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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 , D ' AG ( x , x ' ) = - 470 ( x - x ' ) ( 1 . 39 ) where 1 G ( x , x ' ) = - + F ( x , x '
) ( 1 .
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 ' , O ' and
Then Q = 0 , and A satisfies the homogeneous wave equation . ... Since the time
is involved , the Green ' s function will depend on the variables ( x , x ' , t , t ' ) , and
will satisfy the equation , 1 22 v2 - 5 ) G ( x , t ; x ' , t ' ) = - 41 8 ( x – x ' ) 8 ( t – t ...
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Introduction to Electrostatics
References and suggested reading
Multipoles Electrostatics of Macroscopic Media
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