Lesson 15 of 15
Skin Depth
The Skin Effect
At high frequencies, alternating current doesn't flow uniformly through a conductor — it concentrates near the surface. The skin depth is the depth at which the current density falls to of its surface value:
ho}{omegamu}} = sqrt{ rac{ ho}{pi f mu}}$$ - $delta$ — skin depth (m) - $ ho$ — resistivity of the conductor (Ω·m) - **f** — frequency (Hz) - $mu = mu_0 mu_r$ — magnetic permeability (H/m) For non-magnetic materials $mu approx mu_0 = 4pi imes 10^{-7}$ H/m. ### Practical Consequences | Material | f | δ | |----------|---|---| | Copper ($ ho = 1.68 imes10^{-8}$) at 50 Hz | ~9 mm | | Copper at 1 MHz | ~66 μm | | Copper at 1 GHz | ~2 μm | At RF frequencies, only a thin surface layer carries current. High-frequency cables are plated with silver (lower resistivity) to reduce loss. ### Examples (copper, $ ho = 1.68 imes10^{-8}$ Ω·m, $mu = mu_0$) | f (Hz) | δ (m) | |--------|-------| | 50 | **9.33e-03** | | 1000 | **2.09e-03** | | 1×10⁶ | **6.61e-05** | | 1×10⁹ | **2.09e-06** | ### Your Task Implement `skin_depth(rho, f, mu)` returning $delta$ in metres.Pyodide loading...
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