# The simplest form of a traveling electromagnetic wave is a plane wave. For a wave traveling in the x direction whose electric

###### Question:

1. In these formulas, it is useful to understand which variables are parameters that specify the nature of the wave. The variables E_0and B_0 are the of the electric and magnetic fields.

a. maximas

b. wavelenghts

c. amplitudes.

d. velocities

2. The variable omega is called the of the wave.

a. wavenumber

b. wavelength

c. velocity

d. frequency

3. What is the mathematical expression for the electric field at the point x=0, y=0, z at time t?

4. For a given wave, what are the physical variables to which the wave responds?

## Answers

please the answer below

Explanation:

A general electromagnetic plane wave, traveling in the x direction, can be expressed in the form:

[tex]\vec{E}=E_0e^{-i(k\cdot x-\omega t)}\hat{j}\\\\\vec{B}=B_0e^{-i(k\cdot x-\omega t)}\hat{k}\\\\[/tex] (1)

1.

a. amplitudes

from (1) we can observe that E_0 and B_0 are the amplitudes.

2. frequency

3.

By replacing (1) we obtain:

[tex]\vec{E}=E_0e^{-i(k(0)-\omega t)}\hat{j}=E_0[cos\omega t+sin\omega t]\hat{j}[/tex]

4.

the wave respond to the followinf physical variables: amplitude, frequency, time and position, as we can see in (1).

hope this helps!!

1) Eo and Bo. They are maximum amplitudes. Answer 1 and 2

2) .w is angular frequency. Answer 2

3) k is wave number. Answer 1

Explanation:

The electromagnetic wave is given by

[tex]E_{y}[/tex] = E₀ sin (kx –wt)

This is the equation of a traveling wave on the x axis with the elective field oscillating on the y axis

The terms represent E₀ the maximum amplitude of the electric field,

The wave vector

k = 2π /λ

Angular velocity

w = 2π f

To answer the questions let's use the previous definitions

1) Eo and Bo. They are maximum amplitudes. Answer 1 and 2

2) .w is angular frequency. Answer 2

3) k is wave number. Answer 1

amplitudes

Explanation:

In everyday physics we define the amplitude of a wave as the maximum (this can also be called the highest)displacement or distance moved by a point on a given vibrating body or wave as measured from its equilibrium position. The key idea in defining the amplitude of a wave motion is the idea of a 'maximum displacement from the position of equilibrium'.

Given the equations;

E= EoSin(kx - ωt)y

B= Bosin(kx- ωt)z

Both Eo and Bo refer to the maximum displacement of the electric and magnetic field components of the electromagnetic wave. This maximum displacement is known as the amplitude of the electric and magnetic components of the electromagnetic wave.

B) Amplitudes

Explanation:

The equations of the electric and magnetic fields given are sinusoidal functions. he sine function varies between the value of -1 and 1 when is multiplied by a number A then varies from -A to A. In this case the variation goes from -E0 to E for the electric field and from -B0 to B0 for the magnetic field. Because the amplitude is half of the distance between the highest and the lowest value of the sinusoidal function. In the electric field is: E0-(-E0)/2=E0 and in the magnetic field B0-(-B0)/2=B0.

In these formulas, it is useful to understand which variables are parameters that specify the nature of the wave. The variables E₀ and B₀ are the amplitudes of the electric and magnetic fields.

Explanation:

Generally, the variables that specify the nature of the wave are:

(1) The amplitude of the electric field, designated as E₀, and

(2) The amplitude of the electric field, designated as B₀.

please read the answer below

Explanation:

We have that both electric field and magnetic field are given by:

[tex]\vec{E}=E_osin(kx-\omega t)\hat{j}\\\\\vec{B}=B_osin(kx-\omega t)\hat{k}[/tex]

I complete with bold words the answers:

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

a. In these formulas, it is useful to understand which variables are parameters that specify the nature of the wave. The variables E0 and B0are the magnitudes of the electric and magnetic fields.

2. amplitudes

b. The variable w is called the angular frequency of the wave.

2. angular frequency

c. The variable k is called the wavenumber of the wave.

1. wavenumber

c.

1. E =E0sin(wt)k^

d.

6. x and t

hope this helps!!

Where the fields are sinusoidal, with amplitudes Eo and Bo

Then the correct answer is C

Explanation:

Given that,

E = Eo sin(kx - wt)y

B = Bo sin(kx - wt)z

The general wave equation is given above

Where the fields are sinusoidal, with amplitudes Eo and Bo

This shows that the Eo and Bo are the amplitudes

Also, the wave number k is related to the wavelength(λ)

k=2π/λ

And the angular velocity(ω) is given as

ω=kv

ω=v•2π/λ=2πv/λ. Where f=v/λ

ω=2πf

Where f is the linear frequency

In empty space, the wave propagates at the speed of light

i.e, v=c

The characteristic behavior of the sinusoidal electromagnetic wave is illustrated in the attachment

We notice that E and B are always in phase attaining maxima and minima at the same time

The relationship between Eo and Bo are

from Maxwell relations we know that

dE/dx=-dB/dt

E =Eoin(kx - wt)y

Then,

dE/dx=kEoCos(kx-wt)

dB/dt=wBoCos(kx-wt)

Then, equating them together

dE/dx=-dB/dt

kEoCos(kx-wt) = wBoCos(kx-wt)

Then, Cos(kx-wt) cancels out

kEo=wBo

So,

Eo/Bo = w/k

Since w/k=v=c

Then,

E/B=c

So the Eo and Bo are amplitudes of the electric and magnetic fields respectively

So the correct option is C