A rod of mass m and length ℓ is being pulled with a constant velocity v on frictionless rails as shown. The initial distance of the rod from the end of the loop is ℓ0. The resistance of loop is R and it's self inductance is negligible. Magnetic field is present in space in vertically upward direction. Initially magnetic field is B0 and it starts decreasing at a constant rate till it becomes zero. m = 2kg. Take R = 5Ω, α = 0.1 T/sec, B0 = 2T, ℓ = ℓ m, ℓ0 = 1m, v = 5 m/s.
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The force required to pull the rod with velocity v = 5 m/s against time is given by :
F = Biℓ
What should be the speed v so that the total induced emf in the loop is always zero.
Enet = Aα = ℓ (ℓ0 + vt) α
t is variable so not possible.
The current through the rod
i increases for t
after which B = 0, hence current becomes zero.