A rotating coil measuring the magnetic field

[lfused]

Homework Statement

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 I_max 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

Homework Equations

E = -d(phi)/dt where phi = magnetic flux
E= IR
phi = BA where B is the magnetic field
E= -N *d(phi)/dt

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.

 

[Irid]

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.