Question

The electric field for a sinusoidal electromagnetic wave is

**E** = *E _{0}*
sin(

with *E _{0}* =40 V/m and

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, the magnetic field and the electric field are in phase, so they both have the same trigonometeric function assocoiated with them (no phase shift). For the wave described above, which unit vector will be associated with the magnetic field?

Answer #1

Let the direction be along the positive Z axis

The wave number is

The wavelength is

The speed of the wave is

The angular frequency is

The period of the wave is

The amplitude of the magnetic field is

The direction of magnetic field is such that the cross product
of electric field's unit vector with magnetic field's unit vector
will give the direction of propagation. Since the unit vector of
the direction of propagation is **k** and the electric
field is **i**, the magnetic field will be Y
direction

Hence unit vector will be associated with the magnetic field is
**j**

An electromagnetic wave in a medium is given by the following
wave function expression:
E=5E0(i-2j)sin(kx-wt).
The wave is known to have a wavelength of 690 nm and frequency of
3.2*1014 Hz. Also E0=104 V/m. For
this wave find the propagation number, angular frequency, direction
of propagation, speed of wave, index of refraction of medium,
direction of E oscillation, direction of
corresponding B oscillation, amplitude of
E, amplitude of B, and calculate
the irradiance of this wave.

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
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A. What is the phase velocity of the wavefront in water?
B. What is the wavenumber of the electromagnetic wave in
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C. What is the linear frequency of the electromagnetic wave in
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D. If the electric field amplitude is 31.0 V/m,...

The electric field of a sinusoidal electromagnetic wave obeys
the equation
E=−(350V/m)sin[(5.89×1015rad/s)t+(1.96×107rad/m)x]E=−(350V/m)sin[(5.89×1015rad/s)t+(1.96×107rad/m)x].
a)what is the amplitude of the electric field of this wave?
b)what is the amplitude of the magnetic field of this wave?
c) what is the frequency of the wave?
d)what is the wavelength of the wave?
e) what is the period of the wave?
f) speed 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
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(b) Find the wavelength λ. ___________µm
(c) Find the frequency f. __________Hz

Consider an electromagnetic wave travelling in vacuum, where the
electric field is given by:
?⃗ (? ,?)=40(?/?) sin[(8×106 ???/?) (?+??)+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.

(a) Write down expressions for the electric and magnetic fields
of a sinusoidal plane electromagnetic wave having a frequency of 3
GHz and traveling in the positive x direction. The amplitude of the
magnetic field is 1 μT. b) Verify that E(x, t) = Ae^(i(kx-wt)) or
B(x, t) = C sinkxsinwt is a solution of the one-dimensional wave
equation; A and C are constants.

An electric field traveling through vacuum can be described as a
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propagation, and electric and magnetic field amplitude of this
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expressed numerically. (c) Write equivalent equations in complex
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Al electromagnetic wave of 4.0 GHz has an electric field, E(z/t)
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permeability µr = 1.0, and relative permittivity εr = 14.0:
a. Determine the constant of propagation, γ = α + jβ.
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a. What is the Electric Field? (show trigonometric form)
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