Electromagnetic waves, Faraday's law

In summary, the conversation discusses Faraday's law and the relationship between E and H in a plane polarized electromagnetic wave. It is assumed that H is equal to B divided by mu. The attempt at a solution involves using a matrix to find the ratio between E and H, but it is noted that this only works if k and E are perpendicular. The conversation ends with a realization that the picture drawn does not show perpendicularity between k and E, leading to a correction in the solution.
  • #1
_Andreas
144
1

Homework Statement


Homework Equations



For a plane polarized electromagnetic wave traveling along the z axis, with its E vector parallel to the x-axis and its H vector parallel to the y axis, Faraday's law

[tex]\nabla\times \textbf{E}=-\frac{\partial \textbf{B}}{\partial t}[/tex]

gives that

[tex]\frac{E}{H}=\frac{\omega\mu}{k}[/tex], where E and H are the moduli of E and H.

ETA: It is assumed that [tex]\textbf{H}=\textbf{B}/\mu[/tex]

My problem is with an em-wave traveling in the x-z plane (were E and k have both x and z components). Apparently, I'm supposed to get the same ratio between E and H as above.

The Attempt at a Solution



[tex]\begin{vmatrix}
\textbf{i} & \textbf{j} & \textbf{k}\\
ik_x & 0 & ik_z\\
E_x & 0 & E_z
\end{vmatrix}=i\omega\mu H\textbf{j} \Longrightarrow \textbf{H}=\frac{1}{\omega\mu}(k_zE_x-k_xE_z)\exp i(k_xx+k_zz-\omega t)\textbf{j}[/tex]

Taking the modulus of H doesn't yield the correct answer, so I'm out of clues.
 
Last edited:
Physics news on Phys.org
  • #2
Hi _Andreas! :smile:

That'll only work if k and E are perpendicular :wink:
 
  • #3
tiny-tim said:
Hi _Andreas! :smile:

That'll only work if k and E are perpendicular :wink:

Hi!

But they are. Take a look at the picture I drew.

BTW, the [tex]k[/tex] in the last expression above (that for H) shouldn't be there.
 
Last edited by a moderator:
  • #4
_Andreas said:
Hi!

But they are. Take a look at the picture I drew.

(wot picture? :confused:)

Exactly … so if k is perpendicular to E, then |k x E| = |k| |E| :wink:
 
  • #5
Where'd my picture go?

tiny-tim said:
Exactly … so if k is perpendicular to E, then |k x E| = |k| |E| :wink:


Ooops! I deserve a facepalm.

Thanks.
 

1. What are electromagnetic waves?

Electromagnetic waves are a type of energy that are created by the movement of electrically charged particles. They are a combination of electric and magnetic fields that oscillate at right angles to each other, and can travel through a vacuum or through various materials.

2. How are electromagnetic waves produced?

Electromagnetic waves are produced when an electrically charged particle moves, creating a changing electric field. This changing electric field then creates a changing magnetic field, which in turn creates another changing electric field, and so on. This process continues, creating a wave of energy that can travel through space.

3. What is Faraday's law?

Faraday's law is a fundamental law in electromagnetism that describes the relationship between a changing magnetic field and an induced electric field. It states that when a magnetic field passing through a conductor changes, an electric field is induced in the conductor.

4. How is Faraday's law used in everyday life?

Faraday's law is used in many everyday applications, such as generators, transformers, and electric motors. It is also used in wireless charging technology, where a changing magnetic field is used to induce an electric current in a device to recharge its battery.

5. What are some examples of electromagnetic waves?

Some common examples of electromagnetic waves include radio waves, microwaves, infrared radiation, visible light, ultraviolet radiation, X-rays, and gamma rays. Each type of wave has a different frequency and wavelength, and is used for various purposes in communication, technology, and medical imaging.

Similar threads

  • Advanced Physics Homework Help
Replies
1
Views
1K
  • Advanced Physics Homework Help
Replies
1
Views
1K
  • Advanced Physics Homework Help
Replies
4
Views
1K
  • Electromagnetism
Replies
3
Views
926
  • Advanced Physics Homework Help
Replies
1
Views
2K
  • Advanced Physics Homework Help
Replies
1
Views
2K
Replies
6
Views
907
  • Advanced Physics Homework Help
Replies
3
Views
887
  • Advanced Physics Homework Help
Replies
5
Views
2K
  • Advanced Physics Homework Help
Replies
18
Views
3K
Back
Top