# Computing the emf induced in a coil

## 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.

## Answers and Replies

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rude man
Homework Helper
Gold Member
They didn't give you the area or diameter of the coil?

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.

rude man
Homework Helper
Gold Member
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.

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?

rude man
Homework Helper
Gold Member
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?