# Problem: Suppose that a 0.45 m-radius, 500-turn coil produces an average emf of 10700 V when rotated one-fourth of a revolution in 4.39 ms, starting from its plane being perpendicular to the magnetic field. What is the peak emf generated by this coil, in volts?

###### FREE Expert Solution

Induced emf (constant magnetic flux):

$\overline{){\mathbf{\epsilon }}{\mathbf{=}}{\mathbf{N}}\frac{\mathbf{∆}\mathbf{B}\mathbf{A}\mathbf{c}\mathbf{o}\mathbf{s}\mathbf{\theta }}{\mathbf{∆}\mathbf{t}}}$

Induced emf in the form of a time-varying equation:

$\overline{){\mathbf{\epsilon }}{\mathbf{=}}{{\mathbf{\epsilon }}}_{{\mathbf{0}}}{\mathbf{sin}}{\mathbf{\left(}}{\mathbf{\omega t}}{\mathbf{\right)}}{\mathbf{=}}{\mathbf{N}}{\mathbf{A}}{\mathbf{B}}{\mathbf{\omega }}{\mathbf{sin}}{\mathbf{\left(}}{\mathbf{\omega t}}{\mathbf{\right)}}}$

A = πr2 = π(0.45)2 = 0.2025π

99% (118 ratings) ###### Problem Details

Suppose that a 0.45 m-radius, 500-turn coil produces an average emf of 10700 V when rotated one-fourth of a revolution in 4.39 ms, starting from its plane being perpendicular to the magnetic field. What is the peak emf generated by this coil, in volts?