Electromagnetic Theory (v2) #22 | Magnetic Forces, Torque & Materials

Instructor: Dr. Süleyman Burak ÇELİK

The last piece of magnetostatics: what does B actually do? We build the full force-and-materials toolbox. Start with a single moving charge (Lorentz's law, F = qv × B), scale to a current-carrying wire (dF = I dL × B), then to a closed current loop where the net force is zero but the torque is not — and it takes the clean form τ = m × B with the magnetic dipole moment m = IA n̂. The same equation governs a compass needle, an electric motor, and MRI. From there we go into materials: magnetization M, bound currents, B = μ₀(H + M), and the three classes — diamagnetic, paramagnetic, ferromagnetic. Static EMT closes here; d23 wraps it up with boundary conditions, inductance, and magnetic energy. Key equations: • F = q(E + v × B) — full Lorentz force • dF = I dL × B — current element • τ = m × B — dipole torque • U = −m · B — magnetic potential energy • B = μ₀(H + M) = μH, μr = 1 + χm Reference: Sadiku 7th Ed, Sections 8.1-8.6