabla,,,cdot,,,left(mathbf,,,{S},,,{e}+mathbf,,,{S},,,{m}right)=0,},,,.,,,Poynting's,,,,theorem[edit].,,,,where,,S,,is,,the,,divergence,,of,,the,,Poynting,,vector,,(energy,,flow),,and,,JfE,,is,,the,,rate,,at,,which,,the,,fields,,do,,work,,on,,a,,charged,,object,,(Jf,,is,,the,,free,,current,,density,,corresponding,,to,,the,,motion,,of,,charge,,,E,,is,,the,,electric,,field,,,and,,,,is,,the,,dot,,product).,,where.,,175:,,,,343361.,,,,30,,,,(5):,,,,983.,,,,

External,,links[edit].,,{displaystyle,,,U=int,,,{V}udV,,,rightarrow,,,,,,{frac,,,{partial,,,U}{partial,,,t}}={frac,,,{partial,,,}{partial,,,t}}int,,,{V}udV=int,,,{V}{frac,,,{partial,,,u}{partial,,,t}}dV.},,,The,,,energy,,,flux,,,leaving,,,the,,,region,,,is,,,the,,,surface,,,integral,,,of,,,the,,,Poynting,,,vector,,,,and,,,using,,,the,,,divergence,,,theorem,,,this,,,can,,,be,,,written,,,as,,,a,,,volume,,,integral:,,,∂,,,V,,,{displaystyle,,,scriptstyle,,,partial,,,V},,,S,,,⋅,,,d,,,A,,,=,,,∫,,,V,,,∇,,,⋅,,,S,,,d,,,V,,,.,,,S,,m,,(,,r,,,,,t,,),,=,,∑,,α,,m,,α,,2,,r,,˙,,α,,2,,r,,˙,,α,,δ,,(,,r,,−,,r,,α,,(,,t,,),,),,.,,The,,time,,derivative,,of,,the,,energy,,density,,(using,,the,,product,,rule,,for,,vector,,dot,,products),,is.,,D,,,=,,,ϵ,,,0,,,E,,,,,,,B,,,=,,,μ,,,0,,,H,,,.,,,∂,,,,D,,,,∂,,,,t,,,,+,,,,J,,,,=,,,,∇,,,,,,,,H,,,,,,,,→,,,,,,,,E,,,,⋅,,,,∂,,,,D,,,,∂,,,,t,,,,+,,,,E,,,,⋅,,,,J,,,,=,,,,E,,,,⋅,,,,∇,,,,,,,,H,,,,.,,,,In,,,words,,,,the,,,theorem,,,is,,,an,,,energy,,,balance:.,,,∇,,,,⋅,,,,S,,,,+,,,,ϵ,,,,0,,,,E,,,,⋅,,,,∂,,,,E,,,,∂,,,,t,,,,+,,,,B,,,,μ,,,,0,,,,⋅,,,,∂,,,,B,,,,∂,,,,t,,,,+,,,,J,,,,⋅,,,,E,,,,=,,,,0,,,,,,,,,{displaystyle,,,,nabla,,,,cdot,,,,mathbf,,,,{S},,,,+epsilon,,,,{0}mathbf,,,,{E},,,,cdot,,,,{frac,,,,{partial,,,,mathbf,,,,{E},,,,}{partial,,,,t}}+{frac,,,,{mathbf,,,,{B},,,,}{mu,,,,{0}}}cdot,,,,{frac,,,,{partial,,,,mathbf,,,,{B},,,,}{partial,,,,t}}+mathbf,,,,{J},,,,cdot,,,,mathbf,,,,{E},,,,=0,},,,,.,,,,Taking,,,,the,,,,dot,,,,product,,,,of,,,,the,,,,MaxwellFaraday,,,,equation,,,,with,,,,H:.,,,,

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