An infinite cylinder of radius R filled with matter with permeability 1 is embedded in an

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An infinite cylinder of radius R filled with matter with permeability μ1 is embedded in an infinite medium with permeability μ2. A wire carries a current Iƒ up the z-axis of the cylinder. Show by explicit calculation that the sum of the fields produced by the free currents and the magnetization currents is equal to the field at every point in space as calculated using Amp`ere’s law directly.


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