Having seen how the pickup coil worked in an electric guitar, you thought you mi

Question

Having seen how the pickup coil worked in an electric guitar, you thought you might try to build one yourself. In attempting to tune a string to the note middle C, you decided to make some estimations in your design. First of all, for the pickup you decided to wrap copper wire tightly into circular coils of radius 3.5 mm and 140 turns. You also did some rough estimations on the maximum magnetic field strength from the magnetized portion of the guitar string at the location of the pickup coil to be in the range of 325.0 T. Knowing that the frequency of oscillation for middle C is about 278.5 Hz, and estimating that the magnetic field will oscillate as a sinusoidal function near the pickup coil, what is the maximum induced voltage in the pickup coil based on these numbers? Express your answer in milliVolts. Treat the pickup coil as a coil, not a solenoid.

Explanation / Answer

N = 140 , r =3.5 mm, f = 2785 Hz,B =325 T

from faradays law induced emf V = NABw

V = 140*3.14*3.5*3.5*10^-6*325*2*3.14*278.5

V = 3.06*10^-6 mV

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