$14.)(10$ pts$.)$ The magnet is dropped through the metal hoop from just slightly above it$,$ speeding up on its way down.

a$)$ Carefully sketch the bar magnet's magnetic field lines.

b$)$ Make a careful graph of the induced emf in the loop $E$ vs$.$ time $t.$ A counter$-$clockwise current as seen from above indicates a positive emf, while a clockwise current indicates a negative emf. Label your axes, but no numbers are required. Pay careful attention to the height, width, and area under your graph!