What is the relationship between magnetic flux and EMF?

[al_201314]

Hi everyone,

Apologise for so many questions within a short period of time. I'm in the midst of my holidays and I can't clarify my doubts in school.

For a particular A.C generator, it has a large rotating rectanglar coil rotating at 50 rev per second in a B field strength of 0.29T. It has 38 turns each 2m long and 1.2m wide.

How do I find the flux cut by one turn of the coil after the coil has rotated 1 degrees from the position parallel to the B field lines of force, which position generates the largest EMF?

I found that the time required for it rotate 1 degrees is 5.56 X 10^-5 s. I know the flux linkage is BAcosx. How do I find the area that is being cut? I couldn't find the surface area of the coil without the radius?

Thanks a lot people.

 

[Hootenanny]

All the answers you need are in the question

For a particular A.C generator, it has a large rotating rectanglar coil rotating at 50 rev per second in a B field strength of 0.29T. It has 38 turns each 2m long and 1.2m wide.

How do I find the flux cut by one turn of the coil after the coil has rotated 1 degrees from the position parallel to the B field lines of force

Firstly I need to correct the function you said that flux linkage is given by $BA\cos\theta$, this is the formula for magentic flux. Flux linkage is given by; $n\Phi$, where $\Phi$ is the magnetic flux and n is the number of turns on your coil. As for your last question;

which position generates the largest EMF?

Look at the formula for emf;

$$emf = - n\frac{d\Phi}{dt} = - n\frac{d(BA\cos\theta)}{dt}$$

HINT: When is $\cos\theta$ at its maximum.

Can you go from here?

 

[arunbg]

Just to correct a little typo in Hootenanny's post and to further what he has said ,
$$emf=- n\frac{d(BA\cos\theta)}{dt}=- nBA\frac{d(cos(\omega t))}{dt}$$

Can you go from here ? :D

 

[Hootenanny]

Thanks arun, I had a constant flux inducing an emf

 

[al_201314]

Thanks guys, but I can't see the picture on what cos1 gives me. Or in other words, how does the magnetic flux lines cut the coil? Does it coil all parts of the coil or just the length of it? How do I find the area that is being cut? This area I have in mind is that the area of the coil being cut (ie, the wires' area) or does the area refer to the area of the coil in the sense length X breadth?

Thanks man!

 

[al_201314]

I maanged to figure out the answers for the entire question already. Thanks a lot for the help.

But I have one more conceptual question. Why is magnetic flux linkage of the coil is the product of the component of the magnetic field lines normal on the surface area of the coil? How does magnetic flux through the space of the coil create EMF?

Thanks!

 

[arunbg]

How does magnetic flux through the space of the coil create EMF?

This is not right. Only a change in magnetic flux through the area enclosed by the coil induces an emf .
Emf is induced as a consequence of the law of conservation of energy .