Question

provides one model for solving this problem. The maximum strength of the earth's magnetic field is about 6.9 x 10-5 T near the south magnetic pole. Suppose we want to utilize this field with a rotating coil to generate 84.5-Hz ac electricity What is the minimum number of turns (area per turn = 0.021 m2) that the coil must have to produce an rms voltage of 170 V?

Answer 1

Answer:

The minimum no. of turns is $3.126 \times 10^{5}$

Explanation:

Given:

Magnetic field $B = 6.9 \times 10^{-5}$ T

Frequency $f = 84.5$ Hz

Area of turn $A = 0.021$ $m^{2}$

Voltage $V_{rms} = 170$ V

From the formula of induced emf,

$V = NBA \omega$

Where $\omega = 2\pi f$ and $V = \sqrt{2} V_{rms}$

So number of turn is,

$N = \frac{\sqrt{2} V_{rms} }{AB2\pi f }$

$N = \frac{\sqrt{2} \times 170 }{0.021 \times 6.9 \times 10^{-5} \times 6.28 \times 84.5 }$

$N = 3.126 \times 10^{5}$

Therefore, the minimum no. of turns is $3.126 \times 10^{5}$