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E = E0 sin(kx - wt)yB = B0 sin(kx - wt)zThe simplest form of a traveling electromagnetic wave is a plane wave. For a wave traveling in the x direction whose electric field is in the y direction, the electric and magnetic fields are given by the picture shown above. This wave is linearly polarized in the y direction.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 __________ of the electric and magnetic fields.(A) maximas(B) wavelenghts(C) amplitudes.(D) velocities

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Kazeemsodikisola

Answer:

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

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