What is the maximum induced emf in a rotating coil generator?

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SUMMARY

The maximum induced electromotive force (emf) in a rotating coil generator can be calculated using the formula Emf = NBA/time, where N is the number of turns, B is the magnetic field strength, and A is the area of the coil. In this discussion, the magnetic field strength is 0.40 T, the coil has 120 turns, and the radius is 4.0 cm, leading to an area A calculated as π(0.04 m)². The frequency of rotation is 5 Hz, resulting in a time period of 0.20 seconds. The correct calculation yields a maximum emf of 1.21 V, but the discussion highlights the need to consider the total flux change over one complete revolution.

PREREQUISITES
  • Understanding of electromagnetic induction principles
  • Familiarity with the formula for induced emf (Emf = NBA/time)
  • Knowledge of circular coil geometry and area calculation (A = πr²)
  • Basic grasp of frequency and its relationship to time period (t = 1/Frequency)
NEXT STEPS
  • Study the concept of magnetic flux and its changes in rotating systems
  • Learn about the time derivative of magnetic flux and its relation to induced emf
  • Explore the effects of coil orientation on induced emf in generators
  • Investigate the differences in induced emf calculations for rectangular versus circular coils
USEFUL FOR

Students in physics, electrical engineering majors, and anyone interested in understanding the principles of electromagnetic induction in generators.

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Homework Statement


In a rotating coil generator, the magnetic field between the poles of an electromagnet has the magnitude .40T. A circular coil between the poles has 120 turns and radius 4.0 cm. The coil rotates with frequency 5Hz. Find the maximum emf induced in the coil.


Homework Equations


Emf= change in magnetic flux/time



The Attempt at a Solution


Emf=change in magnetic flux/time=NBAcosθ/time. need emf max, so theta=1??
Emf max=NBA/time
Frequency = 1/t
so t =1/Frequency=1/5=.20

N,B, and A are all given in the problem (A = pi r^2). I plugged the numbers into my equation and got 1.21 but that is wrong.

I have used this equation for rectangular loops, why isn't it working here and how do i do it?

thanks
 
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what do you mean by theta = 1?
 
you need to calculate total flux change/total time in one revolution.

can you tell me what should be the net change in flux in one complete revolution?
 
The change of flux is zero in one revolution. The magnitude of emf is equal to the time derivative of the flux.

ehild
 
Doesn't the flux through the area encompassed by the coil peak twice per revolution?
 

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