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skin_depth [2019/06/03 18:30]
skin_depth [2020/07/02 22:35] (current)
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 +====== Skin depth ======
  
 +|< 100% >|
 +| //[[user/Stan Zurek]], Skin depth, [[http://Encyclopedia-Magnetica.com|Encyclopedia-Magnetica.com]], {accessed @YEAR@-@MONTH@-@DAY@}// |
 +
 +{{page>insert/just photo}}
 +
 +**Skin depth** (often denoted by lower-case Greek letter delta **δ**) - such a depth of penetration of [[alternating current]] or [[electromagnetic field]], at which the amplitude is reduced to a value of 1/[[e (constant)|e]] (around 37%), as compared to the amplitude at the surface of the [[conductor]]. 
 +
 +Skin depth is a function of frequency of current, as well as [[magnetic permeability]] and [[electric resistivity]] (or [[electric conductivity|conductivity]]) of the conductor in question.
 +
 +For good conductors (like most metals) the function can be defined as:[([[http://google.com/books?isbn=9780387948775|Nathan Ida, Joao Bastos, Electromagnetics and Calculations of Fields, Springer, 1997, ISBN 9780387948775, p. 232]])]
 +
 +|  <html><div style="font-size: 200%;"> $\delta = \sqrt{\frac{2 · \rho }{\omega · \mu_r · \mu_0}} = \frac{1}{\sqrt{\pi · f · \mu_r · \mu_0 · \sigma}}$ </div></html>  |  (m)  |
 +
 +where: //π// - mathematical constant, //f// - frequency (Hz), //μ<sub>r</sub>// - [[relative permeability]] of the conductor, //μ<sub>0</sub>// - [[magnetic permeability of free space]] (H/m), //σ// - [[electric conductivity]] (S/m), //ρ// = 1///σ// - [[electric resistivity]] (Ω·m), //ω// = 2·//π·f// - [[pulsation frequency]] (rad/s).
 +
 +<box 80% right #f0f0f0>
 +Skin depth vs. frequency for some materials (red line denotes 50 Hz):
 +  * dashed black (**Mn-Zn**) - [[magnetically soft ferrite]] [[3C90]]
 +  * light grey (**Al**) - metallic [[aluminium]]
 +  * orange (**Cu**) - metallic [[copper]]
 +  * green (**steel 410**) - magnetic [[stainless steel]], grade 410
 +  * blue (**Fe-Si**) - [[grain-oriented electrical steel]]
 +  * dark grey (**Fe-Ni**) - [[permalloy]] (80%Ni-20%Fe)
 +[[file/skin_depth_magnetica.png|{{skin_depth_magnetica.png}}]]
 +{{page>insert/by_SZ}}
 +</box>
 +<WRAP clear></WRAP>
 +
 +
 +===== See also =====
 +  *[[skin effect]]
 +  *[[Litz wire]]
 +
 +===== References =====
 +~~REFNOTES~~
 +
 +{{tag>Skin_depth Skin_effect Counter}}