You are given a long length W of copper wire. How would you arrange it to obtain the maximum self-inductance? Why?
I am trying to use the equation
$$L=\mu_o n^2 l A$$
I try to solve it using a fixed length wire of 10 units, width 1mm and winding it into a solenoid. I plug in values of circumference 10, 5, 2.5 and finding the inductance through number crunching. However, I am getting a larger values for multiple loops but the answer is a single loop (ie. a circle) rather then a solenoid.
Here are the sample values I got:
$n=1; C=10; r=1.59; L=0.079 \mu_o$
$n=2; C=5; r=0.79; L=0.156\mu_o$
$n=4; C=2.5; r=0.3978; L=0.318\mu_o$
If anyone could enlighten me on the proper way of solving this, I'd appreciate it.