The depth of penetration of a wave in a lossy dielectric increases with increasing 

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 an increase in conductivity and permeability.
• As it is inversely proportional to frequency, the depth penetration is directly proportional to wavelength. Therefore, it increases with an increase in wavelength.