Talk:Relativistic electromagnetism

Regrets (I have a few!)

I really wish Id not started this page now as it is too complex a subject to illustrate without diagrams that I cant draw! Suggestions on how to get out of this mess will be most welcome!--Light current 17:51, 30 April 2006 (UTC)

Diagrams will be inserted to illustrate the text ASAP--Light current 16:03, 21 October 2005 (UTC)

Having trouble getting the equations right. Please bear with me (or help!)--Light current 17:26, 21 October 2005 (UTC)

Lots more work needed on article especially with diagrams & equations. Please bear with me.--Light current 01:46, 22 October 2005 (UTC)

Started work on diagrams. Any help from persons with drawing packages gratefully recieved.--Light current 21:45, 22 October 2005 (UTC)

Request for help

I really need someone to help on improving my very basic (and not ver satisfactory) text based diagrams in this article. Any offers? You will be rewarded with thanks!!--Light current 00:30, 23 October 2005 (UTC)

Cut from article to be worked on

Using angle brackets to denote an average over all points on the shell,

�sin2 θ� = �1 − cos2 θ� = 1− �x2� R2 .

Now since the origin is at the center of the sphere, the average value of x2 is the same as the average value of y2 or z2: �x2� = �y2� = �z2�. (4.9)

But this implies that �x2� = 1 3�x2 + y2 + z2� = 1 3�R2� = R2 3

since x2 +y2 +z2 = R2 and R is constant over the whole shell. Combining equations (4.8) and (4.10) gives

�sin2 θ� = 1− R2 3R2 = 2 3. (4.11) 4.3

So the average energy per unit volume stored in the transverse electric field is

q2a2 48π2�0c4R2.

The physical basis of electromagnetic radiation

                \       wall 
                 \     |
                  \    |
                   \   |
                    \  |
                     \ |
                      \|B 
                      /|\
                     / | \
                    /  |  \ 
                  A/   |   \C  

Consider a positively charged particle, initially traveling to the right at 1/4 the speed of light. It bounces off a wall at point B. The particle is now at point A, but if there had been no bounce it would now be at C. An imaginary circle (actually a cross section of a sphere) encloses the region of space where news of the bounce has already arrived; inside this circle the electric field points directly away from A. Outside the circle the news has not yet arrived, so the field points directly away from C. As time passes, the circle expands outward at the speed of light, and points A and C move away from B at 1/4 the speed of light. The field at your location points away from where the particle would be now if there had been no bounce. We know from special relativity that no information can travel faster than the speed of light

Assume that the information travels at precisely the speed of light, but no faster. This assumption, together with Gauss’s law, is enough to determine the electric field everywhere around the accelerated charge. The complete map of the electric field of an accelerated charge turns out to be quite complicated. An abstract representation in terms of field lines will be used instead. Field lines are continuous lines through space that run parallel to the direction of the electric field. A drawing of the field lines in a region therefore indicates immediately the direction of the electric field.

A map of the field lines for the situation of figure is shown in figure . No field lines through the gray spherical shell in figure are shown, since this is the region that is just in the midst of receiving the news of the particle’s acceleration. To determine the direction of the field here, imagine a curved Gaussian “pillbox”, indicated by the dashed line in the figure, which straddles the gray shell. This surface is symmetrical about the line along which the particle is moving; but viewed from along this line, it would be circular.

The Gaussian surface encloses no electric charge, so Gauss’s law tells us that the total flux of �E through it must be zero.

The direction of the field within the gray spherical shell can be found be considering the flux through the curved Gaussian “pillbox” indicated by the dashed line. Now consider the flux through various parts of the surface. On the outside (right-hand) portion there is a positive flux, while on the inside (left-hand) portion there is a negative flux. But these two contributions to the flux do not cancel each other, since the field is significantly stronger on the outside than on the inside. This is because the field on the outside is that of a point charge located at C, while the field on the inside is that of a point charge located at A, and C is significantly closer than A. The net flux through the inside and outside portions of the surface is therefore positive. To cancel this positive flux, the remaining edges of the pillbox must contribute a negative flux. Thus the electric field within the gray shell must have a nonzero component along the shell, in toward the center of the Gaussian surface. This component is the transverse field, since it points transverse (i.e., perpendicular) to the purely radial direction of the field on either side. To be more precise about the direction of the field within the gray shell, consider the modified Gaussian surface shown in figure.

Since the flux along segment cd must be zero, the electric field within the gray shell must be parallel to this segment. until it subtends the same angle, as viewed from C, that the inner surface ab subtends as viewed from A. Now the fluxes through ab and ef do indeed cancel. Segments bc and de are chosen to be precisely parallel to the field lines in their locations, so there is no flux through these portions of the surface. In order for the total flux to be zero, therefore, the flux must be zero through segment cd as well. This implies that the electric field within the gray shell must be parallel to cd. If you start at A and follow any field line outward, you will turn a sharp corner at the gray shell’s inner edge, then make your way along the shell and slowly outward, turning another sharp corner at the outer edge. The thickness of the gray shell is determined by the duration of the acceleration of the charge.

A complete drawing of the field lines for this particular situation is shown in figure. The transverse portion of the electric field of an accelerated charge is also called the radiation field, because as time passes it “radiates” outward in a sphere expanding at the speed of light. If the acceleration of the charged particle is sufficiently great, the radiation field can be quite strong, affecting faraway charges much more than the ordinary radial field of a charge moving at constant velocity. The radiation field can also store a relatively large amount of energy, which is carried away from the charge that created it.

Strength of the radiation field.

A complete sketch of the electric field lines for the situation shown in the preceding figures, including the transverse radiation field created by the acceleration of the charge.

Consider a somewhat simpler situation, in which a positively charged particle, initially moving to the right, suddenly stops and then remains at rest. Let v0 be the initial speed of the particle, and let the deceleration begin at time t = 0 and end at time t = t0. Assume that the acceleration is constant during this time interval; the magnitude of the acceleration is then a = |�a| = v0 t0. Assume that v0 is much less than the speed of light, so that the relativistic compression and stretching of the electric field discussed above is negligible. Figure shows the situation at some time T, much later than t0. The “pulse” of radiation is contained in a spherical shell of thickness ct0 and radius cT. Outside of this shell, the electric field points away from where the particle would have been if it had kept going; that point is a distance v0T to the right of its actual location. (The distance that

R = cT v0T sin θ ct0 θ v0T θ

For clarity, only a single field line is shown here. it traveled during the deceleration is negligible on this scale. A single field line is shown in the figure, coming out at an angle θ from the direction of the particle’s motion. There is a sharp kink in this line where it passes through the shell, as discussed in the previous section.

The radial component Er of the kinked field can be found by applying Gauss’s law to the pillbox shown. How strong is the electric field within the shell? Break the kinked field up into two components: a radial component Er that points away from the location of the particle, and a transverse component Et that points in the perpendicular direction. The ratio of these components is determined by the direction of the kink; See that Et Er = v0T sin θ ct0 = aT sin θ c

We can find the radial component Er by applying Gauss’s law to a tiny pillbox that straddles the inner surface of the shell. Let the sides of the pillbox be infinitesimally short so that the flux through them is negligible. Then since the net flux through the pillbox is zero, the radial component of �E (that is, the component perpendicular to the top and bottom of the pillbox) must be the same on each side of the shell’s inner surface. But inside the sphere of radiation the electric field is given by Coulomb’s law. Thus the radial component of the kinked field is Er = 1 4π�0 q R2 , where q is the charge of the particle. Combining equations and using the fact that R = cT , it can be shown that Et = qa sin θ 4π�0c2R.

Looking back at the figure, we see that the size of the kink in the field is a qualitative indication of the field strength. Also, the strength of the transverse field is proportional to a, the magnitude of the particle’s acceleration. The greater the acceleration, the stronger the pulse of radiation. This pulse of radiation carries energy. The energy per unit volume stored in any electric field is proportional to the square of the field strength. This implies Energy per unit volume ∝ a2 R2.

Since the volume of the spherical shell (the shell itself, not the region it encloses) is proportional to R2, the total energy it contains does not change as time passes and R increases. Thus when a charged particle accelerates, it loses energy to its surroundings, in an amount proportional to the square of its acceleration. This process is the basic mechanism behind all electromagnetic radiation: visible light and radio waves to gamma rays.

The Larmor Formula

Energy radiated by a charged particle

In any electric field, the energy store per unit volume is epsilon_0/2 E^2

The total energy in the pulse is:

$Ep = \frac{e^2 a^2 t}{6 \pi \epsilon_0 c^3}$ where t is the duration of the acceleration

If we divide both sides by the duration t of the particles acceleration, we obtain the power: P.

$P = \frac{e^2 a^2}{6 \pi \epsilon_0 c^3}$

where a is the acceleration, e is the electronic charge, epsilon0 is the permittivity of free sapce and c is the speed of electromagnetic radiation This is the Larmor formula

If the direction in which the energy goes is not important, we can average equation (4.7) over all directions. Using a mathematical device, introduce a coordinate system with the origin at the center of the sphere and the x axis along the particle’s original direction of motion. Then for any point (x, y, z) on the spherical shell, cos θ = x/R.

To obtain the total energy stored in the transverse electric field, we must multiply equation by the volume of the spherical shell. The surface area of the shell is 4πR2 and its thickness is ct0, so its volume is the product of these factors. Therefore the total energy is Total energy in electric field = q2a2t0 12π�0c3 . The total energy is independent of R; that is, the shell carries away a fixed amount of energy that is not diminished as it expands. There is also a magnetic field, which carries away an equal amount of energy. Many details about magnetic fields have been omitted. A factor of 2 would need putting in. Thus the total energy carried away by the pulse of radiation is twice that of the previous equation or

When a charged particle accelerates, part of its electric field breaks free and travels away at the speed of light, forming a pulse of electromagnetic radiation. Often, in practice, charged particles oscillate back and forth continuously, sending off one pulse after another in a periodic pattern.

An example of the electric field around an oscillating charge is shown in figure. A map of the electric field lines around a positively charged particle oscillating sinusoidally, up and down, between the two gray regions near the center. Points A and B are one wavelength apart. If you follow a straight line out from the charge at the center of the figure, you will find that the field oscillates back and forth in direction. The distance over which the direction of the field repeats is called the wavelength. For instance, points A and B in the figure are exactly one wavelength apart. The time that it takes the pattern to repeat once is called the period of the wave, and is equal to the time that the source charge takes to repeat one cycle of its motion. The period is also equal to the time that the wave takes to travel a distance of one wavelength. Since it moves at the speed of light, we can infer that the wavelength and the period are related by

speed = wavelength period or c = λ T ,

where λ (“lambda”) is the standard symbol for wavelength, T is the standard symbol for period, and c is the speed of light.

Applications of radiation

Electromagnetic Waves

When a charged particle accelerates, part of its electric field breaks free and travels away at the speed of light, forming a pulse of electromagnetic radiation. Often, in practice, charged particles oscillate back and forth continuously, sending off one pulse after another in a periodic pattern. An example of the electric field around an oscillating charge is shown in figure. A B

If you follow a straight line out from the charge at the center of figure you will find that the field oscillates back and forth in direction. The distance over which the direction of the field repeats is called the wavelength. For instance, points A and B in the figure are exactly one wavelength apart.

If you sit at a fixed point and watch the electric field as it passes by, you will again find that its direction oscillates. The time that it takes the pattern to repeat once is called the period of the wave, and is equal to the time that the source charge takes to repeat one cycle of its motion. The period is also equal to the time that the wave takes to travel a distance of one wavelength. Since it moves at the speed of light, we can infer that the wavelength and the period are related by

speed =wavelength.period

or c = λT

where λ (“lambda”) is the standard symbol for wavelength, T is the standard symbol for period, and c is the speed of light. The frequency of an oscillation or a wave is the reciprocal of the period.

extracted/modified from Daniel V Schroeder paper

Diagrams

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Off the beaten track in Wikipedia

A click on the "What links here" toolbox link shows that this article is well off the beaten track in Wikipedia. This could be a reason to consider it for AfD. DFH 21:18, 21 November 2006 (UTC)

As the person who started it, I tend to agree with you. It was a mistake. But maybe some bits of it might be saved for use in other articles.--Light current 22:59, 21 November 2006 (UTC)

OTOH, maybe it could be pruned down to the bare min to explain the concept only. Other more knowledgable editors may then wish to expand it properly in the fullness of time!--Light current 23:18, 21 November 2006 (UTC)

How do we know that Purcell was the first to take this approach to electromagnetism & relativity ?

Are there any sources that show conclusively that this had never been done before Purcell ?

The reason I ask this is that I attended a brilliant lecture course in 1968 (yes - that's after Purcell) on electromagnetism & relativity in which the lecturer derived all of Maxwell's equations from just two postulates: the invarance of c (velocity of light) and e (charge of an electron) through all the standard transformations of special relativity. I don't recall any reference having been made to Purcell's work, though it's feasible that the lecturer had made use of some of his material. My suspicion is that the ideas go back a lot earlier than 1963. (Incidentally, I'm currently reading Subtle is the Lord by Abraham Pais – it was that which led me to browse Wikipedia for articles related to electromagnetism & relativity and hence find this one.) DFH 20:27, 23 November 2006 (UTC)

Thats what Daniel V Schroeder said in his paper on this subject.--Light current 23:41, 23 November 2006 (UTC)

In my 1956 edition of the "Encyclopaedia Britannica" (before Purcell) article on "electricty" v8, p159, it is shown how the "magnetic force" between two parallel wires of current is really an electrostatic attraction due to special relativity. However, the math only went as far to show qualitatively that special relativity demands: A/R = (i/c)^2 where A=attraction due to i, R = repulsion between free electrons. Understanding the connection is basic to a good theoretical understanding of special relativity. Feynman in his famous 1964 physics course derives this relationship in v2 13-6. Ywaz (talk) 17:45, 17 July 2010 (UTC)

Source material

Here [1] is the source material for this article. See if YOU can rewrite it--Light current 03:29, 1 January 2007 (UTC)

Another explanation on "The origin of magnetic forces"

I have a more simple explanation on "why" magnetic forces appear. However, I'm not sure whether it's correct or not:

Consider two identical charged objects with each with mass m moving at the same velocity v at a distance 2x from each other perpendicular to the velocity. Since their time slows down when they move, they repel each other less (slower) than we expect them to. Therefore, we say there's a magnetic force counteracting the repulsive electric force.

Mathematically: The objects' masses, charges and distance are the same in their reference frame as in the observer's. Due to time dilation, however, the acceleration - and therefore also the electric forces - observed in the observer's frame (primed) will be different:

$F' = m \cdot a' = m \cdot \frac{d^2x}{d(t')^2} = m \cdot \frac{d^2x}{dt^2} \cdot (t/t')^2 = m \cdot a \cdot \sqrt{1 - (v/c)^2}^2 = F \left(1 - (v/c)^2\right)$

The observer concludes that there must be a magnetic force accounting for the difference:

$F_m = F' - F = F \left(1 - (v/c)^2\right) - F = -(v/c)^2 F$

Pellishau (talk) 13:04, 18 January 2008 (UTC)

Electricity from magnetism?

This article describes how magnetic fields originate from electrostatics and special relativity. However, it is not apparent to me how the same principles can be used to explain how magnetic fields create electrical currents. This seems like an important subject that needs to be addressed to complete this article.

Just because when you have an electric field from magnetic one (relation can be reverse), you then have a voltage difference, or electromotive force. — Preceding unsigned comment added by Klinfran (talk • contribs) 08:00, 1 September 2011 (UTC)

192.104.67.122 (talk) 18:17, 4 August 2009 (UTC)db —Preceding unsigned comment added by 192.104.67.122 (talk) 17:05, 4 August 2009 (UTC)

Steve and anon BT CENTRAL PLUS, would you please continue this on your talk page (for instance at User_talk:Sbyrnes321/Electricity from magnetism—feel free to move the conversation), as this is obviously never going to end? This back and forth between you seems no longer on topic here, since this talk page is not meant for discussing the subject or someone's understanding or misunderstanding thereof—see WP:TPG. Thanks. - DVdm (talk) 23:01, 10 February 2011 (UTC)

Ummmm, "talk page is not meant for discussing the subject or someone's understanding or misunderstanding thereof—" ?

this is a discussion page unless i'm doing this wrong, and this article is currently focused toward 'Relativistic electromagnetism' as a teaching scenario, the physics is contained elsewhere,(although the title should emphasise that really.) so is also about comprehending, in that context i think this discussion has a great deal of relevance, if only to display some of the problems. if the page had no focus on education i would agree. —Preceding unsigned comment added by 86.175.125.189 (talk) 00:35, 11 February 2011 (UTC)

Well I agree with DVdm, I started User talk:Sbyrnes321/Electricity from magnetism. :-) --Steve (talk) 01:30, 11 February 2011 (UTC)

Ok, I have collapsed the section again. As anon seems not to be prepared to adhere to talk page guidelines (no signatures and improper indentation), the above has become as good as unreadable anyway. Enjoy over there. Cheers - DVdm (talk) 12:20, 11 February 2011 (UTC)

I'm thrilled to see my original comment started such a discussion. My poor wording drove the discussion in a different direction than I intended. I agree the electricity and magnetism are the same thing looked at from two different viewpoints. But from a practical aspect, to make this point clear you need to start with one and derive the other. This article does that by starting with ampere's law and lorentz contraction combined with some vector mechanics to show that magnetism is the same as electricity. Instead of stating that the article should address how "magnetic fields create electrical currents", I should have said that the article should include a vector analysis using the principles already presented that shows why an accelerating or decelerating electrical charge field induces a neighboring electrical charge field to accelerate or decelerate. (or that an accelerating or decelerating electrical charge field resists its own acceleration or deceleration) — Preceding unsigned comment added by 192.104.67.222 (talk) 14:41, 30 November 2011 (UTC)

Education and training

This article relates to the education and training of electrical and electronics engineers. The references show that in the 1960s there was a move to introduce special relativity into the teaching of electromagnetic fields. The textbook by Corson & Lorrain was perhaps the apex of this movement. Since the symmetries of relativity are exactly the symmetries of the EM field, there is good reason to treat the subjects together. However, at most, this program of study provides some intuition on how magnetic and electric fields are observer-dependent. Full derivation of the Maxwell equations is an overstatement. Some investigation is necessary to find why this initiative did not take hold. Edits to the page from today could expand from Purcell to the other sources, and explore engineering and physics education for traces of the movement.Rgdboer (talk) 01:53, 19 November 2009 (UTC)

The additional sources are now mentioned in the lead. Further, A. Einstein's comment on magnetism being electrical has been quoted and sourced. Scanning the sources for appropriate lesson plans may produce material to improve the article.Rgdboer (talk) 03:19, 20 November 2009 (UTC)

Origin of magnetic force

I very doubt about the contraction of lenght that is exposed to talk about the origin of magnetic force, as it is described in most book. Why? First because the case is the one of an infinite wire, thus with an open finite wire, because of conservation of charges, if the whole negative lign, for example, contracts, then the tips will be positive, if you apply it to a closed loop, as there is speed of electron everywhere, and no motion of protons, you will have charge accumulations on some parts, very strange that charges are uniformly reparted in one frame and concentrated in another, this could be because of simultaneity, but simultaneity and time dilation could work in the opposite because charges have a certain pace, regular, to cross the wire section, and accelerate at each angle of the wire. Secondly does this contration is in addition to the transformation of electric field of each charge, that is also an outcome of lenght contration, then does both effects accumulate? This needs a simulation, because books have been written a long time ago.Klinfran (talk) 07:57, 1 September 2011 (UTC)