# Skin effect

Can anyone please describe the reason behind skin effect? All that I have come to know so far is that, due to higher magnetic flux density at the central region of the conductor compared to the region near it's surface, the effective inductance of the conductor is more at its centre and less near its surface..thus in case of flow of AC current, the current concentrates near the conductor-surface. But I don't understand why the flux density is more at its central region. Can anyone explain it with a diagram?

## Answers and Replies

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As current passes through a wire, it sets up a circulating magnetic field around the wire. This is often explained in books with a current-bearing piece of wire passing by a compass.

Michael Faraday noticed that sudden changes in the current passing through a wire would cause induce voltage in nearby wires.

If you perform the following thought experiment, it gives an intuitive example of what happens:

Imagine the wire to be seperated into an inner wire and a surrounding tube, or pipe. Now, suppose you apply a high frequency current to the outer portion, the pipe. The surrounding magnetic field will induce a voltage accross the inner conductor. Now, if you connect the inside wire to the outside pipe at the two ends, the inner conductor will not carry as much current as you would think. Why? Because the outer conducter has created a voltage drop across the inner conductor that is in opposition to the applied voltage. Thus the inner conductor still carries current, but not as much as you might guess.

Now, connect the outer pipe to the inner conductor along the length, and you find the same thing is going on. Voltage induced inside by the surrounding field causes it to oppose flow, thus the current density is higher on the outside.

Now, if you use thinner wire, the effect is decreased, as far as the resistance, but if you simply bundle a group of thinner wires, the ones on the inside will again experience the effect.

This brings up litz wire, which uses tiny, individually insulated, conductors that weave in and out. Thus, each conductor spends about the same amount of time on the outside and inside as all the other conductors. The opposing voltage does not cause the current to favor one wire over another, and the overall resistance approaches what you would expect without the skin effect.

Alternately, when dealing with transformers or inductors, multiple parallel windings will frequently be adequate. Sometimes designers choose to use foil, but for the most part it is overkill.

The reason is given below, but you can read only the words in Blue and bypass all the formulas if you just take my word!!!( warning, dangerous!!!)

Let's assume we use a round wire. If you put a RF voltage across the wire, an E is developed across the wire. using EM theory and the direction of EM wave propagation, you will find the EM wave propagate INTO the wire and towards the center of the round wire.

Let's use cylindrical coordinates:
$$\hat E =-\hat n \times \hat H\;\;\hbox { where }\;\;\hat E, \; \hat n, \; \hat H\;\;\hbox { is the unit vector of the electric, direction of propagation and magnetic field respectively.}$$
Let the wire on z axis and the reference direction of current in z direction, from right hand rule, magnetic field circulate around the wire in $\hat {\phi}\;$ direction. Therefore:
$$\hat E =-\hat n \times \hat H\;\Rightarrow \; \hat z = -\hat n \;\times\; \hat {\phi}\;\Rightarrow \hat n =-\hat r$$
Therefore with $\hat E =\hat z,\;\;\hat H=\hat{\phi}$, propagation is in $-\hat r\;$ direction which is into the wire.

EM wave suffer high loss when propagate into any good conductor like copper. So the amplitude of the E field decrease as the EM wave penetrate deeper into the wire.

The reason is magnitude of electric field in the wire is proportion to $e^{-\alpha (R-d)}\;$ where $\alpha = \sqrt{\pi f \mu σ}\;$, R is the radius of the wire and d is the distance of penetration of the EM wave into the wire. Also σ is the conductance of say copper. $σ_{Cu}≈5.8\times 10^7$, so the magnitude decrease very fast. In fact, the better the conductor, the faster the electric field goes down.

The current density is proportional to the E at any point inside the wire, so as E decrease when moving into the wire, the current density decrease as you go deeper into the wire. For good conductor like copper, most current are conduct at the surface, very little inside the wire. Also you can see, if you assume perfect conductor where σ=∞, no field penetrate into the wire and all current stay on the surface.

This is the harder to understand than the pipe explanation. But this is the theory behind skin effect and also it tell you the skin depth or the penetration depth depend of the frequency and how good the conductor the wire is made of. I don't know your level of understanding EM, so this is a very condense version. If you have any specific question, post back.

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