- #1
SonOfOle
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Homework Statement
Consider an ideal cylindrical solenoid of length L and radius a=L/2 on which a thin wire has been wrapped a total of N turns. A steady current I flows through the wire. Assume the wires are wound so tightly that the solenoid can be thought of as a collection of N parallel current loops. Using the Biot-Savart law, find the induced magnetic field at the exact center of the solenoid.
Homework Equations
Eqn 1: [tex] B_{loop, on center axis} = \frac{\mu_{0} I (L/2)^2 }{2 ((L/2)^2 +Z^2 )^{3/2}} [/tex]
The Attempt at a Solution
First showing Eqn 1 (by using the Biot-Savart Law) we know the field due to one coil. Other than giving the solution as a sum (e.g. [tex] B_{solenoid}=\Sigma^{N}_{n=1} \frac{\mu_{0} I (L/2)^2 }{2 ((L/2)^2 +Z_{n}^{2} )^{3/2}}[/tex] where [tex] Z_{n} = L/2 - (L/N)n[/tex]), does someone see a good way to give the exact answer (we know what we're looking for from Gauss' Law, I just can't figure it out using Biot-Savarts).