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High Hopes

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 « Embed this message on: July 11, 2010, 09:33:38 am » posted from:Alexandria,Virginia,United States

Hello all,

I am new to the forum.  Some years ago, I wrote a Turbo C app that models a charge traveling on an antenna which develops a standing wave.  I didn't know enough about electric magnetic radiation to understand the phase relationship between the E and B fields.

So here are my questions.  I originally sent this as an email to Mr. Fu-Kwun, and he suggested I post this in the forum where all could share in the knowledge.

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I have an EE background which has taught me that currents and voltages are always 90 degrees out of phase when inductive of capacitive devices are involved.  I understand that a peak change in current will introduce a peak change in voltage.  For sinusoidal currents, the peak change is on the positive and negative going slopes.  So the peak voltage is at the zero crossing of the current.

So do radio waves work the same way?  And if so, why are the magnetic and electric fields shown in phase in the animated graphics?

Or is this a general relativity question?  Does the transformation one energy from one field into another take time to occur?  Is time for this to transfer just equal to the time it takes the wave (event) to travel forward, so even though the fields are transferring energy at 90 degrees apart, the time for the new field to form (90 degrees) is equal to the time if takes for the fields to exist (propagate) in space.

And if this is true, does this explain why the waves travel forward, each field pushing the other in the only direction it can go (orthogonal to the field fronts) – forward.  Are they steered this way?  Is this why they are waves in the first place?  Is it because the magnetic and electric fields are in phase?  And they can only exist in phase in space – and cannot exist in phase in a wire?

Thanks,

Steve
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Fu-Kwun Hwang
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 « Embed this message Reply #1 on: July 11, 2010, 02:25:06 pm » posted from:Taipei,T\'ai-pei,Taiwan

The relation you remembered is for R-L-C circuit where
for resistor: $V_R=I R$
for inductance: $V_L= L\frac{dI}{dt}$
for capacitor: $V_C=\frac{1}{C}\int I dt$

That is the reason why for AC signal $I=I_0 sin\omega t$,the voltage for inductance or capacitor are 90 degree out  of phase with current.

For electromagnetic wave, it is another sets of equations (it is also related to the above equations under some conditions)
$\nabla\times\vec{E}=-\frac{\partial \vec{B}}{\partial t}$
and
$\nabla\times{B}=\mu_0 I + \mu_0\epsilon_0\frac{\partial \vec{E}}{\partial t}$
For EM wave in free space, I=0
Combine the above two equations will give us
$\nabla \vec{E}=\mu_0\epsilon_0\frac{\partial^2\vec{E}}{\partial t^2}$
and
$\nabla \vec{B}=\mu_0\epsilon_0\frac{\partial^2\vec{B}}{\partial t^2}$
which are standard form for wave equation.
You can chek out http://en.wikipedia.org/wiki/Electromagnetic_wave for derivation

The wave can be represented with $\vec{E}=\vec{E_0} sin (\vec{k}\cdot\vec{r}-\omega t)$
The change on electric field (flux) will product magnetic field distribution ($\nabla\times\vec{B}$)at near by space.
The time derivative will produce 90 degree phase differences.
However, the curl will also produce another 90 degree phase differences.
That is why the net effect is in phase. The electric field is in the same phase with magnetic field in free space.

It is possible to produce out of phase EM wave in wave guide.

You are welcomed to check out  Propagation of Electromagnetic Wave
:=)
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Life well spent is long. ..."da Vinci (1452-1519, Italian artist, sculptor, painter, architect, engineer and scientist) "