Force on a current sheet from the mean magnetic field (${\mathbf{f}}_S=\mathbf{K}\times ({\mathbf{B}}_{+}+{\mathbf{B}}_{-})/2$)

The Lorentz force per unit area on an ideal current sheet is computed using the mean of its limiting magnetic fields. The sheet's own local magnetic field is equal and opposite on its two sides and cancels in this mean. Equivalently, integrate the Lorentz force density through a thin regularized layer: its self-field contribution averages to zero, leaving the external field acting on the surface current density.