Practice question

**Magnetic dipole in uniform field** experiences torque τ = m B sinθ and potential energy U = -m·B = -m B cosθ, minimum -mB when aligned (θ=0°), maximum +mB at anti-alignment (θ=180°). Work done rotating from θ₁ to θ₂ equals ΔU = mB(cosθ₁ - cosθ₂). B = μ₀ μ_r H . Given: μ_r = 600 , H = 400 A m⁻¹ , μ₀ = 4π × 10⁻⁷ . B = 4π × 10⁻⁷ × 600 × 400 = 0.3016 T ≈ 0.3 T . Substituting values gives 0.3 T, which matches expected magnitude for this magnetic configuration, confirming dipole field dependence on m/r³ and torque