Magnetic skin layer
= Magnetic skin layer
{title2=$\delta=\sqrt{2\eta/\omega}$}
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 $B_y=C'(x)e^{-(1+i)y/\delta}\delta/(1+i)$ to leading order. The tangential-field approximation therefore does not mean that the normal component is exactly zero at finite <magnetic diffusivity>.