Register to reply

Log expansion for infinite solenoid

Share this thread:
Shinobii
#1
Feb15-13, 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. . .
Phys.Org News Partner Science news on Phys.org
World's largest solar boat on Greek prehistoric mission
Google searches hold key to future market crashes
Mineral magic? Common mineral capable of making and breaking bonds
jbunniii
#2
Feb15-13, 12:40 PM
Sci Advisor
HW Helper
PF Gold
jbunniii's Avatar
P: 3,171
What is ##\rho_0##? It appears in the second expression but not the first.
Shinobii
#3
Feb15-13, 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

Shinobii
#4
Feb15-13, 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.


Register to reply

Related Discussions
Magnetic Field Outside Infinite Solenoid Introductory Physics Homework 1
Magnetic Fields In Semi-Infinite Solenoid's Introductory Physics Homework 3
Loop around an infinite solenoid? General Physics 10
Magnetic Field of an Infinite Solenoid Advanced Physics Homework 3
Magnetic fields of infinite solenoid and infinite current carrying plane Classical Physics 17