Sunday, 1 May 2016

Skin Effect and the Maxwell-Faraday Equation

The skin effect is an issue for alternating current where the higher the frequency of the alternating current the more pronounced the skin effect. The material of the conductor also affects the skin effect.

The skin effect on AC transmission lines involves all of the parameters of the telegrapher’s equations. The most important of the parameters involves the electron eddy currents associated with, L, Although most of the inductance, L, will be found outside the conductor some of the inductance or angular momentum. 

Most of the fastest moving electrons will be found at the boundary between the conductor and the dielectric. Fast moving electrons will eddy into the dielectric starting in the direction of current movement and then curling. There will be opposing eddies, the current will eddy into the conductor where it will have a tendency spin and will have the property of angular momentum. 

The eddy currents when viewed from around the conductor and along the length of the conductor will add up constructively towards the surface of the conductor. There will be destructive interference where the eddy currents oppose the direction of normal electron current.


The electrons will have the easiest time accelerating near the cladding of the conductor as they leap-frog their way to an electrical load or away from this load. Some electrons will escape the cladding boundary into the dielectric creating easier acceleration for subsequent electrons in the flow at the cladding.

The acceleration and faster relative velocities near the conductor-dielectric boundary can be seen as a type of easier acceleration because the density of atoms is less outside the conductive lattice when compared with the inside of the lattice. The electrons of an AC current are eddying in both directions and the non-eddy electron shoots down the middle efficiently. As well, with AC, there is a change of direction necessary and this change in direction is facilitated by the capacitance specified by the telegraphers equations.

The velocity or inertia of electrons eddying out around a given nucleus can knock other electrons out of their orbitals and into the curl of the flux of the electron flow. Again with more than 1020 electrons traveling in a very small space the electron density means this may be fairly common. It will be less common for an electron to collide with a nucleus.

The skin effect phenomenon can also be explained using magnetic fields. To see how take a look at the diagram below.

The current will produce a curling magnetic field by the Maxwell-Ampere equation. In turn the changing magnetic field due to the AC current will produce eddy currents within the conductor. At the surface of the conductor the eddy currents will be additive with the prevailing currents. Towards the center of the conductor the eddy currents from around the circumference of the conductor will add up against the conduction current preventing current flow in the middle of the conductor.

Material Referenced from: Johnson and Graham, High Speed Signal Propagation, 2003.

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