A square loop with sides of length d has total resistance R and mass m. It is falling under a constant gravitational force -mgy directed down along the -y direction. The magnetic field varies linearly with height y: B - ayż (a> 0) and is directed out of the page along the z direction. Denote the center of the loop as yo(t) and its speed v- ldyo/dt

a) What is the magnetic flux Ф through the loop as a function of the y-coordinate of the loop? HINT: Because the field varies linearly the flux is just the area times the value of B at the center of the loop.
b) What is the magnitude of the induced emf if the loop is falling at speed v?
c) Is the induced current clockwise or counter-clockwise if the ring is falling? You may use Lenz's law.
d) From the magnitude of the current find the force from the constant field B on each side peed v of the loop (top, bottom, left and right) as a function of the center of the loop yo and the e The loop will eventually fall at a constant speed vo. Calculate vo by balancing the total force on the loop and the gravitational force. What is the rate of work done by the current flowing through the resistance at this speed? Show that this is equal to the work done by gravity.