A solenoid has a core of a material with relative permeability 400. The windings of the solenoid are insulated from the core and carry a current of 1 A. If the number of turns is 1000 per metre, find the magnetic field B inside the core. (μ₀=4π×10⁻⁷ SI)

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(3) 16π×10⁻² T. Given: μᵣ=400, n=1000 turns per metre, I=1 A, μ₀=4π×10⁻⁷ T m A⁻¹. Idea: inside a long solenoid the magnetising field is H=nI, and the core multiplies the field by its relative permeability: B=μ₀μᵣ H=μ₀μᵣ n I. H=nI=1000×1=10³ A m⁻¹. μᵣ H=400×10³=4×10⁵ A m⁻¹. B=4π×10⁻⁷×4×10⁵=16π×10⁻² T, which is about 0.5 T.

A solenoid has a core of a material with relative permeability 400. The windings of the solenoid are insulated from the core and carry a current of 1 A. If the number of turns is 1000 per metre, find the magnetic field B inside the core. (μ₀=4π×10⁻⁷ SI)

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