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Two ends of an inductor of inductance L ...

Two ends of an inductor of inductance L is connected to two parallel conducting rails. A conducting wire of length (that is equal to separation between the rails) can slide on the rails without friction. The wire has mass m. It is projected with a velocity `v_(0)` parallel to the rails (see Figure). Neglect self inductance and resistance of the loop.
(a) Find velocity of the wire as a function of time.
(b) Write current through the wire at time t.
(c) Find speed of the wire as a function of its displacement.
(d) Is the current in the conductor zero when it stops? If no, find this current .
(e) Will the conductor move after it stops?

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