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.

Question

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.

Infinity Learn · Accepted Answer

Fcosθ$$=Mgsin$$θIBLcosθ$$=Mgsin$$θ⇒$$I=Mgtan$$θLB

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