# Magnetic Flux and emf Question (1 Viewer)

#### StudyOnly

##### New Member
Hello Everyone, I can't seem to understand why the graph of Induced emf vs angle of rotation is sinusoidal. (you will need the link).

http://www.citycollegiate.com/generator1.gif

My thinking goes like this, if the coil is vertical (like in the first picture, θ=0) it means it is perpendicular to the B-field, meaning that magnetic flux is at a maximum. Now in the graph when the angle of rotation is 0o, why is the emf shown on the graph 0? Shouldn't it be if flux is maximum then emf should also be maximum, then in the second position of the coil (90o ) shouldn't the emf be minimum as flux is paralell to the field meaning flux is 0.

The equations would also follow, because flux is given by BAcosθ and if θ=90o then flux would also be 0.

Then emf is given by (n x change in flux)/ change in time
which means if flux is 0 then emf is 0.

Thanks for the help.

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#### Drdusk

##### sin(x) = tan(x) = x
This is quite hard to explain haha but I'll try my best

Firstly I'm pretty sure that is a graph of EMF vs time, but they are just showing the angles on the graph, i.e. the axis are still EMF and Time.

If you were to sketch a graph of magnetic flux vs time it would be a cosine curve, as you mentioned in the first image magnetic flux is max and then at 90 degrees it is min(this process continues).

Now EMF is the negative time derivative of the magnetic flux. So if the magnetic flux vs time is a cosine curve, then EMF vs time should be a sine curve which is what you see.

I had the same kind of questions that caused problems for my schools Physics department because HSC Physics is soo brief when teaching such concepts because well no CALCULUS allowed.

• BLIT2014

#### Drdusk

##### sin(x) = tan(x) = x
Also I think your a bit confused with the mathematics of it.

If the CHANGE in flux is zero then EMF is zero not when the Flux itself is zero.

May I ask if you do advanced mathematics or higher? because I think your confused with what is meant by flux and change in flux and this will help me tailor my response Last edited:

#### StudyOnly

##### New Member
Thanks for the reply! I probably need to understand more calculus to understand the concept fully. Yes I do 3U Maths.

#### StudyOnly

##### New Member
I get what you mean, I knew that's where my problem was but wasn't completely sure. I think I understand the concept now. Basically as the coil spins, there is a change in flux (a cosine graph) and this is maximum when the coil is vertical in the field. Then as the coil continues the cosine wave continues (this is the flux changing). On the sine wave it is 0 at the start as there is no change in flux. The emf sine wave then gets going as the cosine flux wave keeps going until a max is reached at 90 degrees. The emf is basically given by this change in flux (shown by the cosine wave), producing this sine wave graph. Thanks heaps!

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#### Drdusk

##### sin(x) = tan(x) = x
Yes there you go!

One thing I hate though is that HSC Physics never bothers to tell you fundamentally WHY there is no change in flux.

Like if you think about it we take the coil to always spin at the same rate, then why is it that as it moves perpendicular the flux changes but parallel it doesn't change?

I always asked these kinds of questions but never got the answers and if you search it up you end up with some like 2 - 3rd year Uni Physics answers hahah. Its sad how all they want you to do is memorize without having a fundamental understanding of WHY.

#### StudyOnly

##### New Member
Now that was the exact question I was googling right now lol, can't find an easy to understand answer!

#### Cujo10

##### Member
• BLIT2014

#### Drdusk

##### sin(x) = tan(x) = x
That description is a bit dodgy IMO but suitable

It says for the first position that the sides are parallel and hence to EMF. However there are sides which are also perpendicular to the magnetic field. They will have an EMF induced. It means to say no Torque, so kinda dodgy

EDIT: Wait nvm I think its just talking about the side AB, in that case yes its correct

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