Answer to Question #106664 in Electricity and Magnetism for Baby Jane

Question

An emf induced by rotating a 1000 turns, 20.0 cm diameter coil in the earth's 5.00×10^-5 T magnetic field. What average emf induced, given the plane of coil is originally perpendicular to the earth's field and is rotated to be parallel to the field in 10.0 ms

Answer 1

The Faraday's law of electromagnetic induction says

$${\rm emf}=-\frac{\Delta\Phi}{\Delta t}.$$

The change of magnetic field

$$\Delta\Phi=NBA(\cos 90^{\circ}-\cos 0^{\circ})$$ $$=-NBA=-\pi r^2NB$$ $$=-\pi\times (0.1)^2\times 10^3\times 5\times 10^{-5}=-1.6\times 10^{-3}\rm Wb$$

Hence

$${\rm emf}=\frac{1.6\times 10^{-3}}{10\times 10^{-3}}=0.16\:\rm V.$$