Answer to Question #91148 in Electricity and Magnetism for James

Question

An electric guitar functions via induction. As the steel strings vibrate a pickup coil of wire has an emf induced due to changing magnetic fields generated by the string. The perpendicular component of the field above the pickup coil is given by: B= 50mT+ 3.2mT·sin(2π 523 t/s) and is uniform at any given time over the area of the pickup coil. If the pickup coil has a radius of 2.7 mm and consists of 30 turns what is the induced emf in the pickup coil a function of time?

Answer 1

According to Faraday's law, the induced emf can be found as

$$emf=NA\frac{dB}{dt}=\\ =N\pi r^2\frac{d(50+3.2\space\text{sin}(2\pi 523t))\cdot10^{-3}}{dt}=\\ =7.23\cdot 10^{-3}\text{cos}(2\pi 523t)\text{ V}.$$