Magnetic $H$ field unit in cgs system

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Solution 1

In essence in the cgs system of units $\mu_0 = 1$

B is the magnetic flux density (or magnetic induction)and has the derived unit gauss which in base cgs units $\rm cm^{-\frac 12}g^{\frac 12}s^{-1}$

H is the magnetic field strength and has the derived unit oersted which in base cgs units $\rm cm^{-\frac 12}g^{\frac 12}s^{-1}$

You may also be interested in the fact that E is the electric field with the derived unit $\rm statV\, cm^{-1}$ which in terms of cgs base units is $\rm cm^{-\frac 12}g^{\frac 12}s^{-1}$, the same as that for B and H.

There are very many examples of cgs units and Gaussian units being explained and discussed on the Internet and in textbooks. For example look at this PDF.

Solution 2

Dimensional analysis with the standard cgs or SI dimensions will not reveal the nature of where the $4\pi$s ought to go. Instead, you have to use an extra dimension, which turns the $4\pi$ into a variable, which becomes either $4\pi$ or $1$, according to the system.

I use the 'rule of substance' here. It is in my physics pdf, but i shall describe it here.

Space, time, fields and fluxes of all kinds, potentials of all kinds, are not substances, and are left unaltered.

Mass, and mechanical quantities with Mass in the dimension (forces, energy, pressure, density, power), charge, dipoles of all kinds, and their respective densities, capacitances and conductances, susceptances and susceptabilities, are quantities of substance and represent a dimension $S^1$.

Resistances and inductances represent a dimension of $S^{-1}$.

In order to change a formula, you tick the substances in the equation, and cross the inverse substances (ie $S^{-1}$). If there is an inbalance of ticks and crosses, this is corrected by a ticked $4\pi$ (cgs->si), or cross $4\pi$ (si->cgs).

So in the equation of the question: $H=B-4\pi M$

$H$ is a field, and thus not a substance. Likewise $B$ is a flux density, and is also not a substance. The $M$ is a magnetic polarisation and is thus a substance. To counter the imbalance of the substabce dimension, you need to divide the $M$ by a 'ticked $4\pi$', which cancels out the $4\pi$, giving $H=B-M$.

This can be done at reading speed.

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Updated on August 01, 2022

Comments

  • Septacle
    Septacle over 1 year

    I'm studying an old E&M textbook which uses cgs unit system. I'm re-writing the formulas in SI unit.

    The book says $\vec{H}=\vec{B}-4\pi\vec{M}$.

    So I guessed that $H$ should have same unit as $B$ in cgs system.

    But I found that $H$ has unit of Oersted, which is same as $1cm^{0.5} g^{-0.5} s^{-1}$.

    How is it possible?

  • Septacle
    Septacle over 5 years
    I'm not sure yet. How can someone write the first equation I quoted when they have different dimension?
  • Septacle
    Septacle over 5 years
    Oh... Thanks. I was confused and thought that g in the unit means gauss, not gram. Units in E&M always seem messy and confuse me. I'd read the linked page. Maybe later I can find some enlightening article about the reasons behind the units.
  • Septacle
    Septacle over 5 years
    Sorry I thought g in the unit means gauss, not gram. Thanks for the answer.
  • Farcher
    Farcher over 5 years
    @Septacle Somewhere out there on the Internet there is a really good pdf file about Gaussian units which I found some time ago but was unable to find it for you. If you do find a better article I would be grateful if you would post the link.
  • Admin
    Admin over 5 years
    In markdown, we begin and end mathjax commands with the $ sign, not [math] and [\math]. I've edited it here. A quick Mathjax tutorial can be found here.
  • wendy.krieger
    wendy.krieger over 5 years
    I also answer a lot of questions on quora, which uses [math] and [/math] as mathjax markers. Yes, i do know Latex.
  • marshal craft
    marshal craft over 5 years
    I though one is gradient of other?