Question

A circular coil of radius 10 cm and a separate square coil of side 20 cm are both rotated in a magnetic field of 1.5 T. If the circular coil is rotated at a frequency of 60 Hz, then at what frequency must the square coil be rotated in order for both coils to have the same maximum induced voltage? A) 47 Hz
B) 60 Hz
C) 76 Hz
D) 19 Hz

Answer 1

Answer:

The frequency of square coil is 47 Hz.

(A) is correct option.

Explanation:

Given that,

Radius =10 cm

Side = 20 cm

Magnetic field = 1.5 T

Frequency = 60 Hz

We need to calculate the the maximum induced voltage

$V_{m}=BAN\omega$

Where, B = magnetic field

A = area of cross section

N = number of turns

$\omega=2\pi f$= angular frequency

Put the value into the formula

$V_{m}=1.5\times3.14\times(10\times10^{-2})^2\times1\times2\times3.14\times60$

$V_{m}=17.75\ V$

If the square coil have the same induced voltage.

Area of square of coil $A =(20\times10^{-2})^2$

$A=0.04\ m^2$

Now, The angular velocity of square coil

$\omega=\dfrac{V_{m}}{AB}$

$\omega=\dfrac{17.75}{0.04\times1.5}$

$\omega=295.8\ \dfrac{rad}{s}$

Now, frequency of rotation

$f = \dfrac{\omega}{2\pi}$

Put the value into the formula of frequency

$f=\dfrac{295.8}{2\times3.14}$

$f=47\ Hz$

Hence, The frequency of square coil is 47 Hz.