Question

6.6. A plane electromagnetic wave is travelling in a non-magnetic medium whose relative permittivity (for field variations of the frequency of the wave) is 4.

(a) Calculate the refractive index of the medium and the velocity of wave propagation.

(b) If the amplitude of the E vector associated with the wave is
10 volt m^{-1} calculate the amplitude of B and show the
relative direction of E, B and the direction of the propagation in
a diagram.

(c) How much energy falls in one second on an absorbing surface
of area 10 cm^{2} placed at right angles to the advancing
wave?

Answer #1

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Q 2. A 2 kHz electromagnetic propagates in a non-magnetic
medium having a relative
permittivity of 20 and a conductivity of 3.85 S/m. Determine
if the material is a
good conductor or otherwise. Calculate the phase velocity of
the wave, the
propagation and attenuation constants, the skin depth and the
intrinsic impedance.

A plane wave of wavelength 100 nm is polarized along z direction
and travelling along -x direction with the electric field amplitude
of 300 V/m (in vacuum). The maximum value of wave is at t=0 and
x=0. Write the wave equation of magnetic field Calculate the
intensity and Poynting vector of electromagnetic wave.

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)?

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.

Al electromagnetic wave of 4.0 GHz has an electric field, E(z/t)
and a magnitude of E0 + = 120π.If the wave propagastes throguh a
material with conductivity σ = 7.5 x 10−3 S/m, relative
permeability µr = 1.0, and relative permittivity εr = 14.0:
a. Determine the constant of propagation, γ = α + jβ.
b. Determine the intrinsic impedance, η.
c. Determine the velocity oft he phase of the wave.
d. Determine the ”skin depth”.
e. Determine the value...

The plane monochromatic electromagnetic wave has frequency ?,
polarized in the positive ?-axis
direction moving towards the positive ?-axis direction. The
amplitude of the electric field is ?0, and
the start of time is chosen so that at ? = 0, the electric field
has a value ?0/2 at the origin.
Give answers with only the variables above and speed of light is c
and permittivity ?0.
a. Write the electric field of the wave.
b. Find the associated magnetic...

The magnetic field of a uniform plane wave propagating in a
lossless medium with εr=2 is H(x,t)=cos(3x10^8 t+4x) ay -
sin(3x10^8 t + 4x)az (A/m)
Find:(1)The phasor form expression for the magnetic field
(2)The direction of propagation for the wave
(3)The velocity vP
(4)The polarization state. If it is a circular polarization, you
need to determine it is left or right handed. Provide details for
your reasoning.
(5)The average power density???̅̅̅̅.

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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