Answer:
Number of turns, [tex]N=5\times 10^5[/tex]
Explanation:
Given that,
The maximum strength of the Earth's magnetic field, [tex]B=6.9\times 10^{-5}\ T[/tex]
This field could be used with a rotating coil to generate 60.0-Hz ac electricity.
Let us assume that the coil must have to produce an rms voltage of 120 V and area per turn is 0.022 meter square.
[tex]\epsilon=\sqrt{2} V_{rms}\\\\\epsilon=\sqrt 2\times 120\\\\\epsilon=169.7\ V[/tex]
The emf induced in the coil is given by :
[tex]\epsilon=NAB\omega\\\\\epsilon=2\pi NABf[/tex]
N is the number of turns
f is the frequency
[tex]N=\dfrac{\epsilon}{2\pi ABf}\\\\N=\dfrac{169.7}{2\pi 0.022\times 6.9\times 10^{-5}\times 60}\\\\N=2.96\times 10^5[/tex]
or
[tex]N=5\times 10^5[/tex]
So, there are [tex]5\times 10^5[/tex] turns in the coil.
