Q.

A straight piece of conducting wire with mass M and length L is placed on a friction less incline tilted at an angle θ from the horizontal (as shown in figure). There is a uniform, vertical magnetic field at all points (produced by an arrangement of magnets not shown in figure). To keep the wire from sliding down the incline, a voltage source is attached to the ends of the wire. When just the right amount of current flows through the wire, the wire remains at rest.Determine the magnitude and direction of the current in the wire that will cause the wire to remain at rest.

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a

Mgtanθ2LBto the left

b

MgtanθLBto the right

c

MgtanθLBto the left

d

3Mgtanθ2LBto the left

answer is C.

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Detailed Solution

Fcosθ=MgsinθIBLcosθ=Mgsinθ⇒I=MgtanθLB
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A straight piece of conducting wire with mass M and length L is placed on a friction less incline tilted at an angle θ from the horizontal (as shown in figure). There is a uniform, vertical magnetic field at all points (produced by an arrangement of magnets not shown in figure). To keep the wire from sliding down the incline, a voltage source is attached to the ends of the wire. When just the right amount of current flows through the wire, the wire remains at rest.Determine the magnitude and direction of the current in the wire that will cause the wire to remain at rest.