Worked example: A compass needle (m = 0.02 A·m², moment of inertia I = 10⁻⁷ kg·m²) sits in Earth's field B = 30 μT. (a) Maximum torque? (b) Small-oscillation period? (c) Work to rotate it from north to south? Step 1: τmax = mB = 0.02 × 30 × 10⁻⁶ = 6 × 10⁻⁷ N·m. Step 2: T = 2π√(I/mB) = 2π√(10⁻⁷/6 × 10⁻⁷) = 2π√(1/6) = 2π × 0.408 = 2.57 s — a leisurely, observable wobble. Step 3: W = mB(cos0° − cos180°) = 2mB = 1.2 × 10⁻⁶ J — tiny, which is why the needle flips so readily; scale m up to a fridge magnet and the same formula explains its stubborn grip.