Question

A 400-turn circular coil (radius = 1.0 cm) is oriented with its plane perpendicular to a uniform magnetic field which has a magnitude that varies sinusoidally with a frequency of 90 Hz. If the maximum value of the induced emf in the coil is observed to be 4.2 V, what is the maximum value of the magnitude of the varying magne?

Answer 1

Answer:

The Magnetic field is 59.13 mT.

Explanation:

Given that,

Number of turns = 400

Radius = 1.0 cm

Frequency = 90 Hz

Emf = 4.2 V

We need to calculate the angular velocity

Using formula of angular velocity

$\omega=2\pi f$

$\omega=2\times3.14\times90$

$\omega=565.2\ rad/s$

We need to calculate the magnetic flux

Relation between magnetic flux and induced emf

$\epsilon=NA\omega B$

$B=\dfrac{\epsilon}{NA\omega}$

Put the value into the formula

$B=\dfrac{4.2}{400\times\pi\times(1.0\times10^{-2})^2\times 565.2}$

$B=0.05913\ T$

$B=59.13\ mT$

Hence, The Magnetic field is 59.13 mT.