$d$ $d$ (attenuating EM wave)

Last modified by

on

Jul 24, 2020, 6:28:07 PM

Created by

on

Jun 3, 2016, 8:46:34 PM

d = \frac{1}{ω \sqrt{\frac{ε \cdot μ}{2}} {[\sqrt{1 + (\frac{σ}{ε \cdot ω})} - 1]}^{\frac{1}{2}}}

$d = 1/ ( omega sqrt(( epsilon * mu )/2) [sqrt(1 + ( sigma /( epsilon * omega ) ) ) -1]^(1/2))$

σ

$sigma$

ε

$epsilon$

ω

$omega$

μ

$mu$

Tags

UUID

42858fa8-29cc-11e6-9770-bc764e2038f2

This equation describes the "skin depth"¹ ( $d$ $d$ ) of an electromagnetic wave in a conducting medium. The "skin depth" is how far the wave can travel before the amplitude of its electric field is reduced by a factor of $\frac{1}{e}$ $1/e$

/attachments/42858fa8-29cc-11e6-9770-bc764e2038f2/Skin Depth.png A graph of the electric field amplitude as it propagates

In the picture, the independent variable is $\frac{x}{d}$ $x/d$ , or how many multiples of the skin depth the wave has traveled. The dependent variable is the ratio of the current Electric Field Amplitude, $E (x)$ $E(x)$ , to the original Electric Field Amplitude, $E_{0}$ $E_0$ . After the wave has propagated one skin depth into the conductor $(\frac{x}{d} = 1)$ $(x/d = 1)$ , then the ratio $\frac{E (x)}{E_{0}} = \frac{1}{e}$ $( E(x) )/ E_0 = 1/e$ , i.e. $E (x) = \frac{E_{0}}{e}$ $E(x) = E_0 / e$ .

For more information on $˜ k$ $tilde k$ and how it's use, please refer to EM waves (attenuating) in a conductor.

^ Griffiths, David J. "Electromagnetic Waves in Matter." Introduction to Electrodynamics. 4th ed. N.p.: Prentice Hall, 2013. 413. Print.

This equation,

d

$d$ (attenuating EM wave), is used in 2 pages

Calculators

• EM waves (attenuating) in a conductor by TylerJones

Equations and Data Items

Collections

• Physics Collection by TylerJones

Comments
Attachments
Stats

No comments

Electric Field Amplitude Graph.png

Skin Depth.png

Last 12 Months

This site uses cookies to give you the best, most relevant experience. By continuing to browse the site you are agreeing to our use of cookies.

dd (attenuating EM wave)

Datasets

Equations and Data Items

Calculators

Equations and Data Items

Collections

$d$ $d$ (attenuating EM wave)