Question

A uniform magnetic field is restricted within a region of radius $r$. The magnetic field changes with time at a rate $\frac{d \vec{B}}{dt}$. Loop $1$ of radius $R > r$ enclosed 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

• A. Zero in loop $1$ and zero in loop $2$
• B. $- \frac{d \vec{B}}{dt} \pi r^2$ in loop $1$ and $- \frac{d \vec{B}}{dt} \pi r^2$ in loop $2$
• C. $- \frac{d \vec{B}}{dt} \pi R^2$ in loop $1$ and zero in loop $2$
• D. $- \frac{d \vec{B}}{dt} \pi r^2$ in loop $1$ and zero in loop $2$

Answer 1

Answer: (D)

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

Answer 2

Induced e.m.f. in loop (1)
$e = - \frac{d\phi}{dt} =- \frac{AdB}{dt}$
$= - \pi r^{2} \frac{dB}{dt}$
Induced e.m.f. in loop (2)
Loop (2) is not in magnetic field so no field change so induced e.m.f. = 0