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Homework Help: Converting mks energy density to cgs

  1. Sep 11, 2007 #1
    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 [tex] U [/tex] 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

    [tex] U_{tot} = E^{2} + B^{2} [/tex]

    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, [tex] \epsilon_{0} [/tex] has been eliminated by redefining the electric charge in the Coulomb law ([tex] \frac{q_{1} q_{2}}{4 \pi \epsilon_{0}} \rightarrow q_{1} q_{2} [/tex]) and [tex] \mu_{0} [/tex] has been eliminated by using the speed of light: [tex] \mu_{0} \rightarrow \frac{1}{c^{2} \epsilon_{0}} [/tex].

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

  2. jcsd
  3. Sep 11, 2007 #2


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    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
  4. May 1, 2011 #3

    Hopefully you found this one already:


    If [tex] \frac {1}{4 \pi \epsilon_{0}} = 1[/tex], then [tex]\epsilon_{0} = \frac {1}{4 \pi}[/tex], 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 [tex] 4 \pi = [/tex] 1, or [tex] \epsilon_{0} =[/tex] 1, despite it's readability difficulties:

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