# A rotating coil measuring the magnetic field

by lfused
Tags: coil, field, magnetic, measuring, rotating
 P: 7 1. The problem statement, all variables and given/known data A rotating coil is a common device for measuring magnetic fields. Consider a coil of area A and N turns that is rotated at angular frequency w in a magnetic field. The position of the coil is adjusted so as to produce a maximum induced current Imax which can be measured by using an appropriate ammeter. R is the total resistance of the coil circuit find the relationship between the unknown magnetic field and Imax 2. Relevant equations E = -d(phi)/dt where phi = magnetic flux E= IR phi = BA where B is the magnetic field E= -N *d(phi)/dt 3. The attempt at a solution I'm not really sure what to do with this problem at all because we didn't really go over how angular frequency related to magnetic flux in class. Since w= (2*pi*r)/T meaning w is related to the change in time I tried using the equation IR= -(BAN)/w but I'm not sure if that's right.. and I wouldn't know how to determine the Imax from that. I know taking a derivative can help determine max and min by setting the equation equal to zero... but I really have no clue what I'm doing.
 P: 208 The magnetic flux across the coil is $$\Phi = NBA\cos \phi = NBA \cos \omega t\, .$$ that is, varies sinusoidally. Taking the derivative, we find the induced EMF: $$E = -\frac{d\Phi}{dt} = NBA\omega \sin \omega t\, .$$ Ohm's law gives $$I = \frac{E}{R} = \frac{NBA\omega}{R} \sin \omega t\, .$$ The maximum value of current can now be clearly seen. So, you've almost guessed your equation right. Next time you could try using dimensional analysis to see if it's a legal expression or not.

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