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 `gt` r encloses the region r and loop 2 of radius R is outside the region of magnetic field as shown in figure. Then, the emf generated is

Zero in loop 1 and zero in loop 2
− d B d t π r 2 in loop 1 and − d B d t π 2 in loop 2
− d B d t π R 2 in loop 1 and zero in loop 2
− d B d t π r 2 in loop 1 and zero in loop 2

Options

A. Zero in loop 1 and zero in loop 2
B. `-(dB)/(dt)pir^(2)` in loop 1 and `-(dB)/(dt)pi^(2)` in loop 2
C. `-(dB)/(dt)piR^(2)` in loop 1 and zero in loop 2
D. `-(dB)/(dt)pir^(2)` in loop 1 and zero in loop 2

Answer

C

Explanation

Induced emf in the region is given by
`|e|=(dhpi)/(dt)`
where, `phi=BA=pir^(2)B`
`rArr" "(dphi_(1))/(dt)-pir^(2)(dB)/(dt)`
Rate of change if magnetic flux associated with loop l,
`e_(1)=-(dphi_(1))/(dt)=-pir^(2)(dB)/(dt)`
Similarly, `e_(2)` = emf associated with loop 2
`=-(dphi_(2))/(dt)=0" "(because phi_(2)=0)`