Practice question

**Magnetic properties** μ_r = 400 indicates 400 times vacuum permeability, so B enhanced 400 times for same nI. H = nI (A/m) for solenoid, M = χ H, B = μ₀(H+M) links microscopic magnetization to macroscopic field. B = μ₀ (H + M) , so M = (B/μ₀) - H . Given: B = 0.45 T , H = 3000 A m⁻¹ , μ₀ = 4π × 10⁻⁷ . (B/μ₀) = (0.45/4π × 10⁻⁷) ≈ 3.581 × 10⁵ A m⁻¹ . M = 3.581 × 10⁵ - 3000 ≈ 3.551 × 10⁵ A m⁻¹ . Substituting values gives 3.551 × 10⁵ A m⁻¹, which matches