A straight wire with radius a and magnetic permeability carries a conduction current density j 0

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A straight wire with radius a and magnetic permeability μ carries a conduction current density j0 = jẑ = ẑ /0 πa2.

(a) Find the induced magnetization M and the volume and surface magnetization current densities when the wire is exposed to a uniform external field B= Bx̂. 

(b) Show that the Lorentz force F = ∫ dr j × B = IBŷ, where j is the total current density and B is the total magnetic field.

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