anonymous
  • anonymous
The coil in a generator has 100 windings and cross-sectional area of 0.0100m^2 a). If the coil turns at a constant rotational speed and the magnetic field between the generator is that of Earth's field, how many 360deg rotations must the coil complete each second to generate a maxiumum induced emf of 1.00V? b). Based on this, does it seem practical to use Earth's magnetic field in electric generators?
Physics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
@ybarrap Would you be able to help me with this one too? X)
anonymous
  • anonymous
I know that the emf is \[\mathcal E=- N\frac{ d \Phi }{ dt }\]But I'm confused about implementing this such in a way where we can calculate while it rotates! :/
anonymous
  • anonymous
@IrishBoy123

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Michele_Laino
  • Michele_Laino
the absolute value of the magnetic flux concatenated with the coil, varies from the min value which is \(0\) to the max value, which is: \[\huge \Phi \left( {\mathbf{B}} \right) = \frac{{4\pi }}{c}\frac{{NI}}{l}S,\quad \left( {CGS\;units} \right)\] where \( \Large S\) is the cross sectional area of the coil
Michele_Laino
  • Michele_Laino
that variation occurs, inside a time interval \((0, T/4\)\) wehre, \(T\) is the period of raotation of the coil, namely: \[\huge \frac{T}{4} = \frac{{2\pi \omega }}{4} = \frac{{\pi \omega }}{2}\] and \( \Large \omega\) is the angular speed
Michele_Laino
  • Michele_Laino
so the requested max value of the induced voltage is: \[\Large {E_{MAX}} = \frac{{\Delta \Phi }}{{T/4}} = \frac{{2\Delta \Phi }}{{\pi \omega }} = \frac{2}{{\pi \omega }}\frac{{4\pi }}{c}\frac{{NI}}{l}S = ...?\]
Michele_Laino
  • Michele_Laino
oops.. I have made a typo: we have this: \[\huge \frac{T}{4} = \frac{{2\pi }}{{4\omega }} = \frac{\pi }{{2\omega }}\] so: \[\Large {E_{MAX}} = \frac{{\Delta \Phi }}{{T/4}} = \frac{{2\omega \Delta \Phi }}{\pi } = \frac{{2\omega }}{\pi }\frac{{4\pi }}{c}\frac{{NI}}{l}S = ...?\]
Michele_Laino
  • Michele_Laino
of course, that value, of the induced voltage refers to one revolution only
anonymous
  • anonymous
Ah okay, I think that makes sense to me.. and in CGS \(\huge \mu_0=4\pi \times 10^{-7}= \frac{4\pi}{c}\) right?
Michele_Laino
  • Michele_Laino
more precisely, going from \(MKS\) to \(CGS\) we have \[{\mu _0} \to \frac{{4\pi }}{c}\] @CShrix
anonymous
  • anonymous
@Michele_Laino ah okay, thanks!

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