How to Find the Inductance of a Long Solenoid?

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To find the inductance of a long solenoid, the formula L = (μ₀N²A)/l is used, where N is the number of turns, A is the cross-sectional area, and l is the length of the solenoid. The magnetic flux is calculated using Φ_B = BA, where B is the magnetic field. The area A can be determined using the formula A = πr², where r is the radius of the solenoid. The user initially struggled with finding the current i but eventually clarified the approach to calculating inductance without needing the current. The discussion concludes with the user successfully solving the problem.
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[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?
 
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Try

<br /> L=\frac{\mu_{0}N^{2}A}{l}<br />

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

I think...
 
Thanks for the quick response. I got it.
 
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