Sketch a solenoid of 5cm length and draw magnetic field lines (if any) outside and inside of it. Shade a cross-section area that the magnetic field lines pierce through inside the solenoid.
Suppose that the solenoid has 100 turns per cm, a radius of 0.1cm, and there is a current that starts at 0A and ramps linearly to 1A in 5s through its windings. What is the magnetic flux through the cross-section of the solenoid at time 2.5s? (Note: the solenoid length >> radius; ok to use equations for a very long solenoid).
What is the self-inductance of this solenoid?
What is the induced back-emf across the 5cm length of the solenoid at time 3s?