Electro Magnetic Induction And Alternating Currents Question 461

Question: A flexible wire loop in the shape of a circle has radius that grown linearly with time. There is a magnetic field perpendicular to the plane of the loop that has a magnitude inversely proportional to the distance from the center of the loop, B(r)1r .How does the emf E vary with time?

Options:

A) Et2

B) Et

C) Et

D) E is constant

Show Answer

Answer:

Correct Answer: D

Solution:

  • Let radius of the loop is r at any time t and in further time dt, radius increases by dr.

    The change in flux:

    dϕ=(2πrdr)B
    e=dϕdt=2πr(drdt)kr
    ,e=2πck (constant) [drdt=c,,B=kr]

    The change in flux: dϕ=(2πrdr)B



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