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# Problem: An emf is induced by rotating a 1000-turn, 20.0 cm diameter coil in the Earth's 5.00 × 10–5 T magnetic field. What is the average emf 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

Induced emf:

$\overline{){\mathbf{\epsilon }}{\mathbf{=}}{\mathbf{N}}\frac{\mathbf{∆}\mathbf{\varphi }}{\mathbf{∆}\mathbf{t}}}$, where Φ  is the magnetic flux, N is the number of turns, t is the time, and A is the cross-sectional area o the coil.

The magnetic flux:

$\overline{){\mathbf{\varphi }}{\mathbf{=}}{\mathbf{∆}}{\mathbf{B}}{\mathbf{A}}{\mathbf{c}}{\mathbf{o}}{\mathbf{s}}{\mathbf{\theta }}}$, where B is the magnetic field and θ is the angle between the A vector and the B field of the coil.

The induced emf is now:

ε = NΔBAcosθ/Δt

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###### Problem Details

An emf is induced by rotating a 1000-turn, 20.0 cm diameter coil in the Earth's 5.00 × 10–5 T magnetic field. What is the average emf 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?