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3 years ago

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A 400-turn circular coil (radius = 1.0 cm) is oriented with its plane perpendicular to a uniform magnetic field which has a magn

itude 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 ?

1 answer:

kenny6666 [7]3 years ago

7 0

Answer:

<u>4.19 V</u>

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 <u>4.19 V</u>

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