---
title: "Short note: Skin depth"
subject: "Electromagnetism"
chapter: 4
key: "semester_3/electromagnetism:skin-depth-short-note"
source: https://www.bctengineer.com/q/semester_3/electromagnetism/skin-depth-short-note
site: BCT Engineering
---

# Short note: Skin depth

Electromagnetism · Chapter 4: Wave equation and Wave propagation

- Asked in: 2068 Chaitra, 2 marks
- Video: [Skin Effect Explained: Basics, Skin Depth, and Derivation](https://www.youtube.com/watch?v=r-DbV-sqWhg) — Engineering Funda
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/electromagnetism/skin-depth-short-note
- Whole chapter: https://www.bctengineer.com/md/semester_3/electromagnetism/chapter-4

## Question

Write a short note on skin depth.

## Short answer

Skin depth δ = 1/√(πfμσ) is the distance in a conductor where field amplitude decays to 1/e of its surface value. It decreases with increasing frequency and conductivity, causing currents to concentrate near the surface (skin effect), raising AC resistance.

## Answer

When a plane wave enters a conducting medium, its fields decay as e^{−αz} and the induced currents flow mainly near the surface. **Skin depth** (depth of penetration) δ is the distance over which the amplitude falls to 1/e (about 37 %) of its surface value:

δ = 1/α

For a good conductor (σ ≫ ωε), α = β = √(πfμσ), so

**δ = 1/√(πfμσ) = √(2/(ωμσ))**

Points:
- δ decreases as frequency, conductivity or permeability increases. At high frequency the current is confined to a thin skin; this is the **skin effect**, which raises the AC resistance of a wire.
- Example: copper (σ = 5.8×10⁷ S/m) at 1 MHz has δ ≈ 66 μm; at 60 Hz it is about 8.5 mm.
- Practical uses: shielding (a few skin depths of metal block fields), surface hardening, plating conductors with silver, hollow conductors/waveguides for microwaves.
- Wave velocity in a good conductor is v = ω/β = ωδ, and the wave is attenuated by e^{−1} per skin depth (8.686 dB per δ).

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What is skin depth?
   A. The distance over which the amplitude falls to zero
   B. The distance over which the power falls to 50 %
   C. The wavelength inside the conductor
   D. The distance over which the amplitude falls to 1/e (about 37 %), delta = 1/alpha
   Answer: D. Fields decay as e^(-alpha z), so delta = 1/alpha is where the amplitude is 1/e of its surface value. (Key point: Definition)

2. How does skin depth change with frequency and conductivity?
   A. It increases as either increases
   B. It increases with frequency but decreases with conductivity
   C. It decreases as either increases (delta = 1/sqrt(pi f mu sigma))
   D. It does not depend on them
   Answer: C. delta = 1/sqrt(pi f mu sigma), so higher f or sigma gives a thinner skin. (Key point: Dependence)

3. What is the practical result of skin depth being small at high frequency?
   A. Current spreads uniformly, lowering resistance
   B. Current is confined near the surface, raising the AC resistance of a wire
   C. The wire's DC resistance falls
   D. The wave velocity in the conductor exceeds c
   Answer: B. This is the skin effect: the usable cross-section shrinks, so AC resistance goes up. (Key point: Skin effect)

## Related in Electromagnetism

- [Skin depth and power in dissipative medium](https://www.bctengineer.com/question.md?key=semester_3%2Felectromagnetism%3Askin-depth-time-average-power-density) — Electromagnetism, chapter 4

## Related in other subjects

- [Negative skin friction on 16-pile group](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Aneg-skin-friction-group-16-piles) — Foundation Engineering, chapter 8