Converting mks energy density to cgs

[syang9]

Homework Statement

In the SI system, the energy density of the electric and magnetic fields is:

<br /> u = \frac {\epsilon_{0} E^{2}}{2} + \frac{B^{2}}{2 \mu_{0}}<br />

From the equation above, derive an exact expression for the energy density U in the Gaussian system of units.

The Attempt at a Solution

Obviously the energy densities must be proportional to the squares of the intensities. So, I can start with

U_{tot} = E^{2} + B^{2}

I know that cgs eliminates the need for epsilon and mu, but I haven't a clue as to how to start from that one equation. Previously in the assignment, my instructor mentions that in Coulomb's law, \epsilon_{0} has been eliminated by redefining the electric charge in the Coulomb law (\frac{q_{1} q_{2}}{4 \pi \epsilon_{0}} \rightarrow q_{1} q_{2}) and \mu_{0} has been eliminated by using the speed of light: \mu_{0} \rightarrow \frac{1}{c^{2} \epsilon_{0}}.

However I haven't a clue as to how to proceed with this information. Any hints would be great! Thanks in advance.

Stephen

 

[dextercioby]

There's an epsilon and a mu in the cgs system as well. There's something linked with #-s and 4\pi-s that differs. On a second thought, since i haven't used cgs since college, go and check the 3-rd and 2-nd editions of JD Jackson's electrodynamics book to see everything exactly.

 

[chaig]

Homework Statement

In the SI system, the energy density of the electric and magnetic fields is:

<br /> u = \frac {\Epsilon_{0} E^{2}}{2} + \frac{B^{2}}{2 \mu_{0}}<br />

From the equation above, derive an exact expression for the energy density U in the Gaussian system of units. Stephen

Hopefully you found this one already:

http://en.wikipedia.org/wiki/Electromagnetic_stress-energy_tensor

If \frac {1}{4 \pi \epsilon_{0}} = 1, then \epsilon_{0} = \frac {1}{4 \pi}, and likewise for magnetic field.

Although, often epsilon is not what it seems in cgs. It really depends on whether you are looking at emu or esu. I recommend this document, which gives you a little taste of the complications of calling 4 \pi = 1, or \epsilon_{0} = 1, despite it's readability difficulties:

http://www.scribd.com/doc/8520766/Cgs-Electricity-and-Magnetism