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Log expansion for infinite solenoid 
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#1
Feb1513, 11:32 AM

P: 34

Hello, I found an approximation for this log function:
[tex] log \Bigg(\frac{\Lambda}{\rho} + \sqrt{1 + \frac{\Lambda^2}{\rho^2}} \Bigg), [/tex] where [itex] \Lambda \rightarrow \infty [/itex]. The above is approximated to the following, [tex] log \bigg(\frac{\rho}{\rho_o} \bigg) + log \bigg(\frac{2 \Lambda}{\rho_o} \bigg). [/tex] How is this done? I tried expanding the [itex] \sqrt{1 + x^2} [/itex] term, but I still don't get how they arrive to the above approximation. Any help would be greatly appreciated! Cheers! I have no idea why this was sent to linear algebra section . . . And I do not know how to move it to classical physics. . . 


#2
Feb1513, 12:40 PM

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What is ##\rho_0##? It appears in the second expression but not the first.



#3
Feb1513, 01:00 PM

P: 34

I do not know what [itex] \rho_o [/itex] is, I assume some constant.
I found this approximation here: http://www.physicsforums.com/showthread.php?t=119419 


#4
Feb1513, 05:04 PM

P: 34

Log expansion for infinite solenoid
Wow, never mind. Clearly I am being silly here, for [itex] \Lambda \rightarrow \infty [/itex].
[tex] log\bigg( \frac{\Lambda}{\rho} + \sqrt{1 + \frac{\Lambda^2}{\rho^2}} \bigg) \rightarrow log \bigg( \frac{ 2 \Lambda}{\rho} \bigg) \rightarrow log(2 \Lambda)  log(\rho). [/tex] As for the [itex] \rho_o [/itex] I have no idea why that enters the equation. 


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