Question

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

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

Answer 1

The correct option is A $-\frac{d\overrightarrow{B}}{dt}\pi r^2$ in loop $1$ and zero in loop $2$.

emf is induced in a coil due to change of flux through it.

In the loop 1, the flux passing through it is $\varphi =B\pi r^2$
Hence, emf induced = $-\frac{d\varphi }{dt}=-\pi r^2\frac{d\overrightarrow{B}}{dt}$
Since the magnetic field does not change inside loop 2, no emf is induced in it.