Skin effect

[bwanaaa]

How dependent is the skin effect on the geometry of the conductor? For example, at the Boston Museum of Science, a guy climbs into a big bird cage and is protected from millions of volts. What if the shape of the container is like a coke bottle? What if one of the metal rods of the cage is kinked inwards? Does the skin effect redistribute the charge to the convex surface of the conductor ?

 

[Paperdoc]

The Skin Effect for a static charge completely moves the excess charge to the outermost surface of the conductor. Basically that's because the excess electrons all try to repel each other, and the largest surface area available to them is the outside. Things change, though, when alternating currents are involved, especially at higher frequencies, because of inductive and capacitive effects of the structure.

 

[Modelworks]

For DC the current flows through the conductor regardless of its shape. Someone standing inside something completely enclosed like you are referring to (Faraday cage) will be protected if the sides were zigzagged or kinked or anything else provided they maintained the continuous form of the cage. DC flows using the entire cross section of the wire, skin effect is tiny.

For AC things change. AC travels on the outside or skin of a conductor. You can use a metal pipe 1" diameter but hollow to carry almost the same current a 1" diameter solid wire will carry. In that situation the guy in the cage could be killed because rather than staying confined to the inside of the conductor like DC, the AC could jump through him when the power is first turned on.

 

[William Gaatjes]

You can see an electric discharge as a very high frequency ac signal.

How higher the frequency of the ac current, the more on the outside of the conductor this current will flow.

With a faraday cage, this is the reason why it works for lighting and other high voltage electrical discharge.

But indeed, the current prefers the path with lowest resistance.
However, when an isolator becomes a good conductor , as good or usual better(heats up enough to form plasma) then for a short moment the high voltage discharge will proceed it's path through the better conducting isolator(turned into a conductor because of the breakdown voltage of the material the isolator is made from.


Note.
When it comes to high frequency signals, when looking at RF signals, one thing always surprised me:
The isolator around the conductor also seem to affect the skin effect of the conductor. I mean if you take a cable, the impedance of the cable changes depending on the material used as an isolator.
For one part this is because of dielectric and therefore a capacitive nature. Between a grounded shield and an inner core i can understand that. But when a single wire radiates EM waves different because of the surrounding isolating material ?
Why is that ? Anybody knows ? It sounds stupid , but i would almost think of refraction.

 

[Modelworks]

But when a single wire radiates EM waves different because of the surrounding isolating material ?
Why is that ? Anybody knows ? It sounds stupid , but i would almost think of refraction.

It is called standing waves, everything from the insulation , length, angles of bends in conductor, and more effect it. Higher the frequency the harder it is to control.
http://en.wikipedia.org/wiki/Standing_wave

 

[William Gaatjes]

It is called standing waves, everything from the insulation , length, angles of bends in conductor, and more effect it. Higher the frequency the harder it is to control.
http://en.wikipedia.org/wiki/Standing_wave

Ah, thank you.
Afcourse, totally forgot about those.

 

[Born2bwire]

Strictly speaking, the skin effect is completely independent of the geometry of the conductor and only depends on the frequency of the signal and the conductivity of the conductor. In terms of shielding, as it seems to be what you mean from the OP, though, the skin effect being the primary means of shielding is really only directly involved with a continuous closed surface I should say. A finite conductivity allows the electromagnetic wave to penetrate the conductor as an evanescent wave. If you were to make a solid wall of conductor, then the thickness would have to be greater than a few skin depths to ensure that no appreciable amount of power penetrates through. However, with a wire mesh instead of a solid conductor, then the geometry matters more than the skin effect. The finite conductivity that gives rise to the skin effect certainly affects the performance of the shield but we are generally concerned with the geometry more than the conductivity since a good conductor like copper, silver, or gold has a very very small skin depth in the first place.

The shape has less to do as well as long as it is a closed surface. What matters most I would say is the size of the gaps in the mesh first and the thickness of the wire used to make the mesh second. Shape and conductivity are far lesser factors for consideration. Shape of the cage usually only matters to what is happening outside of the cage. For example, sharp points and corners gives rise to field enhancement, where the electric field (and magnetic field too of course) has a much higher magnitude in the local volumes of these points. This can give rise to dielectric breakdown and sparks, like when you stick a fork in a microwave. The sparks from a fork are primarily due to the field enhancement at the tines, you may not see such sparks if you placed say a spoon inside the microwave despite both objects being the same metal. But any adequate shielding from the cage will negate any concerns for such phenomenon affecting the occupants.