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In obtaining result ( 1.36 ) —not a solution — we chose the function y to be 1 / | x – x ' ] , it being the potential of a unit point charge , satisfying the equation : 1 V 2 - 478 ( x – x ' ) ( 1.31 ) | x– x'll The function 1 / 6X ...
To see that potentials can always be found to satisfy the Lorentz condition , suppose that the potentials A , 0 which satisfy ( 6.32 ) and ( 6.33 ) do not satisfy ( 6.36 ) . Then let us make a gauge transformation to potentials A ' ...
Then 0 = 0 , and A satisfies the homogeneous wave equation . ... Since the time is involved , the Green's function will depend on the variables ( x , x ' , 1 , t ' ) , and will satisfy the equation , V ? - 1 22 G ( x , t ; X ' ...
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Introduction to Electrostatics
References and suggested reading
Multipoles Electrostatics of Macroscopic Media
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