Question

In a vacuum (without materials, and without sources for electromagnetic fields), use Maxwell's equations to prove that fields E and B propagate as waves.

Answer #1

Using sinusodial plane wave, prove no longitudinal
electromagnetic wave exists in a vacuum. Only use Maxwell's
equation, not stoke's theorem or divergence theorem.

Considering you have monochromatic plane electromagnetic wave
traveling (in a vacuum) in the positive z direction. Use Maxwell's
equation, show that:
C) The electromagnetic wave is transverse
D) the B and E fields are perpendicular to each other

Explain briefly using Maxwell's equations in a vacuum the
propagation of light waves.

2. Prove that no longitudinal electromagnetic wave exists in a
vacuum. (10pt, no partial scores)
Note:
1. You must start from the Maxwell equation included in the
textbook. If you use the form of the Maxwell equation not in the
textbook, your score will be 0.
2. Hint: If you prove this from sinusoidal plane wave, you can
generalize that it is valid for general wave as well (you can use
it without proof.)

Suppose that an electromagnetic wave which is linearly polarized
along the x−axis is propagating in vacuum along the z−axis. The
wave is incident on a conductor which is placed at z > 0 region
of the space. The conductor has conductivity σ, magnetic
permeability µ and electric permittivity ε.
(a) Find the characteristic time for the free charge density
which dissipates at the conductor.
(b) Write the Maxwell equations and derive the wave equation for
a plane wave propagating in...

1) Electromagnetism
a) Explain the equations which describe electromagnetic waves
and what the variables mean.
b) Describe a system that uses electromagnetic waves.

1. True or False. Most of the waves in the
electromagnetic spectrum are not
visible to the naked eye.
a. True
b. False
2. The main difference between x-ray waves and gamma
waves in a vacuum is the
a. wave speed
b. wavelength
3. Which of these waves has the largest
frequency?
a. radio waves
b. infrared waves
c. gamma rays
d. ultraviolet waves
e. light waves
4. Which of these waves has the shortest
wavelength?
a. light waves
b....

Which one of the following statements concerning electromagnetic
(EM) waves is FALSE? Also expalin your reasoning.
(A) The electric and magnetic fields in EM waves are always
perpendicular to each other.
(B) Higher frequency waves have more energy than lower frequency
waves.
(C) EM waves move slower in high-index-of-refraction media.
(D) The index of refraction of a medium varies with the
wavelength of the incident EM wave.
(E) The frequency of EM waves decreases in regions with higher
index of...

At one instant, the electric and magnetic fields at one point of
an electromagnetic wave are E?
=(220i^+300j^?60k^)V/m and B?
=(7.8i^?7.3j^+ak^)B0.
1) What is the value of a?
2) What is the value of B0?
3) What is the Poynting vector at this time and position? Find
the x-component.
4)Find the y-component.
5) Find the z-component.

I read this great answer to this question:
Numerical software to manipulate a light beam in its plane wave
representation?
The main thing that I am trying to clear in my head is the
following:
Given that plane waves are eigenmodes of maxwell's equations in
free space in the absence of sources, shouldn't I be able to use
this to propagate a planar e/m field exactly (ignoring aliasing
effects)?
For example I know the field that exits in the x,...

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