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1. A square loop with sides of length L has total resistance R and mass m. It is falling under a constant gravitational force directed down along the -y direction. The magnetic field varies linearly with height y: and is directed out of the page along the z direction. Denote the center of the loop as y0(t) and its speed
a) What is the magnetic flux Φ 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 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 of the loop (top, bottom, left and right) as a function of the center of the loop y0 and the speed v.
e) The loop will eventually fall at a constant speed vo. Calculate ???????? by balancing the total force on the loop and the gravitational force.
f) What is the rate of work done by the current flowing through the resistance at this speed? Show that this is equal to the rate of work done by gravity.
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