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

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SUMMARY

The discussion focuses on calculating the electromotive force (EMF) generated in a rectangular coil rotating in a magnetic field. The coil dimensions are 75 mm wide and 100 mm long, and it operates in a uniform magnetic field of 0.45 T, resulting in an RMS voltage of 0.25 V. The correct rotational speed for this setup is established as 1000 revolutions per minute (RPM). Key equations include EMF = d[flux]/dt and the relationship between peak and RMS voltage, Vpeak = (√2)·Vrms.

PREREQUISITES
  • Understanding of electromagnetic induction principles
  • Familiarity with the concept of magnetic flux
  • Knowledge of voltage relationships in AC circuits
  • Basic proficiency in calculus for differentiation
NEXT STEPS
  • Study the derivation of EMF in rotating coils
  • Learn about the relationship between magnetic flux and coil orientation
  • Explore the calculation of peak voltage from RMS voltage in AC circuits
  • Investigate the effects of coil dimensions on induced EMF
USEFUL FOR

This discussion is beneficial for physics students, electrical engineers, and anyone interested in understanding the principles of electromagnetic induction and coil dynamics in magnetic fields.

zerobladex
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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.
 
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Vpeak = (√2)·Vrms

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 ΦB=B·A·cos(θ).

dΦ/dt = ‒B·A·sin(θ)·(dθ/dt) .
 

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