Take the 2-minute tour ×
Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It's 100% free.

This may be a stupid question but I am having trouble getting the same result in CGS units as I would if I used SI units for a unitless calculation.

I have to calculate $E_c=\frac{m_e c\, \omega_c}{eB}$ I have in CGS units that $\frac{e}{m_ec}$ is $(1.76\times10^{7}s^{-1}G^{-1})$ and $B=10^{-4}G=10^{-8}T$ and $\omega_c$ is just some frequency. Essentially, when I do this calculation in SI units and in CGS units I get very different results. From this equation it seems clear to me that $\frac{e}{m_ec}$ in CGS and SI should only be off by a few factors of 10 (namely 4) since $B$ is scaled by $10^{-4}$ from CGS to SI, but this is not the case... What am I doing wrong?

Edit: Here are my calculations.

(i) CGS: $\frac{(1.52\times10^{18}s^{-1})}{(1.76\times10^7s^{-1}\,G^{-1})(3\times10^{-4}G)}$

(ii) SI: $\frac{(9.11\times10^{-31}\mathrm{kg})(3\times10^8\mathrm{m \, s^{-1}})(1.52\times10^{18}s^{-1})}{(1.6\times10^{-19}C)(3\times10^{-8}T)}$

Unless the value I'm using for $\frac{e}{m_ec}$ in CGS is wrong...

share|improve this question
Why not show your two sets of calculations? –  Henry Dec 9 '12 at 20:50
Alright... I showed my calcs –  Atreyu Dec 9 '12 at 20:56

1 Answer 1

up vote 1 down vote accepted

The problem comes with the CGS units of charge. One of them is the statcoulomb with $$1 \mathrm{C} \leftrightarrow 2997924580 \,\mathrm{statC} \approx 3 \times 10^9 \mathrm{statC}$$

It is this factor of $3 \times 10^9$ which seems to be the difference between your two calculations, and needs to be taken into account in the CGS calculation. Your $\frac{e}{m_ec}$ may be about $1.76\times10^{7}$ but its units are not $s^{-1}G^{-1}$.

share|improve this answer
Thanks very much for your help –  Atreyu Dec 9 '12 at 21:48
Does this mean the calculation in CGS units is wrong? I mean how can it convert differently if the above calculation is supposed to give a unitless value? (It is supposed to be proportional to the $\gamma$ factor in SR) –  Atreyu Dec 9 '12 at 21:57
I am not certain, but I think you need an extra term in the numerator of the CGS calculation –  Henry Dec 9 '12 at 22:26
The problem is I think that the answer from the CGS calculation gives me the right answer (as is)... But I don't see why the SI calculation would be wrong –  Atreyu Dec 9 '12 at 23:01

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.