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In obtaining result (1.36)—not a solution—we chose the function op to be 1/|x – x',
it being the potential of a unit point charge, satisfying the equation: r 1 - - — w' V2
| - r) = —4trö(x — x') (1.31) The function 1/|x — x' is only one of a class of ...
Then let us make a gauge transformation to potentials A", p" and demand that A', '
D' satisfy the Lorentz condition: f 2 v.A. 11% – o – v. A + 1* + vow – ko (639) C Ot
C Ot co 9to Thus, provided a gauge function A can be found to satisfy 1 32A 1 ...
Then p = 0, and A satisfies the homogeneous wave equation. The fields are
given by E - – 12* ... Since the time is involved, the Green's function will depend
on the variables (x, x', t, t'), and will satisfy the equation, 2 (v. - #) G(x, t: x', t') = —4t
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Introduction to Electrostatics
BoundaryValue Problems in Electrostatics I
References and suggested reading
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