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The Maxwell Speed Distribution in 2D

by fatherdaly
Tags: maxwell
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fatherdaly
#1
Jan8-11, 03:49 PM
P: 8
1. The problem statement, all variables and given/known data


It seemed much easier to screencap than to write out.

2. Relevant equations

It helps to know that the number of states with speed between u and u+du is 2pi*u du

3. The attempt at a solution

I've tried quite a few things but every time I get to trying to normalise I either get stuck integrating by parts over and over, or using http://en.wikipedia.org/wiki/Gaussian_integral<that, which doesn't arrive at the answer wanted.

If someone could give me a push in the right direction it would be much appreciated.
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weejee
#2
Jan8-11, 06:04 PM
P: 199
You need some substitution to make the integral doable.
fatherdaly
#3
Jan9-11, 03:14 PM
P: 8
Ok so I have the integral of v*exp(-[tex]\alpha[/tex]v2) dv between 0 and infinity to normalise. I don't know how a substitution would help because you would still have two functions multiplied by one another.

Edit: I think I'm being stupid. I've substituted for alpha*v^2. Hopefully it will work.


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