# Converting mks energy density to cgs

1. Sep 11, 2007

### syang9

1. The problem statement, all variables and given/known data

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

$$u = \frac {\epsilon_{0} E^{2}}{2} + \frac{B^{2}}{2 \mu_{0}}$$

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

3. 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

2. Sep 11, 2007

### 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.

Last edited: Sep 11, 2007
3. May 1, 2011

### chaig

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

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