A solenoid contains a core of relative permeability μᵣ = 400. The magnetic field inside the solenoid is 1.0 T. If the magnetic field intensity is written as H = α×10⁵ A·m⁻¹ and μ₀ = 4π×10⁻⁷ T·m·A⁻¹, what is α?
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Question

A solenoid contains a core of relative permeability μᵣ = 400. The magnetic field inside the solenoid is 1.0 T. If the magnetic field intensity is written as H = α×10⁵ A·m⁻¹ and μ₀ = 4π×10⁻⁷ T·m·A⁻¹, what is α?

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G1 Physics · Accepted Answer

The relation between magnetic field B and magnetic field intensity H is B = μ₀μᵣH. Therefore, H = B ÷ (μ₀μᵣ). Substitute: H = 1 ÷ [(4π×10⁻⁷)(400)]. Since 400×4π×10⁻⁷ = 16π×10⁻⁵, we get H = 1 ÷ (16π×10⁻⁵) = [1 ÷ (16π)]×10⁵ A·m⁻¹. Thus, α = 1 ÷ (16π). Correct option: B.