Skin effect and currents

Here in this picture

you can see $I_W$ which is induced by H.
But why $I_W$ is not vice versa?
Because of
$$rot , vec B = mu_0 , left( varepsilon_0 frac{partial vec{E}}{partial t} + vec j right)$$ ?
Maybe I have to use
$$oint vec{E}cdot , dvec{r} = – int frac{partial vec{B}}{partial t}cdot , dvec{A} = U_{induced}$$