Two additional examples: In deriving Green's 2nd Identity, one applies the Divergence Theorem to two vector functions defined by F1 = φdivψ F2 = ψdivφ and substracting the two. This forms the foundation for solutions to Poisson's Equation. In deriving Lorentz's Reciprocity Theorem, one applies the Divergence Theorem to two vector functions defined by F1 = E1 x B2 F2 = E2 x B1 then using Faraday's Law and the Ampere-Maxwell Law to substitute curlE and curlB terms, and subtracting the two. This forms the foundation for showing the equivalence of antennas in transmit and receive modes, in particular.
Is there any reason you start with a volume integral with the two E fields dotted together? It just seems so random, I don't understand how it's logical to start there or what it even means.
Two additional examples:
In deriving Green's 2nd Identity, one applies the Divergence Theorem to two vector functions defined by
F1 = φdivψ
F2 = ψdivφ
and substracting the two.
This forms the foundation for solutions to Poisson's Equation.
In deriving Lorentz's Reciprocity Theorem, one applies the Divergence Theorem to two vector functions defined by
F1 = E1 x B2
F2 = E2 x B1
then using Faraday's Law and the Ampere-Maxwell Law to substitute curlE and curlB terms, and subtracting the two.
This forms the foundation for showing the equivalence of antennas in transmit and receive modes, in particular.
Is there any reason you start with a volume integral with the two E fields dotted together? It just seems so random, I don't understand how it's logical to start there or what it even means.
ρ1 is influenced by the potential of V2 @ ρ1, and vice versa.
One could also think of the integral as the interaction energy between the two fields.
Thanks a lot!
Excellent video! Thank you very much.
David Garcia Thanks!
wonderful!