Question

Two travelling sinosoidal electromagnetic waves, each with an
intensity 15 W/m2W/m2 , interfere to form a standing wave. The
resulting electric field E⃗ (z,t)E→(z,t) has nodes (i.e., is zero
at all times) at z=…,−2a,−a,0,a,2a,…z=…,−2a,−a,0,a,2a,… with aaa =
4.0 mm , and satisifes E⃗ (z,0)=0E→(z,0)=0. Furthermore, the
magnetic field B⃗ (z,t)B→(z,t) is observed to point along ±i^±i^
everywhere. You may take ccc = 3.0×10^{8} m/sm/s and
8.9×10^{−12} F/mF/m .

A) What is the wavelength λλlambda of the two constituent travelling waves?

B) When will the electric field be zero everywhere for the first
time after t=0? **Express your answer in units of
ns.**

**c)**When will the magnetic field be zero
everywhere for the first time after t=0

d)What is the amplitude (maximum magnitude) of the electric
field for the standing wave? **Express your answer in units
of V/m.**

e)How far from the origin is the nearest point where the
amplitude of the (instantaneous) Poynting vector is maximum?
**Express your answer in units of meters.**

Answer #1

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.

1) The average intensity of electromagnetic waves at a certain
point is 500 W/m2. What is the amplitude of the wave's electric
field.
a. 265 V/m b. 449 V/m c. 614 V/m d. 736 V/m
2) What is the radiation momentum density of an electromagnetic
wave having an electric field amplitude of 1000 V/m and travelling
in a vacuum?
a. 4.07 x 10^-15 kg m-2 s-1 b. 9.28 x 10^ -15 c. 1.48 x 10^-14
d. 6.25 x 10^-13
3)...

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 plane monochromatic electromagnetic wave with wavelength λ =
4.9 cm, propagates through a vacuum. Its magnetic field is
described by B⃗ =(Bxi^+Byj^)cos(kz+ωt) where Bx = 3.8 X 10-6 T, By
= 3.2 X 10-6 T, and i-hat and j-hat are the unit vectors in the +x
and +y directions, respectively.
1) What is f, the frequency of this wave?
2) What is I, the intensity of this wave?
3) What is Sz, the z-component of the Poynting vector at...

A plane monochromatic electromagnetic wave with wavelength λ =
3.2 cm, propagates through a vacuum. Its magnetic field is
described by
B⃗ =(Bxi^+Byj^)cos(kz+ωt)B→=(Bxi^+Byj^)cos(kz+ωt)
where Bx = 3.6 X 10-6 T,
By = 4.4 X 10-6 T, and i-hat and
j-hat are the unit vectors in the +x and +y directions,
respectively.
1)What is f, the frequency of this wave?
2)What is I, the intensity of this wave?
3)What is Sz, the z-component of the Poynting vector
at (x = 0,...

At one instant, the electric and magnetic fields at one point of
an electromagnetic wave are E⃗
=(210i^+340j^−60k^)V/mE→=(210i^+340j^−60k^)V/m and B⃗
=(7.1i^−8.0j^+ak^)B0B→=(7.1i^−8.0j^+ak^)B0.
Part B
What is the value of B0B0?
Express your answer using two significant figures.
B0 =
μT
Part C
What is the Poynting vector at this time and position? Find the
xx-component.
Express your answer to two significant figures and include the
appropriate units.
Sx =
Part D
Find the yy-component.
Express your answer to two significant figures...

Two waves traveling in opposite directions on a stretched rope
interfere to give the standing wave described by the following wave
function:
y(x,t) = 4 sin(2πx) cos(120πt),
where, y is in centimetres, x is in meters, and t is in seconds.
The rope is two meters long, L = 2 m, and is fixed at both
ends.
In terms of the oscillation period, T, at which of the following
times would all elements on the string have a zero vertical...

Deadline:
100% until Sunday, April 22 at 11:59 PM
Electromagnetic Waves 2
1
2
3
4
1
6
A plane monochromatic electromagnetic wave with wavelength ? =
2.1 cm, propagates through a vacuum. Its magnetic field is
described by
B? =(Bxi^+Byj^)cos(kz+?t)B?=(Bxi^+Byj^)cos?(kz+?t)
where Bx = 2 X 10-6 T,
By = 4.9 X 10-6 T, and i-hat and
j-hat are the unit vectors in the +x and +y directions,
respectively.
1)
What is f, the frequency of this wave?GHz
You currently...

A plane electromagnetic wave varies sinusoidally at 98.2 MHz as
it travels through vacuum along the positive x direction.
The peak value of the electric field is 2.10 mV/m, and it is
directed along the positive y direction.
(a) Find the wavelength.
m
(b) Find the period.
ns
(c) Find the maximum value of the magnetic field.
pT
(d) Write expressions in SI units for the space and time variations
of the electric field. (x is in meters, and t...

1) 2 point charges are separated by a distance of 8 cm. The left
charge is 48 mC and the right charge is -16mC. Using a full sheet
of paper: draw the 2 charges separated by 8cm, centered in the
sheet. (if you are missing a ruler estimate 8cm as ⅓ a paper sheet
length). [6] a) Draw field lines to indicate the electric fields
for this distribution. [4] b) Draw 3 equipotential surfaces, 1
each, that pass: -Through the...

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