STAKGOLD UNITS
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A brief note by Phil dated 12.13.15 comparing the Green's function conventions in Jackson (cgs, Laplacian of Phi = -4 pi rho) and Stakgold (Laplacian of E = -delta). It states the rule that multiplying a Stakgold fundamental solution by 4 pi gives the Jackson cgs form. Two examples are worked: the unit point charge, 1/(4 pi r) becoming 1/r, and the unit line charge, (1/2pi) ln(1/r) becoming 2 ln(1/r), which is checked against Purcell.
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Stakgold Units PhL 12.13.15
Green Jackson writes
2Φ = -4πρ page 13 cgs units
2(1/|x-x'|) = -4πδ(x-x') page 13 Greens is Φ = 1/r for unit point charge
Φ = 1/r potential of a point charge
Stakgold writes
2E = -δ(x) vol 2 page 48 E = fundamental solution Green's
Φ = (1/4πr) fundamental solution for n = 3
Rule: To convert a Stakgold fundamental solution to a Jackson cgs units one, multiply by 4π.
Example 1: Potential of a unit point charge:
Stakgold says E3 = 1/4πr
mult by 4π φ = 1/r Jackson
Example 2: Potential of a unit line chage
Stakgold says E2 = (1/2π)ln(1/r) page 50
mult by 4π φ = 2 ln(1/r) Jackson agrees with Purcell page 43