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). Superconductors achieve perfect conductivity and expel magnetic fields (Meissner effect) below their critical temperature, where induced surface currents counteract the external field, a phenomenon tied to zero resistance and perfect diamagnetism. Substituting values gives Induced surface currents, which matches expected magnitude for this magnetic configuration, confirming dipole field dependence on m/r³ and torque relation τ = m B sinθ.