# Electromagnetic wave and skin depth, skin effect

In EM theory concept of skin depth is induced which is a measure of how much a EM wave can penetrate the medium, from it arises the concept of skin effect which is for EM wave but we use this to explain flow of current in conductor (most of the current flows over the skin of conductor at high frequency). But all this was derived for EM wave then why are we using it to explain flow of current,which is not em wave ???

• What is your source for the statement that the penetration of EM in a medium explains the skin effect in a conductor? – Bob D Aug 13 '19 at 15:29
• The electric current flows mainly at the "skin" of the conductor, between the outer surface and a level called the skin depth. The skin effect causes the effective resistance of the conductor to increase at higher frequencies where the skin depth is smaller, thus reducing the effective cross-section of the conductor – Barry Aug 13 '19 at 15:53
• Yes Harsh, but it is due to the eddy currents produced in the conductor induced by the alternating magnetic field. To my knowledge, the depth of penetration of a medium by EM waves is not based on eddy currents. To you have info to the contrary? – Bob D Aug 13 '19 at 16:04
• What I wanna ask is that skin depth is concept for EM wave, skin effect is for current in a conductor but boundaries set for skin are measured in terms of skin depth, which is measure of how much a EM wave can penetrate a medium. – Barry Aug 13 '19 at 16:34
• @BobD: Since $\vec{J} = \sigma \vec{E}$, the current density in the conductor and the electric field have the same profile. In particular, the characteristic depth for the current in the conductor is the same as the characteristic fall-off depth for the penetration of the wave; both are proportional to $e^{-z/\delta}$ (if the incident wave is in the positive $z$-direction.) See, for example, §9.4.1 of Griffith's Introduction to Electrodynamics for the gorey details. – Michael Seifert Aug 13 '19 at 17:32

## 1 Answer

for EM wave then why are we using it to explain flow of current,which is not em wave ???

The current in the wire is actually related to electromagnetic waves around the wire.

It just happens to be easier in many situations to analyze the currents in and voltages on conductive parts of a system than to analyze the fields in the dielectric parts of the system.

But the currents and voltages are inextricably linked to the fields, and in the case of analyzing skin depth it's easier to understand if we analyze the fields instead of the currents and voltages.

• To clarify; the current and the EM field interact and sustain each other intimately. You cannot have the one without the other. Analysing the one also informs you about the other. – Guy Inchbald Apr 1 at 18:52