Usually a solenoid has field \frac{\mu_0 N I}{L}.
I think that means the units are off in my solution since I essentially have units of \mu_0 I and those are of \frac{\mu_0 I}{L}.
I just double checked the integral, and that was evaluated correctly, which means I set it up incorrectly.
I...
Just tried it now
Using Griffith's formula for on-axis field from a current loop (example 5.6 3rd edition)
B(z) = \frac{\mu_0 I}{2} \frac{a^2}{(a^2+z^2)^{3/2}}
I integrate this with respect to z from -L to L and the result is \frac{\mu_0 I L}{\sqrt{a^2+L^2}}
Seem reasonable?
Homework Statement
A cylindrical shell of radius a and length 2L is aligned around the z-axis from z= -L ot z = +L. A current I is distributed uniformly on the cylinder and moves around the cylinder's z-axis. Find the magnitude of the magnetic field at the origin.
Homework Equations...