A conducting circular loop is placed in a uniform magnetic field of $$0.04\,T$$  with its plane perpendicular to the magnetic field. The radius of the loop starts shrinking at $$2\,mm/s.$$  The induced emf in the loop when the radius is $$2\,cm$$  is

Solution :
Induced emf in the loop is given by
$$e = - B.\frac{{dA}}{{dt}}$$   where $$A$$ is the area of the loop.
$$\eqalign{ & e = - B.\frac{d}{{dt}}\left( {\pi {r^2}} \right) = - B\,\pi \,2r\frac{{dr}}{{dt}} \cr & r = 2\,cm = 2 \times {10^{ - 2}}m \cr & dr = 2\,mm = 2 \times {10^{ - 3}}m,dt = 1s \cr & e = - 0.04 \times 3.14 \times 2 \times 2 \times {10^{ - 2}} \times \frac{{2 \times {{10}^{ - 3}}}}{1}V \cr & = 0.32\,\pi \times {10^{ - 5}}V \cr & = 3.2\,\pi \times {10^{ - 6}}V \cr & = 3.2\,\pi \,\mu V \cr} $$