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?

Answer

(a) `v = v_(0) cos omegat`
(b) `i=v_(0) sqrt((m)/(L))sin omega t` where `omega = (Bl)/(sqrt(mL))`
(c) `v = sqrt(v_(0)^(2) -(B^(2)l^(2))/(mL)x^(2))`
(d) No, `v_(0) sqrt((m)/(L))`
(e) Yes