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Makovka662 [10]

3 years ago

14

A 200 turn coil is in a uniform magnetic field that is decreasing at the rate 0.20 T/s. The coil is perpendicular to the field a

nd its dimensions are 0.20 m by 0.40 m. What is the magnitude of the induced emf in the coil

1 answer:

sattari [20]3 years ago

8 0

Answer:

emf = 3.2V

Explanation:

In order to calculate the magnitude of the induced emf in the coil you use the following formula:

$emf=-N\frac{d\Phi_B}{dt}$ (1)

N: turns of the coil = 200

ФB: magnetic flux = A*B

A: area of the coil = (0.20m)(0.40m) = 0.08m²

B: magnitude of the magnetic field

You take into account that the area of the coil is constant, while magnetic field changes on time. Then, the equation (1) becomes:

$emf=-NA\frac{dB}{dt}$ (2)

dB/dt = rate of change of the magnetic field = -0.20T/s (it is decreasing)

You replace the values of all parameters in the equation (2):

$emf=-200(0.08m^2)(-0.20T/s)=3.2V$

The induced emf in the coil is 3.2V

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The speed of a wave is given by:

$v=f.\lambda$ (1)

Where $f$ is the frequency and $\lambda$ the wavelength.

In the case of light, its speed is:

$c=f.\lambda$ (2)

On the other hand, the described situation is known as Refraction, a phenomenon in which the light changes its direction when passing through a medium with a refractive index different from the other medium.

In this context, the Refractive index $n$ is a number that describes how fast light propagates through a medium or material, and is defined as the relation between the speed of light in vacuum ( $c=3(10)^{8}m/s$ ) and the speed of light $v$ in the second medium:

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In addition, as the light changes its direction, its wavelength changes as well:

$n=\frac{\lambda_{air}}{\lambda_{glass}}$ (4)

Knowing this, let's begin with the answers:

<h2>a) Frequency</h2>

From equation (2) we can find $f$ :

$f=\frac{c}{\lambda}$ (5)

Knowing that $1nm=(10)^{-9}m$ :

$f=\frac{3(10)^{8}m/s}{632.8(10)^{-9}m}$

$f=4.74(10)^{14}Hz}$ (6) >>>Frequency of the helium-neon laser light

<h2>b) Wavelength in glass</h2>

We already know the wavelength of the light in air $\lambda_{air}$ and the index of refraction of the glass.

So, we only have to find the wavelength in glass $\lambda_{glass}$ from equation (4):

$\lambda_{glass}=\frac{\lambda_{air}}{n}$

$\lambda_{glass}=\frac{632.8(10)^{-9}m}{1.48}$

$\lambda_{glass}=427(10)^{-9}m=427nm$ (7) >>>Wavelength of the helium-neon laser light in glass

<h2>c) Speed in glass</h2>

From equation (3) we can find the speed $v$ of this light in glass:

$v=\frac{c}{n}$

$v=\frac{3(10)^{8}m/s}{1.48}$

$v=2.027(10)^{8}m/s$ (8) >>>Speed of the helium-neon laser light in glass

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