# Question about cgs vs SI units in the context of the Debye Length

• A
• ehchandlerjr
ehchandlerjr
TL;DR Summary
Would have thought cgs and SI would give the same debye length when converted to the same units, but they don't. What is the physical meaning difference, and how do I know which equation to use.
Hello - I am trying to understand the physical meaning the undergirds the Debye length as it pertains to different unit systems. I understand that fundamentally its the distance at which the distribution of ions doesn't differ by more than the effect of k_B*T from the rest of the solution, plasma, whatever. But what I don't understand is why cgs and SI can give such radically different values. If they just came out as different values with different units, whatever. But I can convert both to meters, and get completely different numbers. I'm writing a review article, and this isn't really my field, but all the papers I came across had different expressions, and I dug a little deeper, and found this confusion, and I don't know how to resolve it. I'd just be somewhat vague, but I don't even know how to kindof defend the choice of one or the other equation, other than saying, "everywhere else I used SI," which isn't a very good answer.

HELP!

Lord Jestocost
ehchandlerjr said:
TL;DR Summary: Would have thought cgs and SI would give the same debye length when converted to the same units, but they don't. What is the physical meaning difference, and how do I know which equation to use.

Hello - I am trying to understand the physical meaning the undergirds the Debye length as it pertains to different unit systems. I understand that fundamentally its the distance at which the distribution of ions doesn't differ by more than the effect of k_B*T from the rest of the solution, plasma, whatever. But what I don't understand is why cgs and SI can give such radically different values. If they just came out as different values with different units, whatever. But I can convert both to meters, and get completely different numbers. I'm writing a review article, and this isn't really my field, but all the papers I came across had different expressions, and I dug a little deeper, and found this confusion, and I don't know how to resolve it. I'd just be somewhat vague, but I don't even know how to kindof defend the choice of one or the other equation, other than saying, "everywhere else I used SI," which isn't a very good answer.

HELP!
Maybe, the following might be of help (from the University of Maryland):

### Converting between SI and Gaussian units​

DrClaude
SI and cgs units can have different values even for observables with no units. For example the magnetical susceptibility ##\chi## is given in SI by ##\mathbf M = \chi \mathbf M## but in the usual cgs (Gaussian) units it is given by ##\mathbf M = 4\pi \chi \mathbf H##. So in SI, superconductors have ##\chi=-1## and in cgs ##\chi=-\frac{1}{4\pi}##.

THAT SAID: I think that the Debye length should be the same in cgs and SI. What values are you using can you provide an example?

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