[–\dfrac{\text{d}\overrig...] A uniform magnetic field is restricted within a region of radius r. The magnetic field changes with

For Competitive Exams

A uniform magnetic field is restricted within a region of radius r. The magnetic field changes with time at a rate $\dfrac{d\overrightarrow{B}}{dt}$. 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 below. Then the e.m.f. generated is magnetic field loop

$–\dfrac{\text{d}\overrightarrow{B}}{\text{d}t}\pi r^2$ in loop 1 and zero in loop 2

zero in loop 1 and zero in loop 2

$–\dfrac{\text{d}\overrightarrow{B}}{\text{d}t}\pi r^2$ in loop 1 and $–\dfrac{\text{d}\overrightarrow{B}}{\text{d}t}\pi r^2$ in loop 2

$–\dfrac{\text{d}\overrightarrow{B}}{\text{d}t}\pi R^2$ in loop 1 and zero in loop 2

Explanation:

$e = – \dfrac{\text{d}\phi}{\text{d}t}= –\dfrac{\text{d}}{\text{d}t}{\pi r^2B} = – \pi r^2\dfrac{\text{d}B}{\text{d}t}$ in loop 1 & zero in loop 2.

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