Computing the emf induced in a coil

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SUMMARY

The discussion focuses on calculating the electromotive force (emf) induced in a coil with 100 turns, rotating at 25 revolutions per second, in a uniform magnetic field with a flux of 0.002 weber. The relevant equation for this calculation is e = -N(dφ/dt), where e is the emf, N is the number of turns, and φ is the magnetic flux. The provided solution indicates that the answer is 20 Volts, but participants express confusion regarding the role of the rotational speed and the area of the coil in the calculation.

PREREQUISITES
  • Understanding of electromagnetic induction principles
  • Familiarity with the equation e = -N(dφ/dt)
  • Knowledge of magnetic flux and its relationship to area
  • Basic concepts of rotational motion in physics
NEXT STEPS
  • Study the relationship between magnetic flux and coil area in electromagnetic systems
  • Learn about the implications of rotational speed on induced emf
  • Explore the concept of flux linkage in electromagnetic induction
  • Investigate the characteristics of radial magnetic fields and their applications
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Electrical engineering students, physics learners, and professionals involved in electromagnetic systems and applications will benefit from this discussion.

NoPhysicsGenius
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Homework Statement



The following is Problem 1-13 on page 23 from Electrical Engineering Fundamentals, 2nd ed., by Vincent del Toro:

"In the configuration shown in Fig. P1-13 the coil has 100 turns and is attached to the rotating member which revolves at 25 \frac{rev}{s}. The magnetic flux is a radial uniform field and has a value of \phi = 0.002 weber (Wb). Compute the emf induced in the coil."

Here is Fig. P1-13 ...

http://www.flickr.com/photos/jjhobson/8005932239/in/photostream

Homework Equations



e = - \frac{d\lambda}{dt} = -N\frac{d\phi}{dt}

Note that e stands for emf (or electromotive force), \lambda stands for the flux linkage in weber-turns, N stands for the number of turns in the coil, and \phi stands for the magnetic flux.

The Attempt at a Solution



First of all, the answer given in the back of the book is 20 Volts.

e = -N\frac{d\phi}{dt} = -(100)\frac{d\phi}{dt}
\Rightarrow \frac{d\phi}{dt} = -\frac{e}{100}
\Rightarrow d\phi = -\frac{e}{100}dt
\Rightarrow \phi = -\frac{1}{100}\int e dt = 0.002 Wb
\Rightarrow \int e dt = -0.2 Wb

Unfortunately, I don't know where to go from here. Also, I don't know where the 25 rev/s quantity comes into play.

Any help would be greatly appreciated. Thank you.
 
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They didn't give you the area or diameter of the coil?
 
rude man said:
They didn't give you the area or diameter of the coil?

No, they did not. I double-checked to see whether I left anything out in my statement of the problem; but what I have is all that the book gave me. Do you think that the problem doesn't give complete information in order to solve it?

And, thank you for responding.
 
Yes, unless I'm really missing the boat here, you need to know the area, because
flux = B times area and emf = -N{d(flux)/dt} so seems like you need area of coil.

EDIT: oops, i goofed. They're already giving you the flux.

So go ahead with the rest ... realize that the effective flux is a function of the angle of the rotating part though.

BTW I do wonder why they call it a radial field. Its direction is not radial with the rotating member. It's a constant-direction B field across the pole pieces of the magnet.
 
rude man said:
Yes, unless I'm really missing the boat here, you need to know the area, because
flux = B times area and emf = -N{d(flux)/dt} so seems like you need area of coil.

EDIT: oops, i goofed. They're already giving you the flux.

So go ahead with the rest ... realize that the effective flux is a function of the angle of the rotating part though.

BTW I do wonder why they call it a radial field. Its direction is not radial with the rotating member. It's a constant-direction B field across the pole pieces of the magnet.

Um ... I haven't the slightest clue how to set up this problem. Any hints?
 
NoPhysicsGenius said:
Um ... I haven't the slightest clue how to set up this problem. Any hints?

Well, they're giving you the flux when the coil is aligned so its normal is in the direction of the B field. What happens to the flux thru the coil as it turns?
 

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