Question

A rectangular coil with sides 0.150 m by 0.250 m has 487 turns of wire. It is rotated about its long axis in a magnetic field of 0.570 T. At what frequency, in complete cycles per second, must the coil be rotated for it to generate a maximum voltage of 115 V?

Answer 1

Frequency is 1.758 Hz

Solution:

As per the question:

No.of turns, n = 487 turns

Magnetic field, B = 0.570 T

Area of the field, A =
`0.150* 0.250 = 0.0375\ m^(2)`

Maximum Voltage,
`V_(m) = 115\ V`

Now,

To calculate the frequency:

Angular frequency,
`\omega = 2\pi f= 120\pi`

Maximum emf,
`V_(max) = \omega NAB`

Maximum emf,
`115 = 2\pi f* 487* 0.0375* 0.570`

`f = {115}{2\pi f* 487* 0.0375* 0.570} = 1.758\ Hz`