Skin Depth Calculator
Skin Depth Calculator computes skin depth for EM waves in conductors, visualizing vs. frequency.
Formulas Used in Skin Depth Calculator
The calculator uses the following formula for skin depth in a conductor:
Skin Depth:
\\[ \delta = \sqrt{\frac{2}{\omega \mu \sigma}} = \sqrt{\frac{1}{\pi f \mu \sigma}} \\]Where:
- \\( \delta \\): Skin depth (m)
- \\( f \\): Frequency (Hz)
- \\( \omega = 2\pi f \\): Angular frequency (rad/s)
- \\( \mu = \mu_0 \mu_r \\): Permeability (H/m), with \\(\mu_0 = 4\pi \times 10^{-7} \, \text{H/m}\\)
- \\( \sigma \\): Conductivity (S/m)
Example Calculations
Example 1: Copper at 1 MHz
Input: \\( f = 10^6 \, \text{Hz}, \sigma = 5.96 \times 10^7 \, \text{S/m}, \mu_r = 1 \\)
\\[
\delta = \sqrt{\frac{1}{\pi \cdot 10^6 \cdot (4\pi \times 10^{-7}) \cdot (5.96 \times 10^7)}} \approx 6.61 \times 10^{-5} \, \text{m}
\\]
Result: \\(\delta \approx 66.1 \, \mu\text{m}\\)
Example 2: Copper at 10 MHz
Input: \\( f = 10^7 \, \text{Hz}, \sigma = 5.96 \times 10^7 \, \text{S/m}, \mu_r = 1 \\)
\\[
\delta = \sqrt{\frac{1}{\pi \cdot 10^7 \cdot (4\pi \times 10^{-7}) \cdot (5.96 \times 10^7)}} \approx 2.09 \times 10^{-5} \, \text{m}
\\]
Result: \\(\delta \approx 20.9 \, \mu\text{m}\\)