$[14]11.$ A rectangular loop of wire with a width of $3\mathrm{.}0$ cm and a mass of $0\mathrm{.}17$ kg falls from a region of uniform magnetic field with its long edges vertical as shown. The total resistance of the wire in the loop is $0\mathrm{.}5.$ The magnitude of the field is $3\mathrm{.}5$ T and it points perpendicular to the plane of the loop as shown. For the period of time when the top edge of the loop is inside the region of uniform magnetic field and the bottom edge is outside, the loop falls with constant speed.

$($a$)$ What is the magnitude of the magnetic force, $F_B,$ on the rectangular loop while it is falling at constant speed?

$($b$)$ What current must be induced in the loop in order to generate the magnetic force $F_B?($Hint: think about which edge of the loop is acted on by the magnetic force.$)$

$($c$)$ At what constant speed does the loop drop while its upper edge is in the magnetic field and its lower edge is outside? $($Hint: determine the emf necessary to drive the current found in $($b$)$ and then relate that to the speed using Faraday's law of induction.$)$

$($d$)$ In what direction $($clockwise or counterclockwise$)$ does the current flow in the loop as it is dropping out of the region of magnetic field?

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