Question: A straight wire with radius a and magnetic permeability carries a conduction current density j 0 = j 0 z = z /0 a

A straight wire with radius a and magnetic permeability μ carries a conduction current density j₀ = j₀ẑ = 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 B₀= B₀x̂.

(b) Show that the Lorentz force F = ∫ d³r j × B = I₀B₀ŷ, where j is the total current density and B is the total magnetic field.

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