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A solenoid is built of length $L$ with $N$ turns and a radius of $r$. A current $I$ is driven through the solenoid. Derive from basic laws and definitions:

a) The magnetic field $\vec{B}$ inside the solenoid, neglecting end effects (magnitude and direction, given the direction of current flow drawn).

b) The magnetic flux $\phi_m$ through the solenoid, as a function of I?

c) What is the self-inductance of the solenoid?

You might prefer to draw your own picture(s) to facilitate the work.