Question

Consider an electromagnetic wave travelling in vacuum, where the electric field is given by:

?⃗ (? ,?)=40(?/?) sin[(8×10^{6} ???/?) (?+??)+1.57
???]?̂

a) Compute the:

i. frequency

ii. wavelength

iii. period

iv. amplitude

v. phase velocity

vi. direction of motion

b) Write the corresponding expression for the magnetic field of
this travelling wave (don’t forget to include the proper
units).

c) Plot this waveform as a function of x at t=0.

Answer #1

The electromagnetic wave

The magnetic field of an electromagnetic wave in a vacuum is Bz
=(2.6μT)sin((8.50×106)x−ωt)=(2.6μT)sin((8.50×106)x−ωt), where xx is
in mm and t is in s.
What is the wave's wavelength?
What is the wave's frequency?
What is the wave's electric field amplitude?

The magnetic field of an electromagnetic wave in a vacuum is Bz
=(3.8μT)sin((1.15×10^7)x−ωt), where x is in m and t is in s
What is the wavelength, frequency, and electric field amplitude
of the wave?

An electromagnetic wave in vacuum has an electric field
amplitude of 321 V/m. Calculate the amplitude of the corresponding
magnetic field. _________nT

The electric field of an electromagnetic wave in a vacuum is
Ey=(18.0 V/m)cos((4.18 ×10^8)x−ωt), where x is in m and t is in
s.
What is the wavelength, frequency, and magnetic field amplitude
of the wave?

In SI units, the electric field in an electromagnetic wave is
described by Ey = 118 sin(1.40 107x − ωt).
(a) Find the amplitude of the corresponding magnetic field
oscillations.________ µT
(b) Find the wavelength λ. ___________µm
(c) Find the frequency f. __________Hz

The electric field for a sinusoidal electromagnetic wave is
E = E0
sin(ky+wt) i
with E0 =40 V/m and k = 1.40E+8
m-1.
Select the direction of propagation for this wave.
Find the wave number of the wave.
Find the wavelength of the wave.
Find the period of the wave.
Find the frequency of the wave.
Find the angular frequency of the wave.
Find the speed of the wave.
Find the amplitude of the magnetic field.
For sinusoidal electromagnetic waves,...

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The electric field of an electromagnetic wave in a vacuum is
Ey= (24V/m)sin((5.28 x 108)x-ωt), where x is
in m and t is in s.
Part A
What is the wave's wavelength?
Express your answer using three significant figures.
λ =__________nm
Part B
What is the wave's frequency?
Express your answer using three significant figures.
f = __________Hz
Part C
What is the wave's magnetic field amplitude?
Express your answer using two significant figures.
B = __________T

Consider a sinusoidal electromagnetic wave propagating in the +x
direction, whose electric field is parallel to the y axis. The wave
has wavelength 475 nm, and the electric field has amplitude 3.20 x
10^-3 V m-1. What is the frequency of the wave? What is the
amplitude of the magnetic field? What are the vector equations for
E(x,t) and B(x,t)?

A sinusoidal electromagnetic plane wave is traveling in the +y
direction under water, with an index of refraction n = 1.33. The
wave is polarized along the z-axis and has a vacuum wavelength of
A_0 = 500nm.
A. What is the phase velocity of the wavefront in water?
B. What is the wavenumber of the electromagnetic wave in
water?
C. What is the linear frequency of the electromagnetic wave in
water?
D. If the electric field amplitude is 31.0 V/m,...

The magnetic field is given by By = Bo sin(kz - ωt). If the
electromagnetic wave with a wavelength of 650nm is traveling in the
z direction, and the maximum magnetic field is 8mT
a. What is the Electric Field? (show trigonometric form)
b. What is the maximum Electric Field
c. What is the wave number?
d. What is the frequency?
e. Write out the Poynting vector and calculate the magnitude

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