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The function 1 / | x – x ' is only one of a class of functions depending on the variables x and x ' , and called Green's functions , which satisfy ( 1.31 ) . In general , V'2G ( x , x ' ) = -410 ( x - x ' ) ( 1.39 ) where 1 G ( x ...
To see that potentials can always be found to satisfy the Lorentz condition , suppose that the potentials A , which satisfy ( 6.32 ) and ( 6.33 ) do not satisfy ( 6.36 ) . Then let us make a gauge transformation to potentials A ' ...
... Of course , the fields E ' , B ' must satisfy Maxwell's equations and the radiation condition in region II ' if E , B satisfy them in region II . It is easy to show that the required relationship , giving ( 9.79 ) on the surfaces ...
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Introduction to Electrostatics
References and suggested reading
Multipoles Electrostatics of Macroscopic Media
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