I am trying to understand the skin effect, there is a bit in Wikipedia article I don't understand;

"...The change in the magnetic field, in turn, creates an electric field which opposes the change in current intensity. This opposing electric field is called “counter-electromotive force” (back EMF). The back EMF is strongest at the center of the conductor, and forces the conducting electrons to the outside of the conductor, as shown in the diagram on the right."

Why is the induced EMF strongest at the center of the conductor?

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    $\begingroup$ Yep, that's a very poorly thought out explanation, and honestly, I would call it flat out wrong. The current density inside a conductor with skin effect decays towards the inside, and for an infinitely large conductor it would be zero and there would be no fields in there, at all. In technical applications this means that one can use hollow conductors, which can then be cooled from the inside with high pressure water without any significant loss in effective conductivity. $\endgroup$
    – CuriousOne
    Dec 25, 2014 at 13:46

1 Answer 1


When an EM wave penetrates a conductor, the E-field decays as it travels into the medium. The induced current density is proportional to the E-field and directed perpendicularly to the wave motion.

The induced currents lead to Ohmic losses. The skin depth is the characteristic exponential decay length of the electric field. The Poynting vector, which measures how much power per unit area is carried by the fields is proportional to the square of the electric field. Hence the Poynting vector decays a factor of two more quickly.

If one evaluates the Ohmic dissipation, (${\bf J}\cdot {\bf E}$) per unit volume, integrated over the depth that the wave penetrates, one finds it is exactly equal to the energy lost deduced from the diminished Poynting vector.

So the EMF is not strongest at the centre of the conductor, quite the opposite.

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    $\begingroup$ Ok, I understand what you are trying to say, but suppose you are thinking about a normal wire carrying an AC current. How do you theoretically explain the skin effect in that case? $\endgroup$
    – Mark
    Dec 28, 2014 at 12:48
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    $\begingroup$ @Mark The explanation I've given is appropriate if you wish to induce an AC current in a wire. An AC current is an EM wave penetrating into a conductor. $\endgroup$
    – ProfRob
    Dec 29, 2014 at 9:44

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