Q.

A flexible wire loop in the shape of a circle has a radius that grows 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?

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a

E∝t2

b

E∝t

c

E∝t

d

E is constant

answer is D.

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Detailed Solution

Let radius of the loop is r at any time t and in further time dt, radius increases by dr.Then change in flux: dϕ=2πrdrB⇒e=dϕdt=2πr(drdt)kr⇒e=2πck(constant)      [drdt=c,B=kr]Then change in flux: dϕ=2πrdrB
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A flexible wire loop in the shape of a circle has a radius that grows 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?