Find the skin depth $\delta$ of copper (conductivity $\sigma =5.96\times 10^7$ S/m, relative permeability ${\mu }_r=1$) at a frequency of 60 Hz. Give $\delta$ in micrometers.

Step-by-step solution

1. Compute angular frequency $\omega =2\pi f=2\pi \times 60$.
2. Magnetic permeability $\mu ={\mu }_0{\mu }_r=4\pi \times 10^{-7}$ H/m.
3. Use $delta=\sqrt{2/(omegamusigma)}$.
4. Evaluate $omegamusigma=(2\pi \times 60)(4\pi \times 10^{-7})(5.96\times 10^7)\approx 2.8\times 10^4$.
5. Compute $2/(omegamusigma)\approx 7.1\times 10^{-5}$.
6. Take square root: $deltaapprox8.4\times 10^{-3}$ m = $8.4\times 10^3$ μm.

Concept tested: Skin depth in conductors

Published 4 September 2026 · Last updated 16 September 2026 · How this solution was prepared and checked