A conducting wire of length I and mass m is placed on two inclined rails as shown in figure. A current i is flowing in the wire in the direction shown. When no magnetic field is present in the region, the wire is just on the verge of sliding. When a vertically upward magnetic field is switched on, the wire starts moving up the incline. The distance travelled by the wire as a function of time r will be

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Infinity Learn · Accepted Answer

The front view of the arrangement is shown in figure.From initial condition, mg $$sin$$θ $$=$$ μ mg $$cos$$θ⇒μ$$=$$$$tan$$θ$$ma=IBlcos$$θ$$-mgsin$$θ$$-$$μ$$NN=mg$$ $$cos$$θ$$+IBl$$ $$sin$$θ⇒$$a=IBlmcos$$θ$$-2g$$ $$sin$$θ$$-IBlmsin2$$θ$$cos$$θ$$=IBlmcos$$ $$2$$θ$$cos$$ θ$$-2g$$ $$sin$$θNow, $$s=12at2=12IBlmcos$$ $$2$$θ$$cos$$ θ$$-2g$$ $$sin$$θ$$t2$$

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