Permitivity, and relative permitivity

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SUMMARY

The discussion focuses on the relationship between wave vector \( k \), permittivity \( \epsilon \), and permeability \( \mu \) in dielectric materials compared to vacuum. It establishes that for a plane electromagnetic wave in a dielectric, the wave vector is given by \( k = \sqrt{\epsilon_r \epsilon \mu} \cdot w \), where \( \epsilon_r \) is the relative permittivity. The relationship between the speed of light \( c \), permittivity, and permeability is defined by \( \frac{1}{c^2} = \epsilon \mu \), confirming that \( \epsilon \) and \( \mu \) are directly related to the speed of light in a medium.

PREREQUISITES
  • Understanding of electromagnetic wave propagation
  • Familiarity with the concepts of permittivity and permeability
  • Knowledge of the speed of light in vacuum and its relation to dielectric materials
  • Basic mathematical skills for manipulating equations involving \( k \), \( \epsilon \), and \( \mu \)
NEXT STEPS
  • Research the derivation of the wave equation in dielectric materials
  • Learn about the implications of relative permittivity \( \epsilon_r \) in different materials
  • Study the relationship between refractive index \( n \) and speed of light in various media
  • Explore Maxwell's equations and their application in electromagnetic theory
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Students and professionals in physics and electrical engineering, particularly those studying electromagnetic theory and wave propagation in dielectric materials.

neu
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Homework Statement



For a plane em wave in vacuum can write k=\frac{w}{c}

what is the equivalent relation in a dielectric?

Homework Equations



\frac{1}{c^2}={\epsilon}{\mu}


The Attempt at a Solution



k=\sqrt{{\epsilon_{r}}\epsilon\mu}.w

This right?
 
Last edited:
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Yes, but you could keep the c instead of epsilon0 and mu0.
 
ok so: \frac{1}{c}=\sqrt{\epsilon_{0}\mu_{0}}

so how is \epsilon and \mu related to c?

is it \frac{n}{c}=\sqrt{\epsilon\mu}?
 
neu said:
ok so: \frac{1}{c}=\sqrt{\epsilon_{0}\mu_{0}}

so how is \epsilon and \mu related to c?

is it \frac{n}{c}=\sqrt{\epsilon\mu}?
Yes, if you mean \epsilon=\epsilon_r\epsilon_0.
 

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