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 varying magnetic field induced is observed to be 59 mT, what is the maximum value emf in the coil ?

Answer 1

Answer:

4.19 V

Explanation:

Magnetic field flux and induced emf formula is:

$\epsilon_{max}=NA\omega B_{max}$

Where

$\epsilon_{max}$ is the max emf (what we want)

N is the number of turns (N = 400)

A is the Area which is  ($\pi r^2$)

$\omega$ is the angular velocity ( $\omega = 2\pi f$, f is frequency, f = 90)

$B_{max}$ is the max magnetic field value (given as 59 mT)

Finding A, Area:

$A=\pi r ^2\\A= \pi (1)^2\\A=3.14$

In meters squared, it would be:

A = 3.14 * 10^-4 meter squared

Calculating angular velocity:

$\omega = 2 \pi f\\\omega = 2 \pi (90)\\\omega = 565.49 rad/s$

Now, finding max EMF:

$\epsilon_{max}=NA\omega B_{max}\\\epsilon_{max}=(400)(3.14*10^{-4})(565.49)(59*10^{-3})\\\epsilon_{max}=4.19$

So, the max value emf in the coil is around 4.19 V