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The magnetic flux freezing theorem or Alfv\'en's theorem, is a basicprinciple of ideal magnetohydrodynamics (MHD), a commonly used approximation todescribe the aspects of astrophysical and laboratory plasmas. The theoremstates that the magnetic flux---the integral of magnetic field penetrating asurface---is conserved in time as that surface is distorted in in time by fluidmotions. Pedagogues of MHD commonly derive flux freezing without showing how totake the material derivative of a general flux integral and/or assuming avanishing field divergence from the outset. Here I avoid these shortcomings andderive flux freezing by direct differentiation, explicitly using a Jacobian totransform between the evolving field-penetrating surface at different times.The approach is instructive for its generality and helps elucidate the role ofmagnetic monopoles in breaking flux freezing. The paucity of appearances ofthis derivation in standard MHD texts suggests that its pedagogic value isunderappreciated.

On deriving flux freezing in magnetohydrodynamics by direct differentiation