# Stupid electromagnetics question

In an electric wire, the E field is contained within the wire. The E field operates between the electrons moving at the surface and the atomic nuclei inside.
A distinction must be made between the mathematical theoretical Gaussian general description of an E field and an actual E field, and the same for the B field.
In a transformer, you feed an alternating current into the primary winding wire, meaning that the flow of electrons will reverse cyclically in the primary wire. But it is the associated fluctuating B field about the primary wire that induces motion of electrons into the secondary wire winding.
To produce an real E field external to a wire, you need to charge surfaces, one with atoms maintained into an electron depleted state, that will then be electrically positive and the other with excess electrons that will then be electrically negative.
An E field will then be present between these plates.
In a Betatron, you accelerate charged particles with such an E field, but you need a very precisely calibrated B field (separately produced by electromagnets) to contain them on the very precise circular path.
In linear accelerators, you need to calibrate both E and B fields such that v=E/B for the path to be straight
Ref "Principles of Charged Particle Acceleration" by Stanley Humpries.
André Michaud
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On May 11, 8:30 am, snipped-for-privacy@microtec.net wrote:

The distinction is that the actual field is not an E field, it is an em field. Wether it is describable in terms of E and/or B is a matter of relative motion, meaning that E and B are frame dependent fields and by virtue of that fact they cannot be representative of reality. It is only those things that are invariant that even have hope of being described as real causes.

The B field is a composite E field. Again, see Purcell.

The E field is a mathematical representation of the force that a group of charged paticles exerts on point charges. It is no more than that, and no less. The B field consists of E fields with opposing vectors producing a net lateral force on point charges in motion with respect to the sources of those crossed E fields. All conductors consist of both negative and positive charges, thus at least two E fields are associated with any conductor. In current carrying conductors those two charge components are moving relative to each other, giving rise to the velocity dependence of the effect known as the B field. This effect is in turn produced via relativistic changes to the apparent charge densities of those two components in the conductor with respect to the external moving charge.

Which can be translated as "a very precisely calibrated set of E fields (separately produced by electromagnets) to contain them on the very precise circular path".

All of the E fields.

Don't give a damn about such references :)
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snipped-for-privacy@microtec.net wrote:

Correct. It's often called a "capacitor" if configured to conform to circuit theory approximations.

Yes.
No not correct. In a betatron (which as Salmon egg pointed out is a relativistic device capable of accelerating electrons very close to the speed of light) electrons are NOT accelerated by an electrostatic E field. Allow me to quote the freshman physics text, Resnick and Halliday, 1960 ed. p 756.
" The induced electric field that are set up by the induction process are not associated with charges but with a changing flux. Although both kinds of electric fields exert forces on charges there is a difference between them."
And at p 757.
" Electric fields associated with stationary charges are *conservative*, but those associated with changing magnetic fields are *nonconservative*. Since electric potential can only be defined for a conservative force, it is clear that it has no meaning for electric fields produced by induction as in a betatron."
Dare I say it? So much for the famous "one E field" dogma!
Of course there are lots of side engineering issues in betatron design including focusing the beam, keeping the beam circulation in its "doughnut" vacuum tube at a constant diameter, and injection and extraction of the beam at the right time. But these are details that do not impinge on the statements above.
Benj
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My blunder, thanks. I was thinking generally.
I noticed Salmon egg comment after I answered.
I also have this quote regarding the 100 Mev GE Betatron from Halliday and Resnick (I have the 1967 edition), page 884
"The magnetic field in the betatron has several functions: (a) it guides the electrons in a circular path; (b) it accelerates the electrons in this path; (c) it keeps the radius of the orbit in which the electrons are moving a constant; (d) it introduces the electrons into the orbit initially and removes them from the orbit after they have reached full energy; and finally (e) it provides a restoring force that resists any tendency for the electrons to leave their orbit, either vertically or radially. It is remarkable that it is possible to do all these things by proper shaping and control of the magnetic field."
It is a pity that the GE betatron is no longer in operation. I would very much have liked that more experiment would have been carried out regarding the unexplained energy loss reported by John P. Blewett. in his paper "Radiation Losses in the Induction Electron Accelerator", Phys. Rev. 69, 87 (1946).

What I have page 885 (possibly the same quote revised ? )
"The electrons are accelerated by electric fields set up by the changing flux [The current in the GE Betatron coils was made to reverse 60 times per seconds] "

Couldn't locate your quotes in my 1967 edition. Could you refer me to chapters and section numbers ?

Right. All issues apparently dealt with by the magnetic field as H&R quote.
André Michaud
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snipped-for-privacy@microtec.net wrote:

It's Chapter 35; Section 35-7 "The Betatron"
My guess is that as time went on and Betatrons fell out of favor as accelerators, the betatron stuff in the book was dropped or much reduced.
Heh. Here's a great story! At one point many years ago I was offered the Betatron at Case Western Reserve University FREE!!! It was a cute little machine quite a bit smaller than the GE monster in the H&R photo, but still weighed tons due to the iron. All I had to do was haul it away! Happily I came to my senses in time and turned them down!
Benj
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Cool, I got it!
In my edition, it became section 35-6 (3 pages worth)
Your quote about conservative-nonconservative is the last sentence of the previous section (35-5 Time-Varying Magnetic fields)
What I gather from nonconservative bit is simply that E fields associated with changing magnetic fields transmit energy to the test charge, causing it to change its state of motion. changing magnetic field

It is a fact that not much can be found on this wonderful device.
Humphries book "Principles of Charged Particle Acceleration" that I gave a reference to earlier does pretty much cover all aspects of betatron operation.

No kidding ! What a loss! Do you remeber how many tons ? Would you know if they still have it ?
Darn! I must be losing my own senses right now!!!
André Michaud
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On 5/10/07 10:51 PM, in article snipped-for-privacy@o5g2000hsb.googlegroups.com, "RP"

If that is the case, explain how betatrons work. Betatrons, for all you you youngsters, were electron accelerators using a magnetic field to drive them.
At the guts of this is that the electromagnetic field is a consolidated concept of electric and magnetic fields. This combination is a 4 by 4 tensor that is invariant under the Lorentz transformations of special relativity. The components may change values in different uniformly moving coordinate systems, but represents the sam electromagnetic field in all these coordinate systems.
Bill -- Fermez le Bush--about two years to go.
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boost, not accelerat
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Depending on your point of view:-)Actually your question is a very smart one.Maybe it's God's will (or a higher being's) that we can't get energy for free (there's no such thing as a free lunch).Because then we could place a piece of wire in Earth's magnetic field and get electricity,plenty and free, wouldn't we? But maybe He doesn't want to spoil us;-)So we have to rotate generators with prime movers, which on their turn need some fuel....Fuel costs money, and their supply is limited....Google for the perpetuum mobile, for an encore....
-- Tzortzakakis Dimitrios major in electrical engineering mechanized infantry reservist dimtzort AT otenet DOT gr
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wrote:

Fool, learn what induction is. There is already a current in such a field in other media, magnetic or Coriolis or otherwise. It's not much thouh.
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I'm having some trouble getting my head around this:

for
free,
Fool, learn what induction is. There is already a current in such a field in other media, magnetic or Coriolis or otherwise. It's not much thouh. <end quote> Might be, but then, who am I, to tell right from wrong?
-- Tzortzakakis Dimitrios major in electrical engineering mechanized infantry reservist dimtzort AT otenet DOT gr
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The fields produced by the charge and current are the D and H fields. The fields *experienced* by the charge and current are the E and B field.
In a vacuum or near-vacuum, the two sets are linearly related (D epsilon_0 E, B = mu_0 H); but not necessarily so -- even in a vacuum when very close to a charge, to the point of practically being on top of it. Confusion may result from failing to distinguish sufficiently these two sets of fields.
If there were such things as magnetic charges and currents, it would be other way around: the E and B fields would be those produced by magnetic charges and currently, while the D and H fields would be those experienced by the magnetic sources.
*That* is the symmetry you're alluding to! It's not there, because magnetic sources are not known to exist.
In this light, this will also help make more sense of the units in electromagnetism. The units of electric and magnetic charge are, respectively, Coulomb and Weber. The corresponding units of their currents would be Coulomb/second and Weber/second, which are respectively termed the Amp and Volt.
Electric potential has the same units as magnetic current (and vice versa, magnetic potential is equivalent in units to electric current). Older technology, in fact, used such things as magnetic circuits. Though there are no magnetic monopoles, it's still meaningful to talk about effective magnetic currents and the like.
This, in turn, will help further make sense of the three fundamental linear circuit elements and their corresponding units. A resistor and conductor are measured, respectively, in Ohms and Mhos (and a Mho which is Ohm spelled backwards is now called a Siemens). An Ohm is a Volt/Amp or Weber/Coulomb; a Mho a Amp/Volt or Coulomb/Weber.
A capacitor stores electrical energy and has a law of the form I = C dV/dt (or Q = CV). The units of the capacitance (C) are Farad Coulomb/Volt or, equivalently, Amp-second/Volt or Coulomb-second/ Weber. An inductor stores magnetic energy and has a law of the form V = L dI/dt. If there had been an actual magnetic analogue of a capacitor, it would have an analogous behavior to an inductor and satisfy the same relation, only now with V interpreted as magnetic current, and I as magnetic potential. So, the units of inductance (L) are Henri = Weber/Amp = Volt-second/Amp = Weber-second/Coulomb.
In the presence of magnetic sources (with charge density s, current density K) and electric sources (charge density r, current density J), the field laws would read:
div D = rho; curl H - dD/dt = J div B = sigma; curl E + dB/dt = -K
the force density would be
F = r E + J x B + s H - K x D
and the power density
P = J.E + K.H
where (x) denotes vector cross product, and (.) scalar product, and d/ dt the partial derivative with respect to time.
In terms of fluxes and circulations, let V denote a volume, and dV the surface bounding the volume associated with an outward orientation. Let S denote a surface, with a given orientation attached to it, and dS the boundary of the surface equipped with an counter-clockwise orientation around the surface, when the surface is oriented with its "top" side up.
Denote by D(S), B(S), I(S), K(S) respectively, the fluxes of D, B, J and K with respect to a given surface S. Let Q(V), P(V) denote the total charges (corresponding, respectively, to electric charge density r and magnetic charge density s) contained in a volume V. Let E(C) and H(C), respectively, denote the circulations of E and H along an oriented curved C.
Then the 4 equations above read:
D(dV) = Q(V) -- Gauss' Law for electric charges B(dV) = P(V) -- Gauss' Law for magnetic charges H(dS) = d/dt D(S) + I(S) -- Ampere's Law for electric currents -E(dS) = d/dt B(S) + K(S) -- "Ampere's Law" for "magnetic currents"
In the absence of magnetic sources, you have the asymmetry your original question referred to:
B(dV) = 0, while D(dV) = Q(V) E(dS) = -d/dt B(S), while H(dS) = d/dt D(S) + I(S).
There's nothing "static" relating to E(dS), as I(S) does to H(dS).