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

The minimum no. of turns is
`3.126 * 10^(5)`

Step-by-step explanation:

Given:

Magnetic field
`B = 6.9 * 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 = √(2) V_(rms)`

So number of turn is,

`N = (√(2) V_(rms) )/(AB2\pi f )`

`N = (√(2) * 170 )/(0.021 * 6.9 * 10^(-5) * 6.28 * 84.5 )`

`N = 3.126 * 10^(5)`

Therefore, the minimum no. of turns is
`3.126 * 10^(5)`