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Asked in GUJCET 2014 · Magnetisation, intensity and susceptibility
Idea: read the unit off any equation that contains μ₀. Take the force per unit length between two long parallel currents, F/ℓ=(μ₀I₁I₂)/(2π d).
Rearranged, μ₀=(2π d)/(I₁I₂)·F/ℓ.
Units: m/(A²)×N/m=N A⁻² -- the metres cancel.
The same answer comes from B=(μ₀I)/(2π r), which gives T m A⁻¹; since 1 T=1 N A⁻¹ m⁻¹, this is N A⁻² again.
So the unit of μ₀ is N A⁻², the same thing as H m⁻¹.
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