Skin Effect in a Conductor

What you are seeing: the electric field $E(z, t) = E_0 e^{-z/\delta} \cos(\omega t - z/\delta)$ inside a conductor. The skin depth $\delta = \sqrt{2/(\omega \mu \sigma)}$ shrinks with frequency. Cu at 60 Hz: 8.5 mm; at 1 GHz: 2 μm.

Figure 1. Penetration of an AC E-field into a conductor; envelope is

e^{-z/\delta}

log10(f) Hz1e6

material

WHAT TO TRY

Raise the frequency: the field crowds into a thinner and thinner skin, since the penetration depth delta scales as one over the square root of f. At microwave frequencies the current flows in a layer microns thick.
Switch material: a better conductor, or a magnetic one like iron with mu_r = 200, shrinks delta further, which is why high-frequency wires are silver-plated and why iron shields fields so well.
Watch the wave crawl inward and decay: it both attenuates and lags in phase as it penetrates, the e^(-z/delta) envelope riding a wave that dies within a few skin depths.