Physics, 18.01.2020 03:31 Longjeremiahs5797

Learning goal: to practice problem-solving strategy 32.1 electromagnetic waves. an electromagnetic wave in a vacuum traveling in the +x direction generated by a variable source initially has a wavelength λ of 305 μm and a maximum electric field emax in the +y direction of 8.60×10−3 v/m . if the period of the wave is then increased by a factor of 1.70, what is the equation of the resulting magnetic field component of the wave?

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Answer from: edsimms21111

B(z,t) = 2,867 10⁻¹¹ cos (2.06 10⁴ x - 3,635 10¹² t)

Explanation:

The wave equation for an electromagnetic wave is

E = E₀ cos (kx –wt)

B = B₀ cos (kx - wt)

Where these equations are for the electric and magnetic fields, respectively.

The two fields are related through the speed of light

c = E₀ / B₀

Let's apply to our case, the wavelength is 305 μm = 305 10⁻⁶ m, The wave number is

k = 2π / λ

k = 2π / 305 10⁻⁶

k = 2.06 10⁴ m

Period change to by a factor of 1.7, we write based on the initial period (T₀), the angular velocity is

w = 2π f

With the initial data and the relationship

c = λ f

f = c / λ

f = 3 10⁸/305 10⁻⁶6

.f = 9.836 10¹¹ Hz

The frequency and period are related

f = 1 / T

T = 1.7 T₀

f = 1 / 1.7 1 / T₀

f = 1 /1.7 9.836 10¹¹

f = 5,786 10¹¹ Hz

w = 2π f

w = 2π 5,786 10¹¹

w = 3,635 10¹² rad / s

We look for the maximum amplitude of the magnetic field

B₀ = E₀ / c

B₀ = 8.60 10⁻³ / 3 10⁸

B₀ = 2,867 10⁻¹¹ T

the fields and the velocity wave vector are perpendicular to each other, therefore the magnetic field oscillates in the z-direction

We build the equation of the magnetic field

B(z,t) = 2,867 10⁻¹¹ cos (2.06 10⁴ x - 3,635 10¹² t)

Answer from: Quest

answer: the correct answer id option(d).

explanation:

snell's law refraction:

$\frac{n_2}{n_1}=\frac{sin \theta_1}{sin\theta_2}$

the angle of refraction = $\theta_2=38 ^o$

the angle of incidence = $\theta_1=?$

refractive index of air = $n_1$ = 1

refractive index of glycerol $n_2$ = 1.47

$\frac{1.47}{1}=\frac{sin\theta_1}{sin 38^o}, (sin38^o=0.61)$

$sin\theta_2=0.8967$

$\theta_2=24.2^o, (sin^{-1}0.8967=63.72^o)$

from the given options, the most closest answer to 63.72° is 65° of option (d).

Answer from: Quest

fgravity=10x10=100n case 1

fgravity=30x20=600n case 2

6 times more

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Learning goal: to practice problem-solving strategy 32.1 electromagnetic waves. an electromagnetic...

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