Talk:Constitutive equation

"Incorrect constitutive equations"...

Hello 129.13.72.198, you seemed to have corrected a few tensor equations for electromagnetism in this article.

The changed equations I have issues with are:

$\epsilon _{ij}E_{i}=D_{j}-P_{j}\rightarrow D_{i}=\epsilon _{0}E_{i}+P_{i},\,\!$
$B_{j}=\mu _{ij}\left(H_{i}+M_{i}\right)\rightarrow B_{i}=\mu _{0}H_{i}+M_{i}.\,\!$

First, the dimensions are incorrect for the magnetic equation, $\mu _{0}M_{i}\,$ has the same dimensions as B. Sometimes used is the auxillery field to M; the intensity of magnetization I or magnetic polarization J (both are identical) defined as $I_{j}=\mu M_{i}\,$, absorbing the permeability to obtain the equation $B_{i}=\mu _{0}H_{i}+I_{i},\,$ is this what you were going for?

Second, the permittivity and permeability for free space can be replaced by the values for materials, they are not only for free space, i.e. $\epsilon _{0}\rightarrow \epsilon ,\mu _{0}\rightarrow \mu \,\!$ is allowed.

Also, I appriaciate the change of indicies but its confusing - i've seen the indices for permittivity and permeability tensors as $\epsilon _{ij}\leftrightarrow \epsilon _{ji},\mu _{ij}\leftrightarrow \mu _{ji}\,$. Do you know which is correct? The ones you have given (ij) are different to the ones in Maxwell's equations (ji), the ones origally added, as $D_{j}=\epsilon _{ij}E_{i},B_{j}=\mu _{ij}H_{i}.\,\!$ Are those wrong? I suspect so, two resoures which say $D_{j}=\epsilon _{ji}E_{i},B_{j}=\mu _{ji}H_{i},\,\!$ are

http://www.intechopen.com/source/pdfs/16401/InTech-The_eigen_theory_of_electromagnetic_waves_in_complex_media.pdf,
and Mathematical methods for physics and engineering, K.F. Riley, M.P. Hobson, S.J. Bence, Cambridge University Press, 2010.

Thanks anyway, but i'll modify these like so:

$B_{i}=\mu _{0}H_{i}+M_{i}\rightarrow B_{i}=\mu \left(H_{i}+M_{i}\right)\,$
$B_{i}=\mu _{0}H_{i}+M_{i}\rightarrow \epsilon E_{j}=D_{j}-P_{j}\,$

and leave the others.

Maschen (talk) 16:07, 16 September 2011 (UTC)

An explaination has been provided at Talk:Maxwell's equations. Maschen (talk) 08:59, 18 September 2011 (UTC)

this article is in bad shape (like many on WP)...

I plan to expand out some of the tables and write in prose, in particular the shorter tables which are related to laws, and materials, such as fluid mechanics, transport processes, thermal radiation etc. Some tables of definitions + units + dimensions etc can be kept, as this is a good format these (and there is no point in prose). So...

For those that will introduce "proper listing and tabling", using <div class="plainlist">...</div> - don't bother, the tables may be deleted/expanded into paragraphs. I'll insert the lists where needed and clean up the "fiddly" tabling - don't waste your time.

For the EM section - it would be good to go into the edit history of Maxwell's equations and dig out the constitutive relations stuff in this version, and paste it here, then in Maxwell's equations article delete the excessive details of constitutive relations and EM properties of matter, keeping the content on how Maxwell's equations and constituive relations are used to describe EM properties of matter - we can link from Maxwell's equations to here. I plan to do this tommorow. F = q(E+v×B) ⇄ ∑_ic_i 19:30, 21 May 2012 (UTC)

No changes yet - I'm writing this in my sandbox for now... (it doesn't look like anyone will even look at this talk page - who am I talking to??)... F = q(E+v×B) ⇄ ∑_ic_i 21:33, 22 May 2012 (UTC)

Ok, I think what we have now is more sensible than its ever been. The new version has been cut and pasted. Any little bits and pieces can be fixed as and when obviously (just stating the obvious before someone comments on that...). F = q(E+v×B) ⇄ ∑_ic_i 23:45, 22 May 2012 (UTC)

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Should conduction be added to the electromagnetic constitutive equations?

I was wondering whether J=σE should be added to D=εE and B=υH. Where J=current density, E=electric field, σ=conductivity. Constant314 (talk) 16:03, 10 November 2024 (UTC)