Engineering
Physics
Physical Quantities

Question

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 dBdt=α 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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Linked Question 1

The force required to pull the rod with velocity v = 5 m/s against time is given by :

Solution
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F = Biℓ

= (B0 –αt)ℓ(ℓ0+vt)αRℓ

Linked Question 2

What should be the speed v so that the total induced emf in the loop is always zero.

Not possible

2αℓ0B0

αℓ0B0

αℓ02B0

Solution
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Verified by Zigyan

Enet = Aα = ℓ (ℓ0 + vt) α

t is variable so not possible.

Linked Question 3

The current through the rod    

Decreases continuously in magnitude

Increases and then decreases in magnitude

Decreases and then increases in magnitude

Increases continuously in magnitude

Solution
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Verified by Zigyan

i=EnetR=ℓ(ℓ0+vt)αR

i  increases for t≤B0α

after which B = 0, hence current becomes zero.