Energy in Electromagnetic fields

  • Thread starter venomxx
  • Start date
  • #1
39
0

Main Question or Discussion Point

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 cant seem to find out how they do it!

The time averaging formula used is:

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

is worked out to this:

[tex]\epsilon[/tex]E[tex]^{2}[/tex]/[tex]\mu[/tex] H[tex]^{2}[/tex]

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

any thoughts?
 

Answers and Replies

  • #2
Born2bwire
Science Advisor
Gold Member
1,779
18
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).
 
  • #3
clem
Science Advisor
1,308
15
The ratio of [tex]E^2/H^2[/tex] in a good conductor is proportional to
[tex]\omega\mu/\sigma[/tex]. (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).
 
  • #4
jtbell
Mentor
15,500
3,296
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: [itex]\epsilon E^2 / \mu H^2[/itex] (click on an equation to see the code).
 

Related Threads for: Energy in Electromagnetic fields

  • Last Post
Replies
6
Views
2K
Replies
3
Views
731
Replies
0
Views
4K
Replies
18
Views
2K
  • Last Post
Replies
11
Views
2K
  • Last Post
Replies
2
Views
2K
Replies
10
Views
931
Replies
78
Views
10K
Top