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# Thread: Narrower arc from blunt tungsten

1. Originally Posted by Willie B
If I could sneak into that physics course, or spend my life savings to have that knowledge, I'd do it. Otherwise, if you would be willing to enlighten me, I'd be richer for the knowledge. Others would benefit or at least be entertained.
Simple. Calculate the actual skin depth for tungsten for a given AC frequency:

omega = 2π*f = 2π*100Hz (for example).
sigma= 1.79E(7) Siemens/m
mu= 4πE(-7)*(1+6.8E(-5)) = 1.2567E(-6)

Crunch the #s, and

delta=0.0563 meters @ 100Hz.

The radius of a 1/8" tungsten is 0.0015875 m for comparison. At 100Hz as an example, the effective skin depth is ~35x the radius of a 1/8" tungsten to put it in perspective.

Due to the nature of the sigma function, this means that for a 1/8" tungsten you'd have to raise the AC frequency > 5,500Hz for the skin depth to just barely begin to decrease smaller than the radius of the entire electrode (< 0.0625"). In other words, for 1/8" tungsten at any AC frequency less than ~5.5 kHz, the entire cross-sectional area is "consumed" for current transfer.

Different conductors will have different values for mu and sigma, therefore this is only for tungsten and the numbers here cannot be extrapolated for any other conductor because the delta function is non-linear.

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I thought so.

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