Question

A rectangular coil with dimensions 0.14 m 0.14 m by 0.27 m 0.27 m has 550 550 turns of wire. It is rotated about its long axis in a magnetic field of 0.50 T . 0.50 T. At what frequency f f must the coil be rotated for it to generate a maximum potential of 130 V ?

Answer 1

The frequency of coil must be 1.99 Hz

Step-by-step explanation:

Given:

Magnetic field
`B = 0.50` T

Area of rectangular coil
`A = 0.14 * 0.27 = 0.0378`
`m^(2)`

Maximum potential
`\epsilon _(max) = 130` V

Number of turns
`N = 550`

For finding the frequency we use faraday's law

Maximum induced emf in rectangular coil is given by,

`\epsilon _(max) = NBA\omega`

Where
`\omega = 2\pi f`

`\epsilon _(max) = NBA(2\pi f )`

`f = (\epsilon _(max) )/(NBA2\pi )`

`f = (130)/(550 * 0.50 * 0.0378 * 6.28)`

`f = 1.99` Hz

Therefore, the frequency of coil must be 1.99 Hz