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Celso
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Homework Statement
What is the necessary area for a generator that produces an emf of ##\mathcal{E} = 150V## when it spins at a ratio of 60 revolutions per second, in a magnetic field of ##B = 0.5 T##?
Homework Equations
##\oint_{c} E \cdot dl = \mathcal{E} = -\frac{d}{dt}\iint_{s} B \cdot dS ##
The Attempt at a Solution
First I tried solving for the magnetic flux ##\iint_{s}B \cdot dS=\int_{\theta{1}}^{\theta{2}}BAcos(\theta)d\theta##
##B## and ##A## are constant, so ##\iint_{s} B \cdot dS = BA \int_{\theta{1}}^{\theta{2}} cos(\theta)d\theta##
Now here is where I'm in doubt, please correct me if you spot a mistake, it spins 60 times a sec and since these engines switch the field or the current so the emf won't change to the other direction every half revolutions, one must consider the flux being always positive:
##60BA \int_{0}^{\frac{\pi}{2}}2cos(\theta)d\theta##
(##2cos(\theta)## represents a full revolution, considering only the positive domain of the function).
Which leads to ##\frac{d}{dt}120BA = \mathcal{E}##
I'm stuck here
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