You are building an instrument to measure the orientation of Earth's magnetic field. Your device consists of a single conducting coil that encloses an area \(A=400 \mathrm{~mm}^{2}\) and rotates at a speed of 10,000 rotations \(/ \mathrm{min}\). What peak induced emf should you expect if the magnitude of Earth's magnetic field is \(50 \mu \mathrm{T}\) ?