Question

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?

Answer 1

@ybarrap Would you be able to help me with this one too? X)

Answer 2

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! :/

Answer 3

@IrishBoy123

Answer 4

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

Answer 5

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

Answer 6

so the requested max value of the induced voltage is:
\[\Large {E_{MAX}} = \frac{{\Delta \Phi }}{{T/4}} = \frac{{2\Delta \Phi }}{{\pi \omega }} = \frac{2}{{\pi \omega }}\frac{{4\pi }}{c}\frac{{NI}}{l}S = ...?\]

Answer 7

oops.. I have made a typo:
we have this:
\[\huge \frac{T}{4} = \frac{{2\pi }}{{4\omega }} = \frac{\pi }{{2\omega }}\]
so:
\[\Large {E_{MAX}} = \frac{{\Delta \Phi }}{{T/4}} = \frac{{2\omega \Delta \Phi }}{\pi } = \frac{{2\omega }}{\pi }\frac{{4\pi }}{c}\frac{{NI}}{l}S = ...?\]

Answer 8

of course, that value, of the induced voltage refers to one revolution only

Answer 9

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?

Answer 10

more precisely, going from \(MKS\) to \(CGS\) we have
\[{\mu _0} \to \frac{{4\pi }}{c}\]
@CShrix

Answer 11

@Michele_Laino ah okay, thanks!