Energy in Electromagnetic fields

In summary, the conversation discusses the difficulty in proving that energy resides equally in both the electric and magnetic fields in an insulator, with a focus on the time averaging formula used for conductors. It is suggested that the ratio of E^2/H^2 in a good conductor is proportional to the relative permeability, and the 1/2 in the time average of the squares is the time average of sin^2(wt).
  • #1
venomxx
39
0
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 [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?
 
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  • #2
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
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
venomxx said:
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).
 

What is energy in electromagnetic fields?

Energy in electromagnetic fields refers to the energy that is carried by electromagnetic waves, which are created by the oscillation of electric and magnetic fields. These waves can travel through empty space and carry energy from one place to another.

How is energy in electromagnetic fields measured?

The energy in electromagnetic fields is measured in units of joules (J). The amount of energy carried by an electromagnetic wave is directly proportional to its frequency and amplitude. The higher the frequency and amplitude of the wave, the more energy it carries.

What are some examples of energy in electromagnetic fields?

Some common examples of energy in electromagnetic fields include visible light, radio waves, microwaves, X-rays, and gamma rays. These waves are used in various technologies such as communication, medical imaging, and cooking.

What is the relationship between electricity and energy in electromagnetic fields?

Electricity and energy in electromagnetic fields are closely related. Electric currents create magnetic fields, and changing magnetic fields can create electric currents. This back-and-forth relationship between electric and magnetic fields is what allows for the transfer of energy through electromagnetic waves.

How does energy in electromagnetic fields affect our daily lives?

Energy in electromagnetic fields plays a crucial role in our daily lives. It allows us to communicate through cell phones, watch TV, and use the internet. It also enables medical technologies such as MRI and X-ray machines. Additionally, energy in electromagnetic fields is harnessed for power generation through technologies such as solar panels and wind turbines.

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