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Homework Help: A rotating coil measuring the magnetic field

  1. Aug 1, 2008 #1
    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.
  2. jcsd
  3. Aug 2, 2008 #2
    The magnetic flux across the coil is

    [tex]\Phi = NBA\cos \phi = NBA \cos \omega t\, .[/tex]

    that is, varies sinusoidally. Taking the derivative, we find the induced EMF:

    [tex]E = -\frac{d\Phi}{dt} = NBA\omega \sin \omega t\, .[/tex]

    Ohm's law gives

    [tex]I = \frac{E}{R} = \frac{NBA\omega}{R} \sin \omega t\, .[/tex]

    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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