## Field Propagation

### Questions:

• How does an Electromagnetic Field Propagate
• How does a Gravitational Field Propagate
• What are the differences
• How strong is the Electromagnetic Force

### Purpose

The purpose of the first question is to decide how an Electromagnetic field propagates for a charged particle which moves at a high velocity. The same is true when an Electromagnetic field is studied over very long distances. Only when that question is clear the second question can be answered.
The fourth question IMO is the most important one. Only by studying Electromagnetic Forces the first question can be answered.

### Experiment with a charged particle.

In order to find the answer how the field of a charged particle propagate let us perform three experiments and study if we agree among its outcome.
Starting setup of each experiment is a grid at rest.
```                                  y axis
. 0,3

. 0,2

q+. 0,1
q-   -->
.       .       .       .       .       .       .       .       .  x axis
-4,0    -3,0    -2,0    -1,0    0,0      1,0     2,0     3,0     4,0
```
The above figure shows a grid of 12 points, 9 on the x axis and 4 on the y axis
At each of those points there is also a clock. This clock is important for the second and third experiment.
1. The first experiment is what we call the calibration experiment. This experiment consist of 9 subtests. In subtest 1 there is a charge q- at position -4,0 and a charge q+ at position 0,1. In subtest 2 the q- is at position -3,0. Finally at subtest 9 the q- charge is at position 4,0. At each of those positions the force F is measured at q+ and at q-.
Each of those subtests will show that the force F at q+ is in the direction of q- and the force F at q- is in the direction of q+.
2. The second test is almost identical with the difference that the q- is moved with a fast but constant speed along the x axis (Starting point of this movement is to the left of point -4,0). This speed is measured with the aid of clocks along the x axis. The point 0,0 is reached at noon.
The question is are the result of the 9 subtests of experiment 1 and 2 identical ?
3. In the second test q- moves on a straight line. In the third test q- moves on a circle. Only the point 0.0 will be identical as in test 2. Point 0.0 will be reached at noon.
The question is are the result at point 0,0 of experiment 2 and 3 identical ?

### Literature

1. Mechanics, radiation and heat / Richard P.Feynman; Robert B Leighton; Matthew Sands. Reading, Mass.: Addison-Wesley,1971 (The Feynman lectures on Physics 1)
Chapter 28: Electromagnetic Radiation
2. Electromagnetism and matter / Richard P.Feynman; Robert B Leighton; Matthew Sands. Reading, Mass.: Addison-Wesley,1975 (The Feynman lectures on Physics 2)
Chapter 21: Solutions of maxwell's Equations with Currents and Charges
Chapter 26: Lorentz Transfomations of the Fields
3. Electricityand magnetism / Edward M. Purcell. New York, N.Y.: McGraw-Hill, 1965 (Berkeley physics course 2) LC 64-66016
Chapter 5: Fields of Moving Charges
5.6 Field of a Point Charge Moving with Constant Velocity
5.7 Field of a Charge that Starts and Stops
4. Classical electrodynamics / John David Jackson - New York:Wiley 1962 LC 62-8774
Sect 11.10 Special Theory of Relativity pages 553-556
5. Pictures Of Dynamic Electric Fields. / Roger Y Tsien, American Journal of Physics Volume 40, January 1972 page 46-56

### Answer part 1

Literature shows that the answer on question 1 and 2, in relation to direction is the same.

Literature 3 at page 160 specific gives the following answer:
Therefore we can say .. that the electric field of a charge in uniform motion, at a given instant of time, is directed radially from the instantaneous position of the charge, while its magnitude is given by:
 ``` Q (1-Beta˛) E = -- * --------------------------- r˛ SQR(1 - Beta˛*sin˛(Theta))^3 ```
With "Theta" the angle between the direction of motion of the charge and the radius vector from the instantaneous position of the charge to the point of observation

Literature 2 at page 160 also tells the following:
Pause a moment to let this conclusion sink in! It means that if Q passed the origin .. at precisely 12:noon, an observer stationed anywhere .. will report that the electric field in his vicinity was pointing, at 12:noon, exactly radially from the origin. This sounds at first like instantaneous transmission of information! How can an observer a mile away know where the particle is at the same instant? He can't. That wasn't implied. This particle, remember, has been moving at constant speed forevever, on a "flight plan" that calls for it to pass the origin at noon.

### Answer part 2

The last part of the quotation, after "This sounds at" does not improve our understanding. What the above equation tells us, is:
• That all the observers at the y axis, the points (0,1), (0,2), (0,3) etc, will detect the maximum electric field at the same time (for example: at noon), by reading of their clocks. Not only that, that is also the same time when the particle reaches the origin, point (0,0). No transfer of information is required and specific no faster than light transfer of information.
• That it gives us the possibility to synchronise our clocks (along the y axis)
The question is, if both are true.
IMO this is not true.

### Answer part 3

IMO what the outcome of the experiment 1 and 2 will demonstrate is:
• that there is no difference for an observer at q-. The observer q- moves through an electrostatic field generated by q+.
• that there is a difference between the electromagnetic force for the observer at q+
When q- is at 0,0 q+ will detect that the force comes from the retarded position.
Litterature almost only discusses the Electric field. The main question is: is it possible by performing any experiment that demonstrates that the pictures drawn of the Electric field (and for the Magnetic field B) each are correct.
IMO that is not possible for a moving charge.
The only thing that we can measure is the direction and size of the force F
And if we do that we will also see that we cannot synchronise the clocks on the y axis. The only (?) document that discusses this is Literature 2 at page 26-5.
"Imagine two electrons Q1 and Q2 with velocities at right angles, so that one will cross over the path of the other, but in front of it, so they don't collide. At some instant, their relative positions will be as in Fig 26.6."
Fig 26-6 shows the following:
 ```F1 . ^q1v1*B1 . | . | q1E1 . | v1 q2E2=F2 <------Q1-----> Q2-------> B1 | |v2 | V ```
Next is written in the text: "On q2 there is only the electric force from q1, since q1 makes no magnetic field along its line of motion. On q1, however, there is again the electric force but, in addition, a magnetic force, since it is moving in a B field made by q2"

The problem with above sketch is that it is not clear if anything related to the particles their "retarded position" is included. This does not seem the case. IMO that is wrong.

### Answer part 4

The most important experiment is experiment 3, because the outcome of that experiment can be used to compare Electromagnetic forces with Gravitational forces and as such to study the movement of planets.

### Answer in the book Gravitation

The book GRAVITATION by C.W.Misner, K.S.Thorne and John.A.Wheeler figure 4.6 at page 111 gives an answer on the first question.

Figure 4.6 shows the electric field after a particle has moved: from a starting position

• first a distance dx at uniform velocity v to the left and
• secondly with the same uniform velocity, the same distance dx to the right, back to the starting position.
The change of velocity from +v to -v causes a disturbance, and this disturbance moves (radiates away) at speed c, centered at the point from where the velocity change occured.
The field lines start at the current position (final position, starting position). In figure 4.6 there are the same number of field lines in each quadrant. The field lines move towards the disturbance, "swing" through the disturbance and than continue behind the disturbance.
Behind the disturbance the field lines are centered from a point as if the particle continued to move in a straight line.
In effect the field lines behind the disturbance have the same shape as if the particle followed a straight line all along and as if the particle has no velocity or the speed of the field is infinite.

The follow up questions are here:

• what is the shape of the field when the path of the particle is curved,
• what is the strength of the field along the field lines, is it related to 1/r^2,
• and if so what is r.

In order to answer these questions I have redrawn the field lines accordingly to a different concept (Methode 2): All points from the field are centered from the position from where they were emitted and are drawn equally spaced. Together those points form the field lines. The direction of the field lines is implicit
In Methode 1 the direction of the field lines is fixed and the field points are implicit.
The major differences with figure 4.6 are:

• The number of field lines in each quadrant is not any more the same (in effect when the particle moves to the left the field lines have a tendency to move to the right) and
• The "swing" through the disturbance becomes a simple bent.
What did not change is the following:
• The overall shape of the disturbance is the same and is centered at the point where the velocity change occured.
• Behind the disturbance the field is the same as if the particle followed a straight line all along.
• Behind the disturbance the field lines originate from a point as if the particle followed a straight line all along.
• The size of the field is the same (compared over the same period)

### Field Radiation

A comparison of the two methodes is done with the program: RADIATE.BAS. Select: Field Radiation

For a copy of radiate.exe select:15prog.zip 58k.

This program performs a simulation of the 2 methodes.
For each methode the particle can move:

• In a straight line, towards the left.
• In two straight lines, one to the left and one to the right. This is the same as figure 4.6
• In a curved line, towards the left. This movement is more according to reality.

### Reflection part 1

Methode 2 is the most simple and allows you to draw the field of a bending particle. What is most interesting that the size of the field after each generation is the same implying that the major difference of the two methodes is position of field points on each circle.
Still the following questions require to be answered:
1. Is Methode 1 the correct representation of an Electromagnetic field
2. Is Methode 2 the correct representation of an Electromagnetic field
3. If neither what is
4. Is Methode 1 the correct representation of a Gravitational field
5. Is Methode 2 the correct representation of a Gravitational field
6. If neither what is

### Reflection part 2

The same subject is also discussed in the book: "Astronomy and Cosmology - A Modern Course" by Fred Hoyle. At page 239 radiation from atoms moving to the left is discussed. The picture drawn is accordingly to methode 2 i.e. the field lines have a tendency to point towards the right. The angle theta discussed is a function of the speed v. IMO this figure is in conflict with the book Gravitation by MTW.

### Feedback

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Created: 4 May 1999
Last modified: 5 November 2000

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