# Magnetic Energy

1. May 10, 2008

### jesuslovesu

[SOLVED] Magnetic Energy

Whoops, never mind, i didn't use the right B field

1. The problem statement, all variables and given/known data
Show that the magnetic energy per unit length of a nonmagnetic wire is $$\frac{\mu_0 I^2 }{ 16 \pi}$$ (inside the wire)

2. Relevant equations

$$W = 1/2 L I^2$$
$$W = \int \int \int \frac{|B|^2} {2 \mu}$$

3. The attempt at a solution

Well, At first I was going to use W = 1/2 Li^2, but then I realized that I don't know how to find the self inductance of a wire. (inside it at least)

I know the B field of a wire, but when I try to integrate it, I get something completely different.

$$W = \int_0^L \int_0^{2\pi} \int_0^a \frac{(\mu_0 I)^2} {(2 * 2\pi r)^2} rdr d \phi dz$$ (i'll worry about the per unit length part later)
But as you can see that gives me a ln(a/0) which can't happen, so I'm stumped

Last edited: May 10, 2008