Question
The electric field for a sinusoidal electromagnetic wave is E = E0 sin(ky+wt) i with E0...
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, 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?
Homework Answers
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
Not the answer you're looking for?
Similar Questions
An electromagnetic wave in a medium is given by the following wave function expression: E=5E0(i-2j)sin(kx-wt). The...
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...
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)?
In a traveling electromagnetic wave, the electric field is represented mathematically as E = E0 sin[(1.3...
In a traveling electromagnetic wave, the electric field is
represented mathematically as E = E0
sin[(1.3 × 1010 s-1)t - (4.7 ×
101 m-1)x] where
E0 is the maximum field strength.
(a) What is the frequency of the wave?
(b) This wave and the wave that results from its
reflection can form a standing wave, in a way similar to that in
which standing waves can arise on a string (see Section 17.5). What
is the separation between adjacent nodes...
A sinusoidal electromagnetic plane wave is traveling in the +y direction under water, with an index...
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 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...
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...
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
Consider an electromagnetic wave travelling in vacuum, where the electric field is given by: ?⃗ (?...
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...
(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 plane wave E(r,t) = Eoexp[-i(ωt...
An electric field traveling through vacuum can be described as a
plane wave E(r,t) = Eoexp[-i(ωt + k•z)]. (a) What is the angular
frequency, wavelength, wave number, velocity, direction of
propagation, and electric and magnetic field amplitude of this
light wave? (b) Write equations describing the electric and
magnetic fields in sinusoidal form, with all known quantities
expressed numerically. (c) Write equivalent equations in complex
exponential form. (d) What would be the maximum electric and
magnetic forces exerted by this...
Al electromagnetic wave of 4.0 GHz has an electric field, E(z/t) and a magnitude of E0...
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...
ADVERTISEMENT
Need Online Homework Help?
Get Answers For Free
Most questions answered within 1 hours.
ADVERTISEMENT
Active Questions
asked 46 seconds ago
asked 27 minutes ago
asked 28 minutes ago
asked 44 minutes ago
asked 52 minutes ago
asked 1 hour ago
asked 1 hour ago
asked 1 hour ago
asked 1 hour ago
asked 1 hour ago
asked 2 hours ago
asked 3 hours ago