 Magnetic skin layer

A magnetic skin layer is the thin region penetrated by an oscillating magnetic field in a conductor. For locally tangential boundary amplitude $C(x)$, negligible material motion and variations along the boundary much slower than those across it, the resistive induction equation gives $B_x=C(x)e^{-(1+i)y/\delta }$ with time convention $e^{i\omega t}$. The solenoidal magnetic-field constraint requires the smaller component $B_y=C^{\prime }(x)e^{-(1+i)y/\delta }\delta /(1+i)$ to leading order. The tangential-field approximation therefore does not mean that the normal component is exactly zero at finite magnetic diffusivity.