Q.

A uniform magnetic field is restricted within a region of radius “r”. The magnetic field changes with time at a rate dB→dt. Loop 1 of radius R > r encloses the region r and loop 2 of radius R is outside the region of magnetic field as shown in the figure. Then the e.m.f. generated is

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a

zero in loop 1 and zero in loop 2

b

-dB→dtπr2 in loop 1 and -dB→dtπr2 in loop 2

c

-dB→dtπR2 in loop 1 and zero in loop 2

d

-dB→dtπr2 in loop 1 and zero in loop 2

answer is D.

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Detailed Solution

Emf generated in loop 1,ε1=-dϕdt=-ddt(B→·A→)=-ddt(BA)=-A×dBdtε1=-πr2dBdt∵A=πr2 because dBdt is restricted upto radius r.Emf generated in loop 2,ε2=-ddt(BA)=-ddt(0×A)=0
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