Consider the following statements regarding the depth of penetration or skin depth in a conductor

1. It increases as frequency increases.

2. It is inversely proportional to the square root of μ and σ.

3. It is inversely proportional to the square root of f.

4. It is directly proportional to the square root of μ and σ.

Which of the above statements are correct?

1. The skin effect is the tendency of an alternating electric current to become distributed within a conductor such that the current density is largest near the surface of the conductor and decreases with greater depths in the conductor.

2. The electric current flows mainly at the skin of the conductor, between the outer surface and a level called the skin depth.

3. Skin depth is defined as the reciprocal of attenuation constant i.e.,

\(\delta=\frac{1}{\alpha}\)

The attenuation constant is given by:

\(\Rightarrow\alpha=\omega\sqrt{\frac{μ\epsilon}{2}\left[\sqrt{1+\left(\frac{σ}{\omega\epsilon}\right)^2}-1\right]}\)

For an ideal conductor with σ ≈ ∞,

\(\Rightarrow \delta=\frac{1}{\alpha}=\left[\sqrt{1+\left(\frac{σ}{\omega\epsilon}\right)^2}-1\right]≈\frac{σ}{\omega\epsilon}\)

∴ The attenuation constant becomes:

\(\alpha=\omega \sqrt{\left(\frac{μσ}{2\omega}\right)}\)

\(\alpha=\sqrt{\left(\frac{\omegaμσ} {2}\right)}=\sqrt{\pi fμσ}\)

Thus, \(\delta=\frac{1}{\sqrt{\pi f μσ}}\)

Thus, the skin depth is inversely proportional to the root of frequency, μ, and σ.