Practice question

**Core magnetization** M = (μ_r -1)nI, so B = μ₀(nI + M). High μ_r materials like soft iron increase B dramatically for same nI, used in electromagnets, with μ_r up to 5000, enabling strong fields with low current. In a toroid, magnetic field lines are confined within the core, forming closed loops due to the circular symmetry and the current in the windings. This contrasts with bar magnets or solenoids, where field lines extend externally. Substituting values gives A toroid, which matches expected magnitude for this magnetic configuration, confirming dipole field dependence on m/r³ and torque relation τ = m B sinθ.