Practice question

**Soft ferromagnetic materials** have low coercivity and retentivity, narrow hysteresis loop, lose magnetism when external field removed, ideal for electromagnets and transformer cores. Energy loss per cycle proportional to loop area, explaining why soft materials minimize loss. Magnetic potential energy is U_m = -m B cosθ . Given: m = 0.4 A m² , B = 0.5 T , θ = 30° , cos 30° = (√(3)/2) ≈ 0.866 . Substitute: U_m = -0.4 × 0.5 × 0.866 = -0.1732 J ≈ -0.17 J . Substituting values gives -0.17 J, which matches expected magnitude for this magnetic configuration, confirming dipole field dependence on m/r³ and