Electromagnetic Wave: Exploring Phase Difference

In summary, in a vacuum, the electric and magnetic fields of an electromagnetic wave are in phase with each other and have no angular difference. This is different from the direction of the fields, which are perpendicular to each other. This is due to the fact that a changing magnetic field induces a curl of the electric field and vice versa. This is described by Maxwell's equations and can be seen in illustrations. In general, there is no difference in phase in a vacuum, but this may differ in material media and waveguides.
  • #1
Wannabeagenius
91
0
Hi Folks,

I understand that a changing magnetic field induces an electric field and a changing electric field induces a magnetic field. I also understand that the greater the time rate of change of one, the greater is the other.

Now in free space, the electric and magnetic field of a wave are in phase. However, as I see it, at the peak of the sign wave of the electric field, the electric field time rate of change is zero. So it seems like this should coincide with a zero magnetic field but since they are in phase, the magnetic field is also at a peak.

It seems like they should have a phase difference of plus or minus pi/2.

What am I missing here?

Thank you,
Bob
 
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  • #2
Wannabeagenius said:
Now in free space, the electric and magnetic field of a wave are in phase.

Where did you read that?
 
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  • #3
granpa said:
Where did you read that?

I've seen it proven in a book on Electricity and Magnetism and I've come across it many times. An illustration shows the plane of the magnetic wave at a ninety degree angle to that of the electric wave but they are in phase meaning one reaches a maximum when the other reaches a maximum and one reaches a minimum when the other reaches a minimum.
 
  • #4
90 degrees out-of-phase is more appropriate.
 
  • #5
I've seen it drawn that way, too.
 
  • #6
JDługosz said:
I've seen it drawn that way, too.

It's not simply a drawing error. I just checked three separate E&M books and they are all drawn the same way. Additionally, the mathematics takes you there using Maxwell's equations!
 
  • #7
pallidin said:
90 degrees out-of-phase is more appropriate.

JDługosz said:
I've seen it drawn that way, too.

The E and B field vectors are oriented at 90 degrees with respect to each other in an electromagnetic wave; however, we do not describe this by saying that they are "90 degrees out-of-phase."

"90 degrees out of phase" means that the waves are described mathematically by something like

[tex]\vec E = \vec E_0 \sin (kx - \omega t)[/tex]

[tex]\vec B = \vec B_0 \sin (kx - \omega t + 90^{\circ})[/tex]

or better,

[tex]\vec B = \vec B_0 \sin (kx - \omega t + \pi/2)[/tex]

This is not true for electromagnetic waves in a vacuum.
 
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  • #8
Wannabeagenius is correct. They are in-phase, not 90 degrees out of phase.

If you look at Maxwell's laws in vacuum you will find that it is not quite corect that "a changing magnetic field induces an electric field". It is more correct to say "a changing magnetic field induces curl of an electric field" or in other words "a changing magnetic field (in time) induces a spatially changing electric field". When you express it correctly you immediately see that the electric and magnetic fields should be in phase.
 
  • #9
DaleSpam said:
Wannabeagenius is correct. They are in-phase, not 90 degrees out of phase.

If you look at Maxwell's laws in vacuum you will find that it is not quite corect that "a changing magnetic field induces an electric field". It is more correct to say "a changing magnetic field induces curl of an electric field" or in other words "a changing magnetic field (in time) induces a spatially changing electric field". When you express it correctly you immediately see that the electric and magnetic fields should be in phase.

I get it. Thank you.

Bob
 
  • #10
So, there is NO angular difference in the propagated electric/magnetic fields?
 
  • #11
pallidin said:
So, there is NO angular difference in the propagated electric/magnetic fields?

No difference in phase in a vacuum.

Perhaps someone could address whether or not this is true in general. I'm thinking of material media and waveguides.

Bob
 
  • #12
If you can see maxwell's equations, you will notice that a rate of change in the magnetic field creates a gradient in the electric field in the perpendicular direction and vice versa.
 
  • #13
Ch4_4-3.gif
[PLAIN]http://elementaryteacher.files.wordpress.com/2008/08/maxwells-equations.gif [Broken]
 
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  • #14
pallidin said:
So, there is NO angular difference in the propagated electric/magnetic fields?
There is no PHASE difference. I.e. When the E field is at its peak the B field is also at its peak.

Do not confuse this with the DIRECTION of the fields. If the E field points along the x-axis then the B field will point in the y-z plane (90 degrees). That is not at all the same as the phase relationship.
 
  • #15
OK, thanks...
 

1. What are electromagnetic waves?

Electromagnetic waves are a type of energy that can travel through space or matter. They are created by the movement of electrically charged particles and include forms of radiation like radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays.

2. How do electromagnetic waves differ from other types of waves?

Unlike mechanical waves, which require a medium to travel through, electromagnetic waves can travel through empty space. They also do not lose energy as they move and can travel at the speed of light.

3. What is phase difference in electromagnetic waves?

Phase difference is a measure of the shift in the alignment of the peaks and troughs of two different electromagnetic waves. It is often used to describe the relationship between two waves with the same frequency and direction of propagation.

4. How is phase difference important in the study of electromagnetic waves?

Phase difference is important because it can affect the behavior and properties of electromagnetic waves. For example, waves with a phase difference of 0 or a multiple of 2π are considered in phase and can produce constructive interference, while waves with a phase difference of π or a multiple of π can produce destructive interference.

5. What are some applications of understanding phase difference in electromagnetic waves?

Understanding phase difference is crucial in various fields, including telecommunications, radar technology, and medical imaging. It helps in the design and optimization of antennas, signal processing, and imaging techniques, allowing for efficient and accurate transmission and reception of electromagnetic waves.

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