Monbukagakusho Undergraduate Students Physics 2015 Questao2

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Monbukagakusho Undergraduate Students Physics 2015 Questao2
Figure 2-1 shows a conducting bar of mass m that can slide without friction on a pair of conducting rails separated by a distance d and located on an inclined plane that makes an angle 6 with respect to the ground. The two rails are connected by a resistor. The resistance of the resistor is denoted as R. A uniform magnetic ﬁeld of magnitude B is directed upward, perpendic- ular to the ground over the entire region through which the bar moves. The bar is released from rest and slides down. The acceleration due to gravity is denoted as g. ( 1) Which way does the current ﬂow, from a to b or b to a?
(2) Which of the following is the correct formula for the induced current I?
(3) Besides gravity1 the magnetic force acts on the bar. Find the correct formula for the component of this magnetic force along the inclined plane.
After a sufﬁciently long time the bar moves at a constant speed. At this terminal velocity u the gravity force is balanced by the magnetic force along the inclined plane. (4) Find the correct formula for u.
(5) Which of the following is the correct. formula for the rate of work done by gravity on the bar?