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EMF generated by a rotating coil

Here's the question:

A plane coil of wire, which has 20 turns and an area of 0.04 square m, is placed with its plane at right angles to a uniform magnetic field of flux density 0.3 T.

a) Find an expression for the total flux linkage when the coil is at an angle

\theta

to the original position.

Flux linkage =

BAN cos \theta

0.04 m^2 \times 0.3 T \times 20 \times cos\theta

0.24 cos \theta Wb

This bit is right (according to the book).

b) Deduce the maximum EMF induced if the coil is rotated steadily at 10 revolutions per second.

\epsilon = -N \frac{d \phi}{dt}

= -20 \times -0.24 sin\theta \times \frac{d \theta}{dt}

= 4.8 \omega sin \theta

=4.8 \times 20\pi sin\theta

So the maximum value would be

4.8 \times 20\pi = 301 V

, which is the wrong answer. What I did notice is that if you divide this by the number of turns you get the right answer (15V). But I can't see where I have gone wrong.

Reply 1

nota bene

I may be talking crap, but Faradays law states

-\frac{d\phi}{d\theta}=\epsilon

and measures the rate of change of magnetic flux. I don't see why we'd need the N to be there when concerning induced e.m.f.

So I think you are double counting your turns...

Then again I've finished physics some weeks ago, so it is all a bit of a blurr :redface:

edit: I.e.

\epsilon=-\frac{d \phi}{dt}\newline \epsilon=\omega NBA\sin(\omega t)

Reply 2

Eddie K

You have counted the turns on your coil twice; once in the calculation of the total flux and then again in the application of Faraday's Law. You only need to count them once. This is your only mistake.

Reply 3

physicsgirlie

Where have I counted them twice though? The definition of flux linkage is BAN for a coil, and you need the N in the EMF equation. I know I've included an extra N but I don't know which one shouldn't be there.

Reply 4

nota bene

There shouldn't be an N in b)

You are differentiating NBAcos(wt) to get wNBAsin(wt) (ignoing signs...), so the NBA does not change, and this constant you have from a).

Reply 5

Morbo

physicsgirlie

you need the N in the EMF equation.

No. The equation is:

\epsilon = -\frac{d\phi}{dt}

where

\phi

is defined as the total flux linkage, an expression for which you have found in the first part.

\\\phi = BAN\cos(\omega t)[br]\\\epsilon = -BAN\frac{d}{dt}(\cos\omega t)[br]\\\epsilon = BAN\omega \sin\omega t

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