Electro Magnetic Induction And Alternating Currents Question 481

Question: A conducting rod of length l is hinged at point O. It is free to rotate in vertical plane. There exists a uniform magnetic field B in horizontal direction. The rod is released from position . When rod makes an angle θ from released position then potential difference between two ends of the rod is proportional to:

Options:

A) l1/2

B) The lower end will be at a lower potential

C) sinθ

D) (sinθ)1/2

Show Answer

Answer:

Correct Answer: D

Solution:

  • WET from A to B ωmg=ΔK.E.

    mgL2sinθ=12Iω2 mgL2sinθ=12×mL23ω2

    3gLsinθ=ω2

    Induced emf produced in rod is ε=12(BωL2)=12B×3g,sinθL×L2

    ε=12×B×3g,sin,θ×L4L=12B3g,sin,θL3

    εL3/2

    εsinθ



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