Question

Please tell me the derivation of magnetic field of a solenoid along it's axis

Answer 1

long solenoid has current I flowing through it, also denote N as the turns per unit length. Take its axis to be the z-axis, by symmetry the only component of the magnetic field inside is Bz. Find the magnetic field at the center of the solenoid (on the axis). Also, find the magnetic field at the ends of the solenoid.

For the first part, since the solenoid is long we can approximate the magnetic field inside to be uniform and is given by Bz=μ0NI, so we can say that the magnetic field at the center is also μ0NI. I'm not sure if my argument is correct but based on my understanding, from the uniformity of the B-field inside, it should be the same everywhere inside. Can anyone kindly tell me if this is correct? Any suggestions and insights?