A stiff wire is bent into a semicircle of radius $\frac{1}{\mathrm{\pi }}$ m,  as shown in the figure. It is rotated about its diameter with 30 rev/s in a uniform magnetic field of $20 \times {10}^{-3} T.$ Calculate the maximum value of emf induced in the loop :

A metal rod $AB$ of length $20 \mathrm{cm}$ is kept in contact with a conductor $PQRS$ of negligible resistance to form a loop as shown in the figure. A magnetic field of $0.2 \mathrm{T}$ is acting perpendicular to the plane of the loop. The resistance of the rod $AB$ is $2 \mathrm{\Omega }$. Determine the force required to move the rod at a constant speed of $3 \mathrm{m}/\mathrm{s}$.

A stiff wire is bent into a semicircle of radius $\frac{1}{\mathrm{\pi }}$ m,  as shown in the figure. It is rotated about its diameter with 30 rev/s in a uniform magnetic field of $20 \times {10}^{-3} T.$ Calculate the maximum value of emf induced in the loop :