In a physics laboratory experiment, a coil with $210$ turns enclosing an area of $12c{m}^2$ is rotated in a time interval of $0\mathrm{.}050$ s from a position where its plane is perpendicular to the earth's magnetic field to a position where its plane is parallel to the field. The earth's magnetic field at the lab location is $5\mathrm{.}0{10}^{-5}T.$