Concept

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

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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?