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

Answer:

The frequency of coil must be 1.99 Hz

Explanation:

Given:

Magnetic field $B = 0.50$ T

Area of rectangular coil $A = 0.14 \times 0.27 = 0.0378$ $m^{2}$

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 $\omega = 2\pi f$

   $\epsilon _{max} = NBA(2\pi f )$

    $f = \frac{\epsilon _{max} }{NBA2\pi }$

    $f = \frac{130}{550 \times 0.50 \times 0.0378 \times 6.28}$

    $f = 1.99$ Hz

Therefore, the frequency of coil must be 1.99 Hz