Question 329: Electromagnetic Induction

Question

A uniform magnetic field is restricted within a region of rafius r. The magnetic field changes with time at a rate $${{d\overrightarrow B } \over {dt}}$$. 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

Accepted Answer

Emf generated in loop 1,
$${\varepsilon _1} =  - {{d\phi } \over {dt}} =  - {d \over {dt}}\left( {BA} ight) =  - A 	imes {{dB} \over {dt}}$$
$$ \Rightarrow $$ $${\varepsilon _1} =  - \pi {r^2} 	imes {{dB} \over {dt}}$$
Emf generated in loop 2,
$${\varepsilon _2} =  - {{d\phi } \over {dt}} =  - {d \over {dt}}\left( {BA} ight) =  - {d \over {dt}}\left( {0 	imes A} ight)$$ = 0

Answer

zero in loop 1 and zero in loop 2

Answer

$$ - {{d\overrightarrow B } \over {dt}}\pi {r^2}$$ in loop 1 and $$ - {{d\overrightarrow B } \over {dt}}\pi {r^2}$$ in loop 2

Answer

$$ - {{d\overrightarrow B } \over {dt}}\pi {R^2}$$ in loop 1 and zero in loop 2

Answer

$$ - {{d\overrightarrow B } \over {dt}}\pi {r^2}$$  in loop 1 and zero in loop 2

Electromagnetic Induction

Choose the correct answer: