How to Find the Inductance of a Long Solenoid?

[ttiger2k7]

[SOLVED] Simple Self-Inductance Problem

Homework Statement

Find the inductance L of a long solenoid of length 39.0 cm, and radius 2.30 cm, which has 3.10E2 turns. (Express you answer in units of H for henrys).

Homework Equations

$$L=\frac{N\Phi_{B}}{i}$$
$$\Phi_{B}=BA=\frac{\mu_{0}NiA}{2\pi*r}$$

The Attempt at a Solution

Okay, so the way I am thinking to solve this problem is to first get the magnetic flux. But I have no idea how to find the current $$i$$ for a solenoid. Since I don't know how to find $$i$$, I simply plugged in the formula for flux into the formula for inductance to get:

$$L=\frac{N\Phi_{B}}{i}=\frac{\mu_{0}N^{2}A}{2\pi*r}$$

That's where I get stuck. *If* I am in fact going about this the right way, do I just find area by using pi*r^2?

 

[montoyas7940]

Try

$$L=\frac{\mu_{0}N^{2}A}{l}$$

Where A is cross sectional area and l is the length of the solenoid.

I think...

 

[ttiger2k7]

Thanks for the quick response. I got it.