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In regards to a graph of the changing magnetic flux in a generator such as this one:

a) The equation of the graph should be $\Phi = BA \cos \theta$. As $\theta=\omega t$ (angular velocity*time), doesn't that mean the x axis should be wt, and not just time? (because a normal $\cos$ graph is $\cos(x)$, and this is $\cos(wt)$. Or am I misunderstanding cos wave equations?

b) How can the angular velocity/frequency of rotation be determined from this graph? Can $\omega = 2 \pi f$ be used? ($f=1/T$)

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This is just a homework question with no other context. Perhaps you could ask something about the general principles of the problem or SOMETHING. Voting to close. – Jerry Schirmer Sep 7 '11 at 8:37
I'm not sure what you mean, my question is entirely about the principles of the problem. I can't figure out how to interpret the graph given - my problem is entirely concept-based. I have the answers, I just have no idea how to approach the graph interpretation. – Parachuting Panda Sep 7 '11 at 9:05
@Jerry - I've edited the question to include just the conceptual part, I figured out the rest. – Parachuting Panda Sep 7 '11 at 10:11
I've converted you math to LaTeX notation. The site has the MathJax engine running to support these kinds of expressions. That said, I'm afraid the concepts you're focusing on are more mathematical concepts than physics one (that is, you're having trouble understanding why the graph is drawn a particular way and how to extract useful number from it, rather than having trouble understanding the magnetic fields). Question for the student. What does the graph of $\cos 2x$ look like? Do you rescale the axis when drawing that graph? – dmckee Sep 7 '11 at 14:43

1 Answer 1

The argument in $cos(x)$ must be dimensionless and as such you have used $\omega t$. However when graphing the function we are graphing the relationsip between two variables, $\Phi$ and $t$. The factor of $\omega$ is a constant (in the simple case) and so its effect is to give some scale to your $x$-axis.

You could try plotting $\Phi$ vs $t$ for several different $\omega$ and seeing what effect this has...

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