Calculating EMF in a Current Loop: 1000 Revolutions/Min with B = 0.45 T"

[zerobladex]

Hi all,

I have a certain problem I'm getting stuck on hopefully someone here can help

Homework Statement

A rectangular coil is 75 mm wide in the y-axis, 100mm long in the x-axis. What is the speed of the rotation if an rms voltage of 0,25 V is developed in the uniform field of B = 0.45 T in the Z direction.

The correct answer is supposed to be 1000 revolutions/min.

Homework Equations

emf = d[flux]/dt

*Sorry a little unsure of how to use the symbols and such

The Attempt at a Solution

:

I honestly am not sure where to start. Normally i would try to find the expression for magnetic flux, plug in the numbers and solve for the frequency, but it doesn't work so in this case.

 

[SammyS]

V_peak = (√2)·V_rms

The Peak Voltage is seen when dΦ/dt is maximum.

Does it matter whether the axis of rotation of the coil is along the x-axis or along the y-axis? No.

Suppose the loop is centered at the origin and the angle between the z-axis and the normal to the plane that the loop lies in is θ. Then the magnetic flux is Φ_B=B·A·cos(θ).

dΦ/dt = ‒B·A·sin(θ)·(dθ/dt) .