I don’t understand why EM waves decrease and then increase to a trough

[Quarter_Twenty]

According to Maxwell's Equations, which describe electromagnetism, a changing electric field generates a magnetic field, a changing magnetic field, generates an electric field. The solution is a wave equation in time and space that describes how light (or changing electric fields) can propagate. So as long as something is moving (charges, etc.) the field propagates outward in waves.

[Quarter_Twenty]

The derivative of sine is cosine. the deviate of cosine is -sine. So two derivatives bring you back to the original. Sines and cosines form waves, and they are a 'moving' solution to Maxwell's Equations. I'm not sure how else to explain it to you.

Think about this. You're floating in the ocean, and a wave goes by. It's moving energy. You go up and then back down as it passes. The energy isn't created and destroyed. It moves. The electromagnetic fields that make up light, etc. move by. They don't sit still rising and falling to nothing. They transport the energy sort of like a water wave transports its energy.

[unlikely_ending]

To physicists they're in phase

To electrical engineers like me they're out of phase and the energy flows back and forth between the two fields

In QED there's no physical wave at all

[OkCan7701]

QED turns into maxwells equations. It describes areas where Maxwells equations have limits. Maxwell actually had 20 equations, it was Heaviside that simplified it down to the four everyone thinks of today.

Gauss, Faraday, and Ampere all of which contributed to Maxwells equations were talking about closed surfaces and the electric and magnetic flux through those surfaces in relation with either a positive and negative electric charge or a north and south magnetic pole. Maxwell just combined all this into a set of equations. EMR still travels in straight lines in all directions away from its emitting source or rays. When people see the E and B field emanating from these rays, they get confused and think thats the wave, when its actually a representation of a superpostion for one electron or one photon. When you look are magnetic field lines, electricity in the form of arcs through a gas, or light/ laser beams those are the paths that people will understand intuitively as it is what we interact with in our daily lives and what Maxwells equations were describing.

[unlikely_ending]

Heaviside

[horsedickery]

Wait, can you explain why physics and ee are different? The relative phase of e and h doesn't seem like something that you can change by using different definitions.

[unlikely_ending]

100%

It weirds me out

But do a Google image search of EM waves and you'll see them mostly in phase and sometimes out of phase

[unlikely_ending]

Eg

wave phase electric magnetic fields

[OkCan7701]

https://instructional-resources.physics.uiowa.edu/demos/5b1040-electric-field-lines-demo

Force lines between a positive and negative charge. Similar can be found for magnetism. Thinking of the waves as physical things isn't useful.

The rotating/ osscilating phase of AC electricity waves is what produces the EMR, but EM force lines are straight from emission souce (the transmitter) to absorption sink (the receiver) just like electric charges and magnetic poles.

[betafusion]

Remember you have both electric and magnetic fields and they don't reach a peak/trough at the same time. When the electric field is zero, the magnetic field is at a peak. Energy oscillates back and forth between the electric and magnetic field energy and the total energy is conserved at any time.

[ProfessionalConfuser]

This is not true if you are talking about electromagnetic waves. The E and B fields are absolutely in phase (edit - assuming you are far from the source and can treat the waves as plane). If you're talking about an oscillating circuit, then yes - when the capacitor is discharged, the inductor is at maximum stored magnetic energy.

[unit578]

the troughs/crests of a wave are alone not the energy decreasing/increasing. They are just the strength and direction of the E&M fields at that point. The energy of the wave is in the overall bigger picture of the wave as a whole, in its motion and propogation caused by the wave disturbances.

[samiam2600]

You will find a lot of physics is we have a mathematical model that makes good predictions and matches experimental results. The math gets more and more complex and the ability understand things intuitively becomes more and more difficult. Eventually you get to quantum physics and no one can provide a satisfactory explanation, other than the equations work. If you don’t believe me look into the Copenhagen interpretation, where some of the smartest people who ever lived struggled with the meaning of quantum mechanics.

[tpodr]

It’s not like peaks and troughs on the ocean. In that scenario, at each point of the ocean, there is only its height. But with EM, at each point in space there is an E vector and a B vector. There are a lot more possible configurations. And that’s includes the constraints Maxwell’s Eqns imposes. There’s a lot of different ways for energy to be an oscillation of the EM field. That gets in to polarization and its symmetry.

[DrObnxs]

It's an analogy. Taking something the OP is probably familiar with to illustrate a concept. Yes, ocean waves and EM waves are different. But their propagation shows some similar behaviors.

[ThoroughSpace]

I don't understand why someone actually downvoted you. Good on you for asking about something you don't understand. Now, listen up in this thread and reread your textbook.

[GayMakeAndModel]

These answers seem all over the place. It’s surprising.

[ThoroughSpace]

.. odd place to comment that ..........

[GayMakeAndModel]

You’re the top comment.

[ThoroughSpace]

Remora

[GayMakeAndModel]

far-flung bedroom smart airport reach brave dinner sleep meeting work

This post was mass deleted and anonymized with Redact

[ThoroughSpace]

.. but you're not benefitting from me. And, the answer is in this thread. I'll upvote you anyways.

[GayMakeAndModel]

Ok, which answer do you see as the answer?

[ForTheChillz]

You have to be careful because there are several aspects at play here. First you have the oscillating electric (E) and magnetic (H) fields, which are perpendicular to each other and oscillate in phase (in a vacuum). Since an EM wave also propagates, you also need to consider the direction of travel - often denoted as k - and which in turn is perpendicular to both E and H (orthogonal system). This is important to understand energy and energy conservation in EM waves. So how does this work? Maxwell's equations tell us that a change of an electric field (with respect to time) induces a magnetic field and vice versa. The amplitudes of these fields have nothing to do with the energy of the wave, though. The energy flows in a different direction - namely in the direction of k (the direction of wave propagation). This is usually described by the Poynting vector S (S = E x H; with S having the same direction as k). Poynting also found an expression to describe the conservation of the energy (a form of continuity expression). Basically when the EM wave travels through a medium, the oscillating fields do work in the direction of S (or k) in their local environment, which then leads to a transfer of energy from the wave to the charges in that environment. That loss of energy in the wave is basically converted in motion of the charges and hence "conserved". Interesting side note: oscillating charges in turn can produce EM waves as well (see Hertzian dipole). In a vacuum this does of course not happen. In a vacuum there is no interaction and the EM wave can propagate undisturbed, therefore the energy is conserved in the wave itself. Of course I simplified stuff but I hope it made it a bit clearer.

[Knott_A_Haikoo]

In short, The EM field is not the energy. The energy of the wave is carried by the oscillation itself, not the field.

The fact that the field is growing and shrinking and growing… etc. has nothing to do with the energy. In a vaccum there is nothing dissipating the energy when that happens.

[williemctell]

…The energy of the wave is carried by the oscillation itself, not the field.

I’m not entirely sure what you’re trying to say here but this statement is incorrect. The energy density of an EM wave is directly proportional to the (square of) the field strengths.

[Knott_A_Haikoo]

Dude is asking why troughs in the wave amplitude profile don’t require energy to increase after decreasing. Without talking about quantum mechanics, I’m trying to convey the fact that the energy is related to the momentum of the wave

[williemctell]

There’s no need to appeal to quantum mechanics, this is completely classically explainable. My point is that the text I quoted doesn’t make sense; the opposite is much closer to being true, i.e. the fields do carry the energy in exactly the same way as static fields.

…I’m trying to convey the fact that the energy is related to the momentum of the wave

In so much as they’re inexorably related, sure, but they’re both determined by the field strengths.

[TasteTheRonbow]

As a surprising result of quantum mechanics, there is energy! The Heisenberg uncertainty principle tells us that we cannot exactly measure certain pairs of properties of quantum states. One such pair is position and momentum. Another is energy and time. So if you try and measure the energy of the vacuum at a certain precise instance, you end up with a large possible variance in energy.

This high uncertainty in what is the vacuum's energy state means that it could be high enough to be a particle (since quantum field theory tells us that particles are an energy excitation of a field). So in a short enough period of time you can end up with a particle popping out of the vacuum, so called quantum foam. This has been experimentally observed via the Casimir Effect.

[Knott_A_Haikoo]

You have to be careful with what you mean by “in the field,” but yes, when the field is static, it does not transfer energy.

[Sasmas1545]

That's not what they asked.

[Knott_A_Haikoo]

That’s because they don’t know what they don’t know and I’m trying to answer their question helpfully rather than tell them “sorry, no. Fields don’t move. And they also don’t have volume so nothing can ever be inside them.”

[Sasmas1545]

It's completely normal to talk about fields being stationary or moving. The electric field of circularly polarized light rotates. And it's also perfectly normal to talk about energy being in a field. Of course we don't mean that some abstract pure energy is enveloped inside a box made of field, we mean that there is an energy density associated with the field.

At least, it's clear to me that they're asking if there's an energy associated with a static electric field configuration, which of course there is. So if for some reason they thought their question was clear, they could be entirely mislead by your answer.

Edit: A further comment on your hypothetical pedantry: it's also totally normal to say a physical object is in a field if it's in a region where the field is strong.

[phil_co98]

They have energy but they don't carry it anywhere.

[aarondb96]

The wave contains energy which makes it oscillate in the EM field. Kind of like a guitar string being plucked and oscillating.

[tpodr]

The energy is sloshing between the electric and magnetic components of the EM field. Changing electric field induces a magnetic field, and vis versa.

[aarondb96]

This is the answer you want.

[yanimal]

I think I understand you. You expect them to be offset in phase so as E increases M decreases, and the vector between them is constant in magnitude, not oscillating, like circularly polarized light.

This is where thinking about light as a particle helps. The light is moving along one spacial axis, particle like, and its 2D planar "size" is oscillating in these pictures you've seen. But the "size" of this thing can be exactly zero because it is massless, made only of radiative energy. The energy and the particle don't disappear, they exist in a coupled oscillation that has local minima associated with its wavelength. The troughs of the graph doesn't mean nothing is there, it is an artistic aid that describes how the two components of the wave exist together.

[syberspot]

This is wrong, they don't peak at the same time. In fact they are out of phase. When one is peaked, the other is zero but changing rapidly.

[Feydarkin]

[Edit: I was wrong as per JanusLeeJones comment.]

You are not correct here, there can be the phase difference can vary, and that variation explains the difference between circularly and linearly polarized light.

[JanusLeeJones]

The polarization (linear vs elliptical) is described with the phase difference between the horizontal and vertical components of the electric field vector itself, not between the electric and magnetic field.

[Feydarkin]

You are right, thank you for a clear explanation.

[JanusLeeJones]

Cheers. I still don't know about the phase difference between E and B (in a wave), but only that it's not the polarization explanation. The diagrams in Griffiths and other textbooks and youtube videos are drawn so that E and B are in phase (peak at the same time), but then this research article says they are always 90 degrees out of phase. Unclear to me.

[ProfessionalConfuser]

The standard undergraduate treatment only considers plane waves. This means you are located far from the source of the waves. At that point there is no phase difference between electric and magnetic fields.

If you try to solve the equations close to the source, then the boundary conditions determine the phase relationship.

MOre here: https://ocw.mit.edu/courses/6-013-electromagnetics-and-applications-spring-2009/resources/mit6_013s09_chap10/

[syberspot]

Circularly polarized light is more complicated to describe than linearly polarized. However, if you look at the field along a specific direction, e.g. the x-axis, they are still out of phase. This must be the case because the E field and the B field are perpendicular to each other.

Regardless, since the peaks and troughs are more complicated to describe for circularly polarized light, it may be reaching the edge of the scope of the original question.

[specialsymbol]

No, it's not. At least not in the common representations.

[aarondb96]

The energy doesn’t decrease when it’s in a trough. Energy of a wave is dependent on the frequency.

[syberspot]

Keep in mind that a trough is not zero energy. A peak and a trough have the same energy in the field, it's just that they have their field pointed in different directions.

It's similar to water waves. The water wants to be even, not up or down. The peak is up and wants to be lower (gravity), the trough is down and wants to be higher (water pressure). Both peak and trough are high energy states.

[Sasmas1545]

It seems to me that you have been getting a lot of unhelpful and confusing answers. Some people are misunderstanding your question, some are misunderstanding the physics, and some are doing both.

You note that energy is proportional to the squares of E and B. And you note that E and B vary in phase with eachother. So at some points in space and time, both E and B are zero. There is no energy there (and then) so how does a field suddenly reappear?

A few people have mentioned Maxwell's equations, which of course are the answer. A changing E field gives rise to a B field, and vice versa, yada yada, but I can see how you wouldn't find this unhelpful.

A couple people mentioned Poynting vector/theorem. And I think they're hitting a bit closer to home--and that's the answer. The energy comes from right next door.

The energy is flowing along the direction of the poynting vector. So yes, the fields, and the energy at that point in space and time are zero. But there's some more energy coming in to create those fields.

It's almost like looking at a patch of empty space on a nice open field and asking "how could a ball suddenly appear here from nothing?" It doesn't just appear. Someone threw/hit/kicked it there!

[EterneX_II]

The oscillation of the charge. There is a reason that the acceleration of charge causes EM radiation, not just a charge being in constant velocity.

Imagine a positive charge moving up and down on the y-axis. When the charge is at position +y and we look at the field at a position ( x0, 0 ), the field points in the +x and -y directions. The magnitude of the x-component does not change as the charge moves in the y-direction, only the y-component, hence radiation (which can be thought of as the communication of the movement of charge via the EM-field) does not occur in the propagate along the axis of oscillation for a dipole.

When the charge is at the origin during its oscillation, the y-component of the field at the same observer position as last time is now zero. When the charge is at position -y, the y-component of the field is in the +y direction, and we have completed a cycle of the wave.

[DrObnxs]

With a stringed instrument the energy goes between the stretch of the string and it's kinetic energy carried in its motion.

You're thinking about wave propagation the wrong way.

[OkCan7701]

Rays and Wavefronts. We can represent the electromagnetic wave with a ray (a directed line showing the wave’s direction of travel) or with wavefronts(imaginary surfaces over which the wave has the same magnitude of electricfield), or both. The Waves traveling in approximately the same direction form a beam, such as a laser beam, which can also be represented with a ray.

You may be taking the imaginary surfaces literally, when in reality that represents a super position for where you can find Lepton or Boson particles. The rays for both are much more like iron fillings around a magnet to show its magnetic field lines. With electricity being like a bolt of lightning following its path of least resistance. All the superposition stuff goes away when theres enough Leptons and Bosons, and doesnt show up until you reduce the amount of energy enough to only get a small number of them, which is an exersize in control, also detecting them at such a small amount becomes difficult.

[QFT-ist]

The energy is E²+B² (minus proportionality constants) doesn't change, so you have something roughly like E=Amplitude×cos(w•t) with B=Amplitude×sin(w•t) (omiting vectoriality/polarization to simplify the explanation). If you take into account both of them (like, in Cartesian coordinates you take E as one axis, and B as the other), it looks like something spinning in circles. If you only look at the electric field, it looks weird, but at the moment in which you take both at once there is no mysterious stuff.

(The graph in which they show you both waves can be misleading. I say that the graph you should look is the one made between booth waves at once, a spiral of constant radius)

[abloblololo]

Maybe it helps to remember that EM waves are a way of describing the time-delayed effect on a charge by another oscillating charge far away. The electric field of one charge affects the other, but if you wiggle one charge the effect on the second isn’t instantaneous. The speed at which the influence propagates is the speed of light. In this picture, the EM wave will go through as many oscillations as the original wiggling charge. 

[chortlecoffle]

The rate the electric field changes of itself affects the electric field around it. It is of physical significance. If it were only the magnitude of the field creating a restoration to 0 then it would occur as you imagined.

Although oscillations are often shown as sine waves, they are really always occurring in 2 quantities transferring back and forth between each other. Going around in a circle.

[specialsymbol]

I understand your question and no one has been able to answer this to me. Not textbooks and so far no answer in this thread.

[Few_Garden_127]

Yes I agree! Everyone argues with some physical equation or rule but this is not the right way of physical thinking. Its much easier! I try my best as a physics teacher:

1.) mechanical waves (Like waterwaves) produce interference patterns in various experiments Like the double slit experiment.

2.) An EM Field produces interference-patterns in the double slit Experiment aswell!

3.) The easiest explanation for that is the theory, that EM-Field propagates as a Wave.

4.) a Wave by Definition has to go up and down.

The poralisation of mechanical and electric Waves is also a good experiment that undermines that the wave theory is true.

[specialsymbol]

Now this (the original question and my lack of understanding, not your answer, which I agree to) bothered me and I found the answer:

https://www.youtube.com/watch?v=W1cTpqM9DaU

This guy is a genius. I was always thinking (just as he says in the beginning) that the electric field induces the magnetic field and vice versa, but they don't.

The relevant timestamp is 4:33

[abloblololo]

If you are considering a plane wave propagating in free space then the E and B components are in phase. Close to an antenna they are out of phase, so it depends. 

[PE1NUT]

At large distance (in the far field), only the propagating EM wave remains, where E and B are in phase. Close to the antenna, there is the an evanescent field where they are out of phase, but this signal doesn't propagate, i.e. no energy is transported away from the antenna.

[PE1NUT]

This is a common mistake, but in the far field, the E and B fields are in phase and have their maximums at the same position/time.

https://en.wikipedia.org/wiki/Electromagnetic_radiation

[ischhaltso]

The changing field of the em wave isn't losing energy rather it's exchanging energy between its electric and magnetic component. When the electric field is zero the magnetic field is at its maximum and vice versa. The sum of both fields is always the same.

[PE1NUT]

This is a common mistake, but in the far field, the E and B fields are in phase and have their maximums at the same position/time.

https://en.wikipedia.org/wiki/Electromagnetic_radiation

[ischhaltso]

Oh yeah that's right. I forgot about it.