# Shape of Electromagnetic Waves

Thread Starter

#### rahulpsharma

Joined Sep 5, 2010
31
The shape of EM waves are often shown as in Time Phase but space quadrature.... Electric and Magnetic field become zero at the same time... But shouldnt it be just the opposite...?? Rate of change of E field generates a changing B field and vice versa... Now a sine wave will have maximum rate of change at while crossing the zero line and will have zero rate of change at the peaks... So shouldnt B field be Zero when E field peaks and vice versa...??

Sorry about my lack of understanding but seems I am missing something important here... Request you to kindly help me bridge this gap please...

Thanks and Regards
Rahul

#### nsaspook

Joined Aug 27, 2009
8,157
The shape of EM waves are often shown as in Time Phase but space quadrature.... Electric and Magnetic field become zero at the same time... But shouldnt it be just the opposite...?? Rate of change of E field generates a changing B field and vice versa... Now a sine wave will have maximum rate of change at while crossing the zero line and will have zero rate of change at the peaks... So shouldnt B field be Zero when E field peaks and vice versa...??

Sorry about my lack of understanding but seems I am missing something important here... Request you to kindly help me bridge this gap please...

Thanks and Regards
Rahul
You should see the Electric and Magnetic field elements of the wave in terms of propagation not creation. "Rate of change of E field generates a changing B field and vice versa..." Generates is a misnomer in this context because it gives the impression that one field collapses and forms the other but we can see by simple experimental measurement that not the case in a far field EM wave because it is Time Phase but space quadrature.
http://hyperphysics.phy-astr.gsu.edu/hbase/Waves/emwavecon.html

A simple answer:
http://van.physics.illinois.edu/qa/listing.php?id=22370
In a classical propagating EM wave a spatial derivative of the E field matches up with the time derivative of the B field, and vice-versa. So they're both changing (say crossing zero) or not changing (say at a peak) at the same places. For a linearly polarized wave, that leaves Eand B in phase in the sense that they have nodes and peaks at the same places, but they're at 90° angles to each other, thanks to the type of spatial derivative involved (a curl).

If we look at this using a circuit theory analogy:
Both the electric (voltage) and magnetic fields (current) are varying with time in the purely resistive Impedance of free-space so they must be in time phase.

Last edited:

#### Glenn Holland

Joined Dec 26, 2014
705
The simplest way to visualize the shape of an electro magnetic wave is to look at a chain where each link interconnects to another link.

One link will be like the loop of the electric field and the next link will be like the loop of the magnetic field. The electric and magnetic field loops will be at 90 degrees to each other.

The three dimensional diagram that represents the electric and magnetic fields as sine waves is just the mathematical relationship rather than the actual form of the phenomenon.

#### MrAl

Joined Jun 17, 2014
8,063
The shape of EM waves are often shown as in Time Phase but space quadrature.... Electric and Magnetic field become zero at the same time... But shouldnt it be just the opposite...?? Rate of change of E field generates a changing B field and vice versa... Now a sine wave will have maximum rate of change at while crossing the zero line and will have zero rate of change at the peaks... So shouldnt B field be Zero when E field peaks and vice versa...??

Sorry about my lack of understanding but seems I am missing something important here... Request you to kindly help me bridge this gap please...

Thanks and Regards
Rahul

Hi,

If you go out on a lake and slap your hand down on the surface of the water, you see ripples go out in all directions and they look smooth like sine waves. However, if you have three friends with you and they slap their hands down one three times faster than you, one five times faster than you and one seven times faster than you, and they use a force that is 1/3 times your force, 1/5 and 1/7 respectively, you'll see a wave going out that has a more square shape, and if you have 101 friends with you and they follow that general rule you should see a very squarish looking wave going out from the center.

Granted this would be very hard to do in real life, but that should illustrate the property of a wave: that it can be almost any shape. In fact at this time in history i think the only requirement is that it has to be a true function and with propagation limited by the speed of light. That may change as we learn more about time travel, but for now i think we would stick with that and the amazing wave equation in three spacial dimensions:
∂^2u/∂^2x+∂^2u/∂^2y+∂^2u/∂^2z=(1/v)*∂^2u/∂^2t

Interestingly, the only limit seems to be that it has to be a function like u(x,y,z,t) and that it can not travel faster than a certain speed due to the limit on the speed of light when v=c.

Looking at the one dimensional form:
∂^2u/∂^2x=(1/v)*∂^2u/∂^2t

we see that this is satisfied with any function that can be differentiated twice in both time and distance, and the equality must still hold. There is also the property of superposition, so that if we found several solutions and added them together that would be a solution also, and that means there must be a lot of solutions for u(x,t).

An interesting way to study this is to wire up a little circuit with several inductors and capacitors and resistors, forming a piecewise transmission line. There would be one resistor in series with each inductor, and one large value resistor in parallel with each capacitor, and the circuit would be arranged like a series of cascade low pass filters. Each node between each inductor and capacitor would represent one distance unit, so if you use five such low pass filters you will have a total of five distance units. You could excite the input with whatever signal you wanted to try, and observe the outputs at each node and since each LC node represents one distance unit that would be like looking at the wave farther and farther away from the source. This of course can be easily done in a circuit simulator.

Another view is that it is more like a field of influence. The old writers from long ago used to call this "propensity", and would say something like that the field has the propensity to create a change at a point in space. That is, we may not have to understand what it is so much as what it is capable of doing. It is capable of inducing change at some place at a distance from where it originated due to the way it travels, and so something measurable will change at that distant point, and when we measure that change we then know more about the properties of the wave that forced that change to occur. If the change was large, then we know the wave was large, and if the change was small, then we know the wave was small.

Last edited:
Thread Starter

#### rahulpsharma

Joined Sep 5, 2010
31
Thanks you very much for your detailed replies... For the lack of my proper understanding of the subject, I am somehow unable to understand the -ve in the equation of changing magnetic field with respect to time...

Also what happens to the energy contained in the EM waves... From the shape of it, as shown in standard texts, both E and B fields become zero at the same time. Does it mean that the EM energy too becomes zero at that point...??

Thanks and regards

#### MrAl

Joined Jun 17, 2014
8,063
Hi,

Have you ever cooked in a microwave oven? You might have noticed egg carton 'nodes' where cooking is more intense at certain spots. Standing waves will have stationary nodes but traveling waves will keep moving along the direction of travel so the zero will not stay in one place. All my microwave ovens had rotating platters to help get around the local heating problem.

#### nsaspook

Joined Aug 27, 2009
8,157
Thanks you very much for your detailed replies... For the lack of my proper understanding of the subject, I am somehow unable to understand the -ve in the equation of changing magnetic field with respect to time...

Also what happens to the energy contained in the EM waves... From the shape of it, as shown in standard texts, both E and B fields become zero at the same time. Does it mean that the EM energy too becomes zero at that point...??

Thanks and regards
The energy is moving (wave propagation).
Analogy:
Imagine a stream of bullets tip to end moving across space were the E and B fields both represent the circular cross section of each individual bullet as they each move down the line. A one fixed point in that line we can see as the bullet moves down the line the circular cross section starts at zero, increases to the size of the bullet circumference and then reduces back down to zero. So the energy does not become zero in the wave, the wave moves and the energy in the fields follows in step.

Thread Starter

#### rahulpsharma

Joined Sep 5, 2010
31
The energy is moving (wave propagation).
Analogy:
Imagine a stream of bullets tip to end moving across space were the E and B fields both represent the circular cross section of each individual bullet as they each move down the line. A one fixed point in that line we can see as the bullet moves down the line the circular cross section starts at zero, increases to the size of the bullet circumference and then reduces back down to zero. So the energy does not become zero in the wave, the wave moves and the energy in the fields follows in step.
So in your example, is the outer cylindrical shell of the bullet analogus to energy...??

Thanks and regards

Last edited:
Thread Starter

#### rahulpsharma

Joined Sep 5, 2010
31
Hi,

Have you ever cooked in a microwave oven? You might have noticed egg carton 'nodes' where cooking is more intense at certain spots. Standing waves will have stationary nodes but traveling waves will keep moving along the direction of travel so the zero will not stay in one place. All my microwave ovens had rotating platters to help get around the local heating problem.
But doesn't that convey a sense that energy becomes zero at half the wavelength of microwave leading to cold spots...?? So if this wave was travelling and not standing, even then wouldnt the energy become zero at every half wavelength and cold spots would be created, albeit, at different random locations...!!

Thanks and regards

Last edited:
Thread Starter

#### rahulpsharma

Joined Sep 5, 2010
31
May I also request you to kindly help me visulaize the 'Curl of an Electric Field'...!! I understand to some extent that a curl is a measure of rotation of a field... I can visualize the curl of magnetic field around a wire carrying current as a 'circle around the cross section' of the wire... Would curl of an electric field also have to be 'assumed' to be a similar circle around the cross section of the wire...??

Regards,
Rahul

Last edited:

#### shortbus

Joined Sep 30, 2009
8,429
I'm surprised BR-549 hasn't stepped into this discussion with his Pi theory. That would clear things up fast.

#### nsaspook

Joined Aug 27, 2009
8,157
So in your example, is the outer cylindrical shell of the bullet analogus to energy...??

Thanks and regards
I hate to stretch the analogy further as it's just a mental visual aid but in such an analogy each infinitesimally thin bullet circular cross section from tip to end would represent the product of the E and B fields at each section of the wave as it moves across space. The EM wave is a physical entity as real as the bullet but I understand it's hard to simply imagine how this is possible at first.
http://thecreatorsproject.vice.com/blog/who-knew-radio-waves-could-look-this-good

http://math.ucr.edu/~jdp/Relativity/EM_Propagation.html

https://www.osapublishing.org/Direc...8-10-10029.pdf?da=1&id=199171&seq=0&mobile=no

http://www.opticsexpress.org/viewmedia.cfm?URI=oe-18-10-10029-1

Last edited:

#### MrAl

Joined Jun 17, 2014
8,063
May I also request you to kindly help me visulaize the 'Curl of an Electric Field'...!! I understand to some extent that a curl is a measure of rotation of a field... I can visualize the curl of magnetic field around a wire carrying current as a 'circle around the cross section' of the wire... Would curl of an electric field also have to be 'assumed' to be a similar circle around the cross section of the wire...??

Regards,
Rahul

NOTE: I had to edit this for clarity in the naming conventions used.

Hi again,

Well for one, it's not my fault that the waves go through zero, but energy is still transferred. Look at an oscillator, where the sine wave goes through zero a lot, yet if we connect a load we still get power transferred to the load.

For the case of the wire...
You noted that the curl of B appears, as we say, around the wire and has direction around that wire. But we dont get any B without a continuous path, which for a simple example, means a continuous loop of wire.
We also know some other things here from curl B=J*u0 and curl E=-dB/dt...
1. The curl of B is perpendicular to the current in the wire and so 'rotates' around the wire in a circular path.
2. The curl of E is perpendicular to the change in B with time, and the change in B occurs as amplitude changes in the rotation of B, meaning B just gets lower and higher with time.

Taking the three things together that means that the circulation of E must be inside the wire, so that it too 'circulates', but it circulates perpendicular to the B circulation. In order to get this to happen, E must be inside the wire so that it can circulate around the circulation of B at every place. So the circulation of E follows the path of the current around the closed loop of wire.
The actual curl of B is along the wire.

Look at the first diagram in the attachment Fig A.
Is that the circulation of B or is that the circulation of E? We cant tell which it is yet.

Look at Fig B and the color coding scheme Fig D.
In figure B, the wire is green and the circulation of B is red, and the curl of B is green out of the page.

In figure C, the B is still red and the wire is still green, but now green is also E and the curl of E is black out of the page.

#### Attachments

• 18.2 KB Views: 4
Last edited:

#### nsaspook

Joined Aug 27, 2009
8,157
An intuitive view of curl.

A flow of water.

If the paddle turns, it means this field has curl (twisting or pushing force) at that point.

#### MrAl

Joined Jun 17, 2014
8,063
An intuitive view of curl.

A flow of water.

If the paddle turns, it means this field has curl (twisting or pushing force) at that point.
Hi,

Your drawing inspired me to make a drawing too in order to help illustrate in post #14. I attached it there.
Nice drawing BTW

It might be worth mentioning that to measure the curl of B that paddle wheel could hypothetically be placed in the field with the shaft perpendicular to the flow of current. The difference in B near the wire and farther from the wire would cause the wheel to turn. That makes it seem like the current is causing the rotation like a corkscrew where the handle turns like the curl of B and the current advances like how the screw goes into the cork. As the screw keeps moving forward, the curl keeps rotating around the screw. The curl however is not a spiral it's more like just circular lines.

Last edited:

#### MrAl

Joined Jun 17, 2014
8,063
Hi again,

I had to do a quick edit of my original post as the naming conventions were not very clear and some things were mislabeled. It should be correct now though. The drawing was also corrected. It should also be noted that the example shown is for non zero curl E and would be that for a B that is changing in a linear fashion like that of a ramp which never changes slope, which i believe is the simplest example.
Also, i realize that i did not show the information for an EM wave going out into space. I'll have to save that for next time but we know right off that the electric part has to be orthogonal to the magnetic part, and the magnetic part appears as circles around the wire, so the electric part must be circular around the magnetic circle borders. Should look something like a magician's two loop trick before the two loops are pulled apart 'magically'. One loop is B the other is E.
Someone else feel free to jump in on this with some more links or info.

Last edited:

#### killivolt

Joined Jan 10, 2010
796
I've enjoyed all of the examples, I thought about this guy and how much damage he might be doing to parts of his body? Specifically, the field propagating toward his nether parts?

kv

#### nsaspook

Joined Aug 27, 2009
8,157
I've enjoyed all of the examples, I thought about this guy and how much damage he might be doing to parts of his body? Specifically, the field propagating toward his nether parts?

kv
It's looks somewhat impressive but the radiated non-ionizing RF power is small. I spent years on ships loaded from head to toe with high power emitters with very efficient antennas. The nether parts seem to be still working after all those years.

#### nsaspook

Joined Aug 27, 2009
8,157
A little trick (a high speed laser shutter/scanner similar to a film shutter that makes wagon wheels slow or stop in movies) to slow EM wave propagation to something watchable.

Last edited:
Similar threads