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A solenoid is built of length $L = 0.1$ meter with $N = 10^4$ turns and a radius of $r = 1$ cm as drawn. A current $I = 5$A is driven through the solenoid.

a) Find the magnetic field $\vec{B}$ inside the solenoid, neglecting end effects (magnitude and direction, given the direction of current flow drawn). Show algebraically how you got your numerical answer in SI units. Draw the direction of the field lines in on your picture.

b) Find the self-inductance of the solenoid.