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). tau = m B sinθ . Given: m = 0.7 A m² , B = 0.2 T , θ = 45° , sin 45° = (1/√(2)) ≈ 0.707 . tau = 0.7 × 0.2 × 0.707 = 0.09898 N m ≈ 0.1 N m . Substituting values gives 0.1 N m, which matches expected magnitude for this magnetic configuration, confirming