Correct Answer - Option 3 : Wavelength
Concept:
The depth of penetration δ of a plane electromagnetic wave incident normally on a good conductor is mathematically defined as:
\(\delta=\frac{1}{α}\)
α is the attenuation constant given by:
\(α=\omega\sqrt{\frac{\mu\epsilon}{2}\left[\sqrt{1+\left(\frac{σ}{\omega\epsilon}\right)^2}-1\right]}\)
For a good conductor σ >>1. The above expression for the attenuation constant can be approximated as:
\(\alpha=\left[\sqrt{1+\left(\frac{σ}{\omega\epsilon}\right)^2}-1\right]≈\frac{σ}{\omega\epsilon}\)
∴ The attenuation constant becomes:
\(α=\omega \sqrt{\left(\frac{\muσ}{2\omega}\right)}\)
\(α=\sqrt{\left(\frac{\omega\muσ} {2}\right)}\)
\(\therefore~\alpha =\sqrt{\pi f\muσ}\)
Thus, the skin depth becomes:
\(\delta=\frac{1}{\sqrt{\pi f \muσ}}\)
Application:
- Depth penetration is inversely proportional to frequency, permeability and conductivity and hence the depth penetration decreases with increase in conductivity and permeability.
- As it is inversely proportional to frequency, the depth penetration is directly proportional to wavelength. Therefore, it increases with increase in wavelength.