# Solving EM Field Questions: Understanding Retarded Potentials

• Dathascome
In summary: I don't think that's what he means.In summary, the electric field takes values (possibly zero values) at every point in space, and these values generally change in time.
Dathascome
Hi there,
This year I finished two semesters of E&M, and think I understood much of it but had something of a problem understanding something concering fields and EM waves. Something always seemed sort of odd to me when reading about retared potentials and how it takes time for the field to travel, I tried explaining my problem to the professor (who happened to be one of the best I've ever had) but I don't think he knew what I meant, or maybe my question just didn't make sense.
So what bothered me was how the EM field travels. At first when you learn about static fields you learn that they are instantly transmitted. Then you learn that actually they travel at the speed of light, and in the form of a wave. So for example I have a long straight wire where the current was just turned on. It will take time for the field to travel out so I have a sort of double cone (two cones with the round sides touching) of where the field has gotten to which depends on the speed of light and how long I've waited after turning it on. So the field travels out in a wave right? And after a long enough time the parts closer to the wire wil start to only have the typical static mag field of a long straight wire. The wave part dies down near the wire and there's just a field there now? Before the field needed to travel out there in a wave, but after it is just maintained there, and there's no more waves emenating from the wire? I have a feeling that this may not makes sese but oh well.
Another thing that confused my about this was reading feynman's lectures. At some point he says " The electromagnetic field can carry waves...", This totally through me off. Is he trying to say that the EM field is the medium through which the waves are travelling? I thought that the EM field isn't there until the wave goes by? I thought there was no medium needed for it to travel though?
Is it wrong of me to think of the EM waves as sort of carryying the field to everywhere in space?
I'd really like to understand this and any help would be greatly appreciated. thanks.

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The EM field takes values (possibly zero values) at every point in space, and these values generally change in time. (Relativistically, the EM field takes values (possibly zero values) at each event in spacetime.) So, in this sense, the field is always there.

The "wave" is a disturbance of the field, that is, a certain type of configuration of the field, ... that's what propagates.

I don't know if I go for this (the fist part at least, the second sounds ok). Doesn't it take time for the field to travel out from the wire? I don't have the book on me now, but I did problems this past semester from griffith's book in like chapter 11 or something where we talk about the retardation of the field and how it takes time to travel a ditstance where the speed it travlels at is c. Am i sorely mistaken, or just remembering wrong?

Dathascome said:
I don't know if I go for this (the fist part at least, the second sounds ok). Doesn't it take time for the field to travel out from the wire?
Yes, it does.
However, you seem to be hung up on the idea that the field only exists when it is nonzero. Note as well that if the electric field vector is zero at a point, the electric potential is [locally] constant, which could be nonzero.

Dathascome said:
I don't have the book on me now, but I did problems this past semester from griffith's book in like chapter 11 or something where we talk about the retardation of the field and how it takes time to travel a ditstance where the speed it travlels at is c. Am i sorely mistaken, or just remembering wrong?
Sounds ok.
So, this means that if you suddenly "turn on" a point charge (or, maybe more realistically, momentarily displace a point charge), then its effect [the disturbance of the field.. that is, the information about the new configuration of the field near that charge] travels out as you say. It also means that if you suddenly "turn off" that point charge, then its effect [a similar disturbance of the field] also travels out.

As I said above, the field exists everywhere in space, even in regions where the field is zero.

I think you're I do sort of have a problem with that. I get what you're saying about the potential and all, but if at a point the electric field vector is zero that isn't it not at that point (even if it's just momentarily)?
The other problem I think I have is with you saying that "...in this sense, the field is always there", but then also agreeing that it takes time for the field to travel out (say from a wire or something). I understand the point about displacing a charge and it taking time for the disturbance to travel, but what about a situation where I just brought this charge in, or, I have a long straight wire and then set up a current in the wire? What happens right after I turn it on? The EM field can't instantly be everywhere because it travels at the speed of light and takes time to get everywhere no? Isn't this different than just having a charge and the displacing it?

Dath-

It's the *changes* in the field which take time to propogate. The static
fileds are "already there" at the remote points because the experiments
(we are thinking about) are set up that way.

Right,so if it's the change in the field that takes time to propagate, then having a long straight wire with no current in it will not create a field, I send a current though and both and electric and magnetic field wil start to propagate, there is a change in the field right? First there is no field because there is no current, I set up a current, (which will create a change in the field, from no field to field) and this change propagates. So first I have no field anywhere then after some time I do. So the field is not instantly there at some point in space.After some time these fields will become like static fields.
I understand that if I have some experiment set up where there is already a field then the change will propagate, but I don't understand what happens when I first set up the field (introduce charge or a current or something).
I'm sorry to keep going on, I just don't see what's wrong with my logic and really want to

Actually, you understand it well.

Pretend that you burn wood and use the heat to turn a generator which
charges a battery. As the battery charges slowly there will be a field near the
battery terminals which slowly changes. This change will move away from the
battery in all directions at the speed of light. If the wood runs out, the field
is still there and the change (which has stopped) is still moving away from the
battery terminals at the speed of light.

## 1. What are retarded potentials?

Retarded potentials are a concept in electromagnetism that describes the electromagnetic fields generated by a moving charge. They are calculated based on the position and velocity of the charge at a previous time, taking into account the time it takes for the electric and magnetic fields to propagate through space.

## 2. How do I solve EM field questions?

Solving EM field questions involves using mathematical equations and principles from electromagnetism, such as Maxwell's equations and Coulomb's law, to calculate the electric and magnetic fields at a given point in space. It also requires an understanding of how these fields interact with each other and with charges in the vicinity.

## 3. What is the difference between electric and magnetic fields?

Electric fields are created by stationary or moving charges, while magnetic fields are created by moving charges. Electric fields are responsible for the attraction and repulsion of charges, while magnetic fields are responsible for the force experienced by moving charges in a magnetic field. Both fields are interrelated and can produce each other under certain circumstances.

## 4. How does the speed of light factor into retarded potentials?

The speed of light is a fundamental constant in electromagnetism and plays a crucial role in the calculation of retarded potentials. The time it takes for the electric and magnetic fields to propagate through space is determined by the speed of light, and this is taken into account when calculating the fields at a given point in space.

## 5. Can retarded potentials be applied to real-world situations?

Yes, retarded potentials have numerous applications in real-world situations. They are used in the design and analysis of electromagnetic devices, such as antennas, motors, and generators. They are also used in the study of electromagnetic waves, such as radio waves and microwaves, and in the understanding of the behavior of charged particles in electric and magnetic fields.

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