A Faraday cage
only works with static electricity
(the storage spheres on top of our Van De Graaff are Faraday cages.)
What happens there is that the negative charges on a Faraday cage
repel each other and try to get as far away from each other as
possible. The best way to do that is to occupy only the outside of
the cage. Hence there is no electricity on the inside.
When a lightning bolt hits, however, the electricity is not
static--it is moving very rapidly! Some other effect must be at
work.
Lightning is an example of a very high frequency alternating
current. This may seem illogical
as the electricity in a lightning bolt normally only moves down, but
looking at the current/time diagrams below will show that it is more
like a short piece of alternating current than direct current.
All electric currents generate magnetic fields that in turn can
affect the current (this is the principle behind electric guitar
pickups). In a direct current case everything is constant and so
nothing seems to happen. With an alternating current, however, there
is a delay in the magnetic field's response to the change in current
and the 'old' magnetic field tends to push the current towards the
outside of the conductor. As the frequency
increases, so does the effect until at very high frequencies the
entire current flows in a very narrow skin on the conductor--hence
the name.
The earliest work on explaining the skin effect was done by Lord
Kelvin (of temperature fame) in 1887. Tesla also investigated the
effect.
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