We present two derivations of the hyperfine interaction in the ground state of hydrogen using classical electrodynamics. We calculate, at the site of the proton moment m p, the magnetic field B e due to the magnetization source M e ( r ) of the relatively extended 1 s electron state. This gives the magnetic interaction via m p · B e. One derivation applies the Biot–Savart law to the bound 1 s electric current J b = × M to directly find B e; the other derivation applies the magnetic version of the Coulomb Law to the bound 1 s magnetic charge density ρ b = · M to first obtain μ 0 H e and then adds μ 0 M to find B e. We show, for any source M , that these two approaches give the same B ( r ), as is expected within classical electrodynamics.

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