FormulaDen.com

Physics Chemistry Math Chemical Engineering Civil Electrical Electronics Electronics and Instrumentation Materials Science Mechanical Production Engineering Financial Health

Skin Depth or Depth of Penetration Formula

Fx Copy

LaTeX Copy

Skin Depth refers to the distance at which the amplitude of an electromagnetic wave decreases to approximately 1/e (about 37%) of its initial value as it propagates through a conductive material. Check FAQs

δ = \frac{1}{σ} \cdot \sqrt{π \cdot μ r \cdot [Permeability-vacuum] \cdot f}

δ - Skin Depth?σ - Conductivity of Antenna?μ_r - Relative Permeability?f - Frequency of Conductor Loop?[Permeability-vacuum] - Permeability of vacuum?π - Archimedes' constant?

Skin Depth or Depth of Penetration Example

With values

With units

Only example

Here is how the Skin Depth or Depth of Penetration equation looks like with Values.

Here is how the Skin Depth or Depth of Penetration equation looks like with Units.

Here is how the Skin Depth or Depth of Penetration equation looks like.

0.0065 = \frac{1}{0.96} \cdot \sqrt{3.1416 \cdot 0.98 \cdot 1.3E-6 \cdot 10}

0.0065m = \frac{1}{0.96mho/m} \cdot \sqrt{3.1416 \cdot 0.98H/m \cdot 1.3E-6 \cdot 10Hz}

0.0065 = \frac{1}{0.96} \cdot \sqrt{3.1416 \cdot 0.98 \cdot 1.3E-6 \cdot 10}

Tip: Use pencil ( Pencil

) icon above to edit Input Values and Units.

Calculate

Recalculate

Solution

Copy

Reset

You are here -

Home » Category

Engineering » Category

Electronics » Category

Antenna and Wave Propogation » fx Skin Depth or Depth of Penetration

Skin Depth or Depth of Penetration Solution

Follow our step by step solution on how to calculate Skin Depth or Depth of Penetration?

FIRST Step Consider the formula

δ = \frac{1}{σ} \cdot \sqrt{π \cdot μ r \cdot [Permeability-vacuum] \cdot f}

Next Step Substitute values of Variables

∴

δ = \frac{1}{0.96mho/m} \cdot \sqrt{π \cdot 0.98H/m \cdot [Permeability-vacuum] \cdot 10Hz}

Next Step Substitute values of Constants

∴

δ = \frac{1}{0.96mho/m} \cdot \sqrt{3.1416 \cdot 0.98H/m \cdot 1.3E-6 \cdot 10Hz}

Next Step Convert Units

∴

δ = \frac{1}{0.96S/m} \cdot \sqrt{3.1416 \cdot 0.98H/m \cdot 1.3E-6 \cdot 10Hz}

Next Step Prepare to Evaluate

∴

δ = \frac{1}{0.96} \cdot \sqrt{3.1416 \cdot 0.98 \cdot 1.3E-6 \cdot 10}

Next Step Evaluate

∴

δ = 0.00647920428481428m

LAST Step Rounding Answer

∴

δ = 0.0065m

Skin Depth or Depth of Penetration Formula Elements

Variables

Constants

Functions

Skin Depth

Skin Depth refers to the distance at which the amplitude of an electromagnetic wave decreases to approximately 1/e (about 37%) of its initial value as it propagates through a conductive material.

Symbol: δ

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Skin Depth

Conductivity of Antenna

The Conductivity of antenna refers to the electrical conductivity of the subsurface of the antenna.

Symbol: σ

Measurement: Electric ConductivityUnit: mho/m

Note: Value can be positive or negative.

Formulas to find Conductivity of Antenna

Relative Permeability

Relative Permeability is a fundamental parameter used to characterize the response of a material to magnetic fields.

Symbol: μ_r

Measurement: Magnetic PermeabilityUnit: H/m

Note: Value should be greater than 0.

Formulas to find Relative Permeability

Frequency of Conductor Loop

The Frequency of conductor loop the rate at which something occurs over a particular period of time or in a given sample.

Symbol: f

Measurement: FrequencyUnit: Hz

Note: Value can be positive or negative.

Formulas to find Frequency of Conductor Loop

Permeability of vacuum

Permeability of vacuum is a fundamental physical constant that relates the magnetic field within a vacuum to the current producing that field.

Symbol: [Permeability-vacuum]

Value: 1.2566E-6

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

Other formulas in Wave Propagation category

Go Critical Frequency of Ionosphere

F c = 9 \cdot \sqrt{N max}

Go Electron Density

N max = \frac{(1 - {η r}^{2}) \cdot {f o}^{2}}{81}

Go Refractive Index of Ionosphere

η r = \sqrt{1 - (\frac{81 \cdot N max}{{f o}^{2}})}

Go Maximum Usable Frequency in F-region

F muf = \frac{f c}{\cos (θ i)}

How to Evaluate Skin Depth or Depth of Penetration?

Skin Depth or Depth of Penetration evaluator uses Skin Depth = 1/Conductivity of Antenna*sqrt(pi*Relative Permeability*[Permeability-vacuum]*Frequency of Conductor Loop) to evaluate the Skin Depth, Skin Depth or Depth of Penetration refers to the distance at which the amplitude of an electromagnetic wave decreases to approximately 1/e (about 37%) of its initial value as it propagates through a conductive material. It quantifies how deeply the electromagnetic wave can penetrate into the material before its intensity is significantly attenuated. Skin Depth is denoted by δ symbol.

How to evaluate Skin Depth or Depth of Penetration using this online evaluator? To use this online evaluator for Skin Depth or Depth of Penetration, enter Conductivity of Antenna (σ), Relative Permeability (μ_r) & Frequency of Conductor Loop (f) and hit the calculate button.

FAQs on Skin Depth or Depth of Penetration

What is the formula to find Skin Depth or Depth of Penetration?

The formula of Skin Depth or Depth of Penetration is expressed as Skin Depth = 1/Conductivity of Antenna*sqrt(pi*Relative Permeability*[Permeability-vacuum]*Frequency of Conductor Loop). Here is an example- 0.006479 = 1/0.96*sqrt(pi*0.98*[Permeability-vacuum]*10).

How to calculate Skin Depth or Depth of Penetration?

With Conductivity of Antenna (σ), Relative Permeability (μ_r) & Frequency of Conductor Loop (f) we can find Skin Depth or Depth of Penetration using the formula - Skin Depth = 1/Conductivity of Antenna*sqrt(pi*Relative Permeability*[Permeability-vacuum]*Frequency of Conductor Loop). This formula also uses Permeability of vacuum, Archimedes' constant and Square Root (sqrt) function(s).

Can the Skin Depth or Depth of Penetration be negative?

No, the Skin Depth or Depth of Penetration, measured in Length cannot be negative.

Which unit is used to measure Skin Depth or Depth of Penetration?

Skin Depth or Depth of Penetration is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Skin Depth or Depth of Penetration can be measured.

Let Others Know

✖

Facebook

Twitter

Copied!

: Value
: Unit