# Log expansion for infinite solenoid

by Shinobii
Tags: expansion, infinite solenoid, magnetostatics
 P: 34 Hello, I found an approximation for this log function: $$log \Bigg(\frac{\Lambda}{\rho} + \sqrt{1 + \frac{\Lambda^2}{\rho^2}} \Bigg),$$ where $\Lambda \rightarrow \infty$. The above is approximated to the following, $$-log \bigg(\frac{\rho}{\rho_o} \bigg) + log \bigg(\frac{2 \Lambda}{\rho_o} \bigg).$$ How is this done? I tried expanding the $\sqrt{1 + x^2}$ 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. . .
 PF Patron HW Helper Sci Advisor P: 2,588 What is ##\rho_0##? It appears in the second expression but not the first.
 P: 34 I do not know what $\rho_o$ is, I assume some constant. I found this approximation here: http://www.physicsforums.com/showthread.php?t=119419
P: 34

## Log expansion for infinite solenoid

Wow, never mind. Clearly I am being silly here, for $\Lambda \rightarrow \infty$.

$$log\bigg( \frac{\Lambda}{\rho} + \sqrt{1 + \frac{\Lambda^2}{\rho^2}} \bigg) \rightarrow log \bigg( \frac{ 2 \Lambda}{\rho} \bigg) \rightarrow log(2 \Lambda) - log(\rho).$$

As for the $\rho_o$ I have no idea why that enters the equation.

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