Energy in Electromagnetic fields

[venomxx]

Problem:
Iv been trying to prove that the energy reisdes in the magnetic field in a good conductor and equally in both electric and magnetic for an insulator. My problem lies in the time averaging part of the problem...i can't seem to find out how they do it!

The time averaging formula used is:

For conductor:
<1/2 \epsilon E^{2}>/<1/2 \mu H^{2}>

is worked out to this:

\epsilonE^{2}/\mu H^{2}

The epsilons and mu's look like superscripts but there just multipled in!

any thoughts?

 

[Born2bwire]

As I recall the energy density is dependent on the integral of the summation of the squares of the magnitudes of the electric and magnetic field, not the ratios. In a good conductor the imaginary part of the permittivity is very very large which would greatly decrease the contribution of electric field, leaving the magnetic contribution to dominate (if that is the case).

 

[Meir Achuz]

The ratio of E^2/H^2 in a good conductor is proportional to
\omega\mu/\sigma. (The \mu is the relative permeability.) The sigma in the denominator is why E^2 is negligible.
The 1/2 in the time average of the squares is just the time average of sin^2(wt).

 

[jtbell]

The epsilons and mu's look like superscripts but there just multipled in!

When you want to use LaTeX "inline", i.e. inside of text, use "itex" and "/itex" tags, not "tex" and "/tex". You might as well do the whole equation at once, while you're at it: \epsilon E^2 / \mu H^2 (click on an equation to see the code).