Question

The skin depth of a wave propagating through aluminium medium of conductivity \(\sigma = 38.2~\text{MS/m}\) is computed at \(1.6~\text{MHz}\) frequency as \(64.4~\mu m\). The skin depth into the same medium at \(6.4~\text{MHz}\) frequency is ________.

• A. 32.2 \(\mu m\)
• B. 128.8 \(\mu m\)
• C. 16.1 \(\mu m\)
• D. 64.4 \(\mu m\)

Hint:

Skin depth decreases with the square root of frequency. So higher frequency means shallower penetration.

Answer 1

The Correct Option is A

The skin depth \(\delta\) is given by: \[ \delta = \sqrt{\frac{2}{\omega \mu \sigma}} = \frac{1}{\sqrt{\pi f \mu \sigma}} \] This implies: \[ \delta \propto \frac{1}{\sqrt{f}} \] So, for two frequencies: \[ \frac{\delta_2}{\delta_1} = \sqrt{\frac{f_1}{f_2}} = \sqrt{\frac{1.6}{6.4}} = \sqrt{\frac{1}{4}} = \frac{1}{2} \] Thus: \[ \delta_2 = \frac{1}{2} \cdot \delta_1 = \frac{1}{2} \cdot 64.4 = 32.2~\mu m \] Final Answer: 32.2 \(\mu m\)