Maxwell's equations using vectors D and H

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SUMMARY

The discussion focuses on the formulation of Maxwell's equations in differential form for linear materials using the vectors D and H. The equations presented include Gauss' law (div D = ρ), Gauss' law in magnetism (div H * μ * μ0 = 0), Faraday's law (curl (D/(ε * ε0)) = -dB/dt), and the Ampere-Maxwell law (curl H = j_f + dD/dt). The user seeks validation of their equations and clarification on the terms ε_r and μ_r, which represent the relative permittivity and permeability, respectively, in materials compared to free space.

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  • Understanding of Maxwell's equations in electromagnetism
  • Familiarity with vector calculus
  • Knowledge of material properties such as permittivity and permeability
  • Basic understanding of differential equations
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blueyellow

Homework Statement



Write Maxwell's equations for electromagnetism in differential form:

in matter, for a linear material, using the vectors D and H

The Attempt at a Solution



div D= ro (Gauss' law)
div H*mu*mu0=0 gauss' law in magnetism
curl (D/(epsilon*epsilon0))=-dB/dt(partial derivative) faraday's law
curl H=j(subscript f)+dD/dt (partial derivative) ampere-maxwell law

I wanted to check whether they were correct
 
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blueyellow said:

Homework Statement



Write Maxwell's equations for electromagnetism in differential form:

in matter, for a linear material, using the vectors D and H

The Attempt at a Solution



div D= ro (Gauss' law)
div H*mu*mu0=0 gauss' law in magnetism
curl (D/(epsilon*epsilon0))=-dB/dt(partial derivative) faraday's law
curl H=j(subscript f)+dD/dt (partial derivative) ampere-maxwell law

I wanted to check whether they were correct

That looks pretty close. You can check your answer here at hyperphysics:

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/maxeq.html

BTW, if you want to write "epsilon*epsilon0", you should write "epsilonR*epsilon0", because epsilon = epsilonR*epsilon0. Or in LaTeX:

\epsilon = \epsilon_R * \epsilon_0

.
 
sorry, I just realized I don't know what epsilon r and mu r actually are. epsilon 0 and mu0 are the permittivity and permeability in free space aren't they? but what does the r stand for? I have tried looking this up
 

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