A conducting circular loop is placed in a uniform magnetic field, $$B = 0.025\,T$$   with its plane perpendicular to the loop. The radius of the loop is made to shrink at a constant rate of $$1\,mm{s^{ - 1}}.$$  The induced emf when the radius is $$2\,cm,$$  is

Solution :
Magnetic flux $$\phi $$ linked with magnetic field $$B$$ and area $$A$$ is given by
$$\eqalign{ & \phi = B \cdot A = \left| B \right|\left| A \right|\cos \theta \cr & {\text{Here,}}\,\,\theta = {0^ \circ } \cr & {\text{So,}}\,\,\phi = BA = B\pi {r^2} \cr} $$
Now, Induced emf, $$\left| e \right| = \left| {\frac{{ - d\phi }}{{dt}}} \right| = B\pi \left( {2r} \right)\frac{{dr}}{{dt}}$$
$$\eqalign{ & = 0.025 \times \pi \times 2 \times 2 \times {10^{ - 2}} \times 1 \times {10^{ - 3}} \cr & = \pi \mu V \cr} $$