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“Skin
effect: What it is, what it does" With
trilingual summary
A magnetic field surrounds any conductor carrying electric current.
Alternating current creates a field that varies, its movement
generating an induced voltage within the conductor that acts to
oppose current flow. That opposition is least towards the surface of
the conductor, and greatest at its center, resulting in the current
flow being greatest at the surface.
That is commonly called the "skin effect." The effective depth of
current penetration into the conductor surface is calculable from
conductor dimensions and resistivity as well as the frequency. At 50
Hz, most current flow in any round copper wire is within 9
millimeters of the surface. Hence, skin effect is insignificant at
that frequency unless conductor diameter exceeds 18 mm.
As frequency increases, however, current penetration decreases
rapidly. For example, at 1000 Hz, the depth becomes only 0.2 mm. To
prevent overheating at the desired current flow, a conductor may have
to be extremely large in diameter to provide enough area at so small
a thickness. High frequency conductors are therefore often either
thin sheets or hollow tubes.
Tubular conductors are also common at power line frequencies when
currents are so large that the diameter of a solid conductor would
far exceed twice the depth of penetration. For current density of 155
amperes per square centimeter, for example, conductor area at 5000
amperes would need to be 32 square cm. A solid round bar of that area
would be 6.4 cm in diameter. But at 50 Hz, only the outermost layer
0.9 cm thick would carry most of the current. The diameter would have
to be 11.3 cm to provide a later that thick of sufficient area. A
tubular conductor 10 cm in diameter with a 1 cm wall thickness would
suffice, with the added cooling provided by its inner surface.
Published formulae for penetration depth are usually in the
simplified form of a numerical constant divided by the square root of
frequency. These must be used carefully. The constant involves
material resistivity, which varies with temperature, and the
applicable value is seldom stated.
From “Skin
effect: What it is, what it does," Electrical Apparatus
August 2006
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