Question

The maximum strength of the earth's magnetic field is about 6.9 10-5 T near the south magnetic pole. In principle, this field could be used with a rotating coil to generate 60.0-Hz ac electricity. What is the minimum number of turns (area per turn

Answer 1

Answer:

Number of turns, $N=5\times 10^5$

Explanation:

Given that,

The maximum strength of the Earth's magnetic field, $B=6.9\times 10^{-5}\ T$

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.

$\epsilon=\sqrt{2} V_{rms}\\\\\epsilon=\sqrt 2\times 120\\\\\epsilon=169.7\ V$

The emf induced in the coil is given by :

$\epsilon=NAB\omega\\\\\epsilon=2\pi NABf$

N is the number of turns

f is the frequency

$N=\dfrac{\epsilon}{2\pi ABf}\\\\N=\dfrac{169.7}{2\pi 0.022\times 6.9\times 10^{-5}\times 60}\\\\N=2.96\times 10^5$

or

$N=5\times 10^5$

So, there are $5\times 10^5$ turns in the coil.