where: ρ ρ f is the density of free charge; P is the polarization density ; J f is the density of free current; and M is the magnetization density. In this way, the Lorentz force can explain the torque applied to a permanent magnet by the magnetic field. The density of the associated power is ( J f + ∇ ∇ × × M + ∂ ∂ P ∂ ∂ t ) ⋅ ⋅ E .