Question

Interactive Solution 22.43 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 54.1-Hz ac electricity. What is the minimum number of turns (area per turn = 0.024 m2) that the coil must have to produce an rms voltage of 170 V?

Answer 1

Answer:

427097

Explanation:

V = Voltage = 170 V

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

f = Frequency = 54.1 Hz

A = Area = $0.024\ m^2$

Number of turns is given by

$N=\dfrac{V\sqrt{2}}{BA2\pi f}\\\Rightarrow N=\dfrac{170\sqrt{2}}{6.9\times 10^{-5}\times 0.024\times 2\pi\times 54.1}\\\Rightarrow N=427096.933536\approx 427097\ turns$

Number of turns is 427097