# Problem: An emf is induced by rotating a 1527 turn, 20.0 cm diameter coil in the Earth's 3.73  10-5 T magnetic field. What average emf is induced, given the plane of the coil is originally perpendicular to the Earth's field and is rotated to be parallel to the field in 10.0 ms?

###### FREE Expert Solution

Average induced emf:

$\overline{){{\mathbf{\epsilon }}}_{{\mathbf{avg}}}{\mathbf{=}}\frac{\mathbf{∆}\mathbf{\varphi }}{\mathbf{t}}}$

Magnetic flux:

$\overline{){\mathbf{\varphi }}{\mathbf{=}}{\mathbf{N}}{\mathbf{B}}{\mathbf{A}}{\mathbf{c}}{\mathbf{o}}{\mathbf{s}}{\mathbf{\theta }}}$

Area, A = π(d/2)2

Initial magnetic flux:

$\begin{array}{rcl}{\mathbf{\varphi }}_{\mathbf{i}}& \mathbf{=}& \mathbf{\left(}\mathbf{1527}\mathbf{\right)}\mathbf{\left(}\mathbf{3}\mathbf{.}\mathbf{73}\mathbf{×}{\mathbf{10}}^{\mathbf{-}\mathbf{5}}\mathbf{\right)}\mathbf{\left[}\mathbf{\pi }{\mathbf{\left(}\frac{\mathbf{20}\mathbf{.}\mathbf{0}\mathbf{×}{\mathbf{10}}^{\mathbf{-}\mathbf{2}}}{\mathbf{2}}\mathbf{\right)}}^{\mathbf{2}}\mathbf{\right]}\mathbf{c}\mathbf{o}\mathbf{s}\mathbf{\left(}\mathbf{0}\mathbf{°}\mathbf{\right)}\end{array}$

Φi = 1.789 × 10-3 T•m2

###### Problem Details

An emf is induced by rotating a 1527 turn, 20.0 cm diameter coil in the Earth's 3.73  10-5 T magnetic field. What average emf is induced, given the plane of the coil is originally perpendicular to the Earth's field and is rotated to be parallel to the field in 10.0 ms?

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