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/What is wrong with the flux cutting model?
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Γ dτ
Waveguides with certain symmetries may be solved using the method of separation of variables. Rectangular wave guides may be solved in rectangular coordinates. [2]: 143 Round waveguides may be solved in cylindracal coordinates. [2]: 198
Talk:Speed_of_electricity#Incorrect section: Speed of electromagnetic waves in good conductors
Some text with strike through.
Talk:Displacement current#Untrue assumptions in the “Current in capacitors” sub section
This section may be
confusing or unclear to readers. In particular, the known variables and the unknown variables of the system of equations is not clear. The rules given do not cover the case where two loops share nodes, but neither contains the other.. |
********************************************************************************
This topic should always be on the top.
curl E = -∂B/∂t
curl H = ∂D/∂t + Jconduction + Jsource = curl H = ∂D/∂t + σE + Jsource
User:Constant314/Tow-Thomas active filter
Add alternate explanations of skin effect.
Add magnetic vector potential to the transformer page.
The solutions of the telegrapher's equations [3]: 381–392 are functions of two parameters which are the propagation constant, , and the characteristic impedance, . The propagation constant is often written as where is called the attenuation constant and is called the phase constant. The natural units for and are nepers per unit length and radians per unit length, respectively.
There are two solutions which can be interpreted as a forward propagating wave and a reverse propagating wave. The forward wave, which has a voltage of and a current of , is given by:
The reverse wave, which has a voltage of and a current of , is given by:
where
The negative sign in the expression for indicates that the current in the reverse wave is traveling in a direction that is opposite to the reference direction, which is the direction of the forward propagating wave. and are secondary parameters which means that they can be expressed in terms of the primary parameters and .
The propagation constant and the characteristic impedance may be factored as
where
where The terms and are relatively independent of frequency. The frequency dependent behavior of and can be separated into nine regions according to whether the ratios and are much less than unity, much greater than unity or about equal to unity. In practice, four of the combinations do not occur leaving five regions from DC to high frequency.
The graph to the left shows the frequency dependent variation of and of a transmission line with a good dielectric such as high density polyethylene. Separation of the spectrum into regions has been arbitrarily set at the frequencies at which one of the ratios is either 0.1 or 10.
The five regions may be easily seen in the adjacent graph of velocity versus frequency of a transmission line with a good dielectric such as polyethylene:
From lowest to highest frequency the regions are:
The high frequency regime is most associated with transmission line behavior. It includes Ethernet, most broadcasting, ordinary video, computer buses, the higher portions of the digital telephony spectrum ( HDSL, ADSL, VDSL).
The intermediate frequency regime includes the lower portions of the digital telephony spectrum ( ISDN, HDSL, ADSL, the upper frequencies of music,
The low frequency regime includes voice telephony, the lower frequencies of music,
The very low frequency regime includes
If then there is no near DC regime. This is the case if the dielectric is vacuum.
The near DC regime expressions approach their DC values as frequency approaches zero, except wavelength which approaches infinity.
The near DC regime expressions approach their DC values as frequency approaches zero, except wavelength which approaches infinity.
The following gallery shows the frequency dependence of some of the other secondary parameters.
This involves a slight bit of synthesis from Brenner and Javid. Page 599 gives i2/i1 = 1/n and 1/n = n1/n2 which can be combined by simple arithmetic to give i1n1 = i2n2 or i1n1 - i2n2 = 0.
Hayt & Kemmerly in Engineering Circuit Analysis, 5'th on page 446 state plainly that i1n1 = i2n2, but it doesn't seem worth adding a reference for that.
(i1n1 - i2n2) is the magnetomotive force, using the current reference directions given in the figure in the same section.
First, an analogy. I can compute the velocity of my car by computing the time derivative of the number displayed on the odometer. That doesn’t mean the odometer causes the car’s velocity. The relationship holds because they are both caused by the same thing, which is the motor. Faraday's law of induction (FLI) states that the EMF (path integral of the electric field) in closed loop is proportional to the time derivative of the total flux the enclosed in the loop, including the flux in the core. This is a very useful relationship for designing transformers and predicting their behavior. This doesn’t mean that the flux in the core causes the EMF in the secondary, although it is often taught that way. Most of the time, that is good enough. But, in fact, if the flux in the core actually caused the EMF in the secondary, that would be action at a distance. Feynman makes this point in Volume 2 of the Feynman lectures, chap 15 section 5 in the second paragraph following equation 15.36.
Modern physicists have worked very hard to eliminate action at a distance. The modern formulation is that the currents produce the magnetic vector potential, A, at the wires. A produces a component of the electric field, E in accordance with E = -∂A/∂t (actually E= -∇φ -∂A/∂t, but I am ignoring φ). The line integral of -∂A/∂t over a closed path is the EMF. Faraday’s law of induction (FLI) works because B = ∇ × A; E at the wires has the same cause as B in core. FLI is useful for engineers because they almost always have the transformer connected to a circuit which provides a complete path. However, E = -∂A/∂t, gives the E field at each infinitesimal part of the path.
I am not going to try to put this in the article; it is probably too technical. I’m going for WP:RIGHTGREATWRONGS, but I will try to edit the article so it is not in conflict with the modern formulation. For example, instead of “EMF is caused by the changing flux in the core” I may write “EMF is equal the rate of change of the flux in the core.” The first version is simpler and more direct, but it is a fiction whereas the second version is a correct statement.
Your comments are invited.
Apparently they knew this in 1913
And 1971
Files uploaded by Roy McCammon
By definition, the diameter of #. 36 AWG is 0.005 inches, and # 0000 is 0.46 inches. The ratio of these diameters is 1:92, and there are 40 gauge sizes from #. 36 to # 0000, or 39 steps. The diameter of a # n AWG wire is determined, for gauges smaller than # 00 (36 to 0), according to the following formula:
The gauge can be calculated from the diameter using
In the ideal transformer section it notes that the ideal transformer is lossless, therefore power out = power in. If output volts go down then output current must go up. That’s a conclusion and not an explanation. Unfortunately, the reliable sources tend to write a bunch of equations and conclude that current transforms inversely with the turns ratio. Again it is a conclusion and not an explanation. I have an explanation, but without any reliable sources, it would be WP:OP. I’ll outline it here, hoping that maybe someone else can find a reliable source or determine that it is supportable by the sources already in the article. The gist is this, take a transformer with turns NP and NS and a load on the secondary and try to force a current IP into the primary. If the quantity NP × IP – NS × IS ≠ 0, then you are forcing flux into the nominally infinite (or very large) self-inductance. It responds with an infinite (or very large) voltage seen on both the primary and the secondary. But there is a load on the secondary that would draw an infinite (or very large) current, so you can’t really get an infinite voltage. In fact, the secondary voltage that you can get is just enough to satisfy NP × IP – NS × IS = 0. The transformer, in effect, generates the voltage required to get the secondary current that will satisfy NP × IP – NS × IS = 0. A transformer with an infinite self-inductance is, so to speak, intolerant of NP × IP – NS × IS ≠ 0. You can sort of make a Lenz's law argument that any deviation from NP × IP – NS × IS = 0 would create huge reaction that would oppose the deviation.
The speed of electromagnetic waves in a low-loss dielectric is given by
where
The speed of electromagnetic waves in a good conductor is given by
where
In copper at 60 Hz, . Some sprinters can run twice as fast. As a consequence of
Snell's Law and the extremely low speed, electromagnetic waves always enter good conductors in a direction that is normal to the surface, regardless of the angle of incidence. This velocity is then the speed with which electromagnetic waves penetrate into the conductor and is not the
Drift velocity of the conduction electrons.
I have seven reliable sources of which two use plain language and the others simple formulas to state that the speed of an electromagnetic wave propagating in a good conductor is very much slower than the speed of light.
Plain language
Simple formula
[5]: 142
Rao
[6]: 332 ,(professor of electrical and computer engineering at U. of Illinois at Urbana) Elements of Engineering Electromagnetics page 332 equation 6.81c
Kraus, Electromagnetics, page 450, equation 11
Sadiku, Elements of Electromagnetics, 1989, p446, section 10.6 Plane waves in good conductors. equation (10.51)b
Taking
yields
Two simple formulas
[7]: 50–52
and on page 50 gives for a good conductor
Using the previous values gives
Stratton,(professor of physics emeritus at MIT) Electromagnetic Theory, 1941, McGraw-Hill, page 522
gives the wavelength within a conductor as
and by common knowledge
yielding
Note that Jackson cites Stratton, Harrington, Sadiku, and Kraus
Jackson 2nd page 337 and 3'rd page 354, eq. 8.9 and 8.10 give the phase term for a wave propagating into the conductor as where ξ=depth into conductor and δ=skin depth.
Magnetic current is, nominally, a fictitious current composed of fictitious moving magnetic mono-poles. It has the dimensions of volts. Magnetic currents produce an electric field analogously to the production of a magnetic field by electric currents. Magnetic current density is usually represented by the symbol M, which has the units of v/m² (volts per square meter). A given distibution of electric change can be mathematically replaced by an equivalent distribution of magnetic current. This fact can be used to simplify some electromagnetic field problems. [a] [b]
The direction of the electric field produced by magnetic currents is determined by the left-hand rule (opposite to the right-hand rule) as evidenced by the negative sign in the equation curl E = -M. One component of M is the familiar term ∂B/∂t, which is referred to as the magnetic displacement current or more properly as the magnetic displacement current density. [c] [d] [e]
[11]: 286
[11]: 286
[f]: 291
[g]: 291
As late as 1963, Purcell offered the following low velocity transformations as suitable for calculating the electric field experienced by a jet plane tranvelling in the Earth's magnetic field.
In 1973 Bellac and Levy-Leblond state that these equations are incorrect or misleading because they do not correspond to any consistent Galilean limit. Rousseaux gives a simple example showing that a transformation from an initial inertial frame to a second frame with a speed of v0 with respect to the first frame and then to a third frame moving with a speed v1 with respect to the second frame would give a result different from going directly from the first frame to the third frame using a relative speed of (v0 + v1).
Bellac and Levy-Leblond offer two transformations that do have consistent Galilean limits as follows:
The electric limit applies when electric field effects are dominant such as when Faraday's law of induction was insignificant.
The magnetic limit applies when the magnetic field effects are dominant.
Statement by Germain Rousseaux: "For the experiments of electrodynamics of moving bodies with low speeds, the Galilean theory is the most adapted because it is easier of stake in work from the calculus point of view and does not bring in the kinematics effect of Special Relativity which are absolutely unimportant in the Galilean limit.
[13]: 12 .
_________________________________________________________
Electromagnetic units are part of a system of electrical units based primarily upon the magnetic properties of electric currents, the fundamental SI unit being the ampere. The units are:
In the electromagnetic cgs system, electric current is a fundamental quantity defined via Ampère's law and takes the permeability as a dimensionless quantity (relative permeability) whose value in a vacuum is unity. As a consequence, the square of the speed of light appears explicitly in some of the equations interrelating quantities in this system.
Symbol [18] | Name of Quantity | Derived Units | Unit | Base Units |
---|---|---|---|---|
I | electric current | ampere ( SI base unit) | A | A (= W/V = C/s) |
Q | electric charge | coulomb | C | A⋅s |
U, ΔV, Δφ; E | potential difference; electromotive force | volt | V | kg⋅m2⋅s−3⋅A−1 (= J/C) |
R; Z; X | electric resistance; impedance; reactance | ohm | Ω | kg⋅m2⋅s−3⋅A−2 (= V/A) |
ρ | resistivity | ohm metre | Ω⋅m | kg⋅m3⋅s−3⋅A−2 |
P | electric power | watt | W | kg⋅m2⋅s−3 (= V⋅A) |
C | capacitance | farad | F | kg−1⋅m−2⋅s4⋅A2 (= C/V) |
E | electric field strength | volt per metre | V/m | kg⋅m⋅s−3⋅A−1 (= N/C) |
D | electric displacement field | coulomb per square metre | C/m2 | A⋅s⋅m−2 |
ε | permittivity | farad per metre | F/m | kg−1⋅m−3⋅s4⋅A2 |
χe | electric susceptibility | (dimensionless) | – | – |
G; Y; B | conductance; admittance; susceptance | siemens | S | kg−1⋅m−2⋅s3⋅A2 (= Ω−1) |
κ, γ, σ | conductivity | siemens per metre | S/m | kg−1⋅m−3⋅s3⋅A2 |
B | magnetic flux density, magnetic induction | tesla | T | kg⋅s−2⋅A−1 (= Wb/m2 = N⋅A−1⋅m−1) |
Φ | magnetic flux | weber | Wb | kg⋅m2⋅s−2⋅A−1 (= V⋅s) |
H | magnetic field strength | ampere per metre | A/m | A⋅m−1 |
L, M | inductance | henry | H | kg⋅m2⋅s−2⋅A−2 (= Wb/A = V⋅s/A) |
μ | permeability | henry per metre | H/m | kg⋅m⋅s−2⋅A−2 |
χ | magnetic susceptibility | (dimensionless) | – | – |
________________________________________________________________________________________________________________
________________________________________________________________________________________________________________
Testing
Talk:Gyroscope#Another animation
These work.
These do not work. They link to the top of the article.
________________________________________________________________________________________________________________
Hayt, William; Kemmerly, Jack E. (1993), Engineering Circuit Analysis (5th ed.), McGraw-Hill, ISBN 007027410X
Reitz, John R.; Milford, Frederick J.; Christy, Robert W. (1993), Foundations of Electromagnetic Theory (4th ed.), Addison-Wesley, ISBN 0201526247
________________________________________________________________________________________________________________
Talk:Telegrapher's equations#Solutions of the Telegrapher's Equations as Circuit Components
________________________________________________________________________________________________________________
Alt text is useful for the visually impaired. The following equation has alt text.
One of the best usenet discussions on Poynting vector and wires and angular momentum. Some day I'm going to write it up as a dialog between the Tortoise, Achilles and some other characters.
A discussion on usenet about the self discharge time constant for some tpyes of capacitors, including polypropylene.
See [19] [remark 1].
Consider the functions:
In engineering, a sinusoid has a negative phase shift with respect to some other sinusoid, if the peaks of the first sinusoid occurs after the peaks of the second sinusoid.
Using a trig identity, and can be written as:
In most cases, consistantly using the changing the sign of the phase only changes the sign of the imaginary part of the computation. In othere words, the result of using one convention or the other produces results that are conjugates of each other.
One place this shows up is in the definition of the Fourier transform.
The following use the same convention:
The following use the same convention:
I've looked in 11 references and found two ways to write down the equation for a plane wave.
(In all cases I have changed i to j for consistancy.)
The following group use a form for the plane wave that involves such as or .
The following group use a form for the plane wave that involves such as or .
I think this list is enough to establish that there is a group that uses and a group that uses
The first group are physicist. The second group, except for Crawford, are engineers. Kraus is an engineer but says he can use either convention.
So what is the difference? Not much, because at the end of the computation you discard the imaginary part and keep the real part. You wind up with terms of either or which are equal.
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________________________________________________________________________________________________________________
Feynman [20] and Jackson [21] give the following integral equations for calculating the electric scalar potential, and the magnetic vector potential, at point and time from the current density distribution and charge density distribution. is a 3 dimensional vector. The notation differs slightly from both sources.
There are a few notable things about equation for . First, the position of the source point only enters the equation as a scalar distance from to . The direction from to does not enter into the equation. The only thing that matters about a source point is how far away it is. Second, the integrand uses retarded time. This simply reflects the fact that changes in the sources propagate at the speed of light. And third, the equation is a vector equation. In Cartesian coordinates, the equation separates into three equations thus [22]:
where and are the components of and in the direction of the x axis.
In this form it is easy to see that the component of in a given direction depends only on the components of that are in the same direction. If the current is carried in a long straight wire, the points in the same direction as the wire.
not posted
When magnetic effects are dominent, equation 8 can be simplified to:
9.
Consider two long straight zero (or very low) resistance wires extending along the x axis. One carries a sinusoidally varying current that produces a magnetic vector potential that is directed in the same direction (along the x axis). The electric field in the second wire has the opposite direction to the magnetic vector potential. So the current in one long wire tends to produce a current of in the opposite direction in a parallel wire.
Terman [24] "The power factor ... tends to be independent of frequency, since the fraction of energy lost during each cycle ... is substantially independent of the number of cycles per second, over wide frequency ranges."
Terman is using older terminology. Power factor in a capacitor is the same as dissipation factor. The comment also applies to the loss tangent of a dielectric.
Griffiths [25], regarding the calculation of the magnitude of the B field in a toroidal inductor "determining its magnitude is ridiculously easy."
Halliday [26] regarding the calculation of the magnitude of the B field in a toroidal inductor "For a close-packed coil and no iron nearby ..." .
Time-Harmonic Electromagnetic Fields, McGraw-Hill, 1961, Reprinted 1987
Page 63, "From the field theory point of view, this is equivalent to assuming that no EZ or HZ exists. Such a wave is called transverse electromagnetic, abbreviated TEM. This is not the only wave possible on a transmission line, for Maxwell's equations show that infinitely many wave types can exist. Each possible wave is called a mode, and a TEM wave is called a transmission line mode. All other waves, which must have an EZ or an HZ or both, are called higher-order modes. The higher-order modes are usually important only in the vicinity of a feed point, or in the vicinity of a discontinuity on the line."
Page 147, "We therefore conjecture that all wave functions can be expressed as superposition of plane waves".
Electromagnetic Theory, McGraw-Hill, 1941
Page 533, "The transport of energy along the cylinder takes place entirely in the external dielectric. The internal energy surges back and forth and supplies the Joule heat losses."
Dreams of a Final Theory, Pantheon Books, 1992
Chapter 6. Beautiful Theories:
Chapter 7: Against Philosophy
Engineering Electromagnetics, McGraw-Hill, 1989
Chapter 11: The Uniform Plane Wave,
Section 5: Propagation in Good Conductors: the Skin Effect
Page 360, "Electromagnetic energy is not transmitted in the interior of a conductor; it travels in the region surrounding the conductor, while the conductor merely guides the waves. The currents established at the conductor surface propagate into the conductor in a direction perpendicular to the current density, and they are attenuated by ohmic losses. This power loss is the price exacted by the conductor for acting as a guide."
Feynman [27] regarding QED, "...you're not going to be able to understand it. ... my physics students don't understand it either. That's because I don't understand it. Nobody does."
Feynman
[28] regarding The ambiguity of field energy, "... but we must say that we do not know for certain what is the actual location in space of the electromagnetic field energy."
Feynman [29] regarding Examples of energy flow, "As another example, we ask what happens in a piece of resistance wire when it is carrying a current. ... . . There is a flow of energy into the wire all around. It is, of course, equal to the energy being lost in the wire in the form of heat. So our crazy theory says that the electrons are getting their energy to generate heat because of the energy flowing into the wire from the field outside. Intuition would seem to tell us that the electrons get their energy from being pushed along the wire, so the energy should be flowing down (or up) along the wire. But the theory says that the electrons are really being pushed by an electric field, which has come from some charges very far away, and that the electrons get their energy for generating heat from these fields. The energy somehow flows from the distant charges into a wide area of space and then inward to the wire.
... that the energy is flowing into the wire from the outside, rather than along the wire. "
Feynman [30] regarding real fields, "What we really mean by a real field is this: a real field is a mathematical function we use for avoiding the idea of action at a distance."
Feynman [31] regarding real fields, "We have introduced A <magnetic vector potential> because ... it is ... a real physical field in the sense that we described above."
Feynman [31] regarding The vector potential and quantum mechanics, "In our sense then, the A-field is real. ... The B-field in the whisker acts at a distance."
Standard Handbook for Electrical Engineers, 11th Edition, Fink, Donald G. editor, McGraw-Hill
Chapter 2, Section 40,
Page 2-13, "The energies stored in the fields travel with them, and this phenomenon is the basic and sole mechanism whereby electric power transmission takes place. Thus the electrical energy transmitted by means of transmission lines flows through the space surrounding the conductors, the latter (conductors) acting merely as guides.
"The usually accepted view that the conductor current produces the magnetic field surrounding it must be displaced by the more appropriate one that the electromagnetic field surrounding the conductor produces, through a small drain on its energy supply, the current in the conductor. Although the value of the latter (current) may be used in computing the transmitted energy, one should clearly recognize that physically this current produces only a loss and in no way has a direct part in the phenomenon of power transmission."
Ether and the Theory of Relativity, address on May 05, 1920 at University of Leyden p6 "More careful reflection teaches us, however, that the special theory of relativity does not compel us to deny ether. We may assume the existence of an ether; only we must give up ascribing a definite state of motion to it, ...
According to the general theory of relativity space without ether is unthinkable; for in such space there not only would be no propagation of light"
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Minor loop feedback#Telescope position servo
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number of rollbackers with link to Users special page: 6,825
number of rollbackers: 6,825
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Magnetic current#Magnetic displacement current
Magnetic current#Magnetic frill generator
/What is wrong with the flux cutting model?
User:Constant314/Telegrapher's equations in the frequency domain
User:Constant314/Generalized Impedance Converter
Wheeler Incremental Inductance Rule
User:Constant314/Derivation of skin depth
Frequency dependent negative resistor
WP:COI Conflict of interest
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WP:NOTDIR , WP:NOTCAT, Wikipedia is not a directory or catalog
WP:LINK, WP:MOSLINK Wikipedia: Manual of Style/Linking
WP:NOTHOWTO not how to manual
WP:NOCODE No computer code
MOS:OL over linking
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WP:RSP List of reliable and unreliable sources.
WP:RIGHTGREATWRONGS Wikipedia does not right great wrongs
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{ { toomanylinks } } place in external links section.
4.35×10−17 mm
Category:Inline cleanup templates a list of cleanup templates such as citation needed, clarify
Note, spaces added between the braces to make the template inactive in this page
Γ dτ
Waveguides with certain symmetries may be solved using the method of separation of variables. Rectangular wave guides may be solved in rectangular coordinates. [2]: 143 Round waveguides may be solved in cylindracal coordinates. [2]: 198
Talk:Speed_of_electricity#Incorrect section: Speed of electromagnetic waves in good conductors
Some text with strike through.
Talk:Displacement current#Untrue assumptions in the “Current in capacitors” sub section
This section may be
confusing or unclear to readers. In particular, the known variables and the unknown variables of the system of equations is not clear. The rules given do not cover the case where two loops share nodes, but neither contains the other.. |
********************************************************************************
This topic should always be on the top.
curl E = -∂B/∂t
curl H = ∂D/∂t + Jconduction + Jsource = curl H = ∂D/∂t + σE + Jsource
User:Constant314/Tow-Thomas active filter
Add alternate explanations of skin effect.
Add magnetic vector potential to the transformer page.
The solutions of the telegrapher's equations [3]: 381–392 are functions of two parameters which are the propagation constant, , and the characteristic impedance, . The propagation constant is often written as where is called the attenuation constant and is called the phase constant. The natural units for and are nepers per unit length and radians per unit length, respectively.
There are two solutions which can be interpreted as a forward propagating wave and a reverse propagating wave. The forward wave, which has a voltage of and a current of , is given by:
The reverse wave, which has a voltage of and a current of , is given by:
where
The negative sign in the expression for indicates that the current in the reverse wave is traveling in a direction that is opposite to the reference direction, which is the direction of the forward propagating wave. and are secondary parameters which means that they can be expressed in terms of the primary parameters and .
The propagation constant and the characteristic impedance may be factored as
where
where The terms and are relatively independent of frequency. The frequency dependent behavior of and can be separated into nine regions according to whether the ratios and are much less than unity, much greater than unity or about equal to unity. In practice, four of the combinations do not occur leaving five regions from DC to high frequency.
The graph to the left shows the frequency dependent variation of and of a transmission line with a good dielectric such as high density polyethylene. Separation of the spectrum into regions has been arbitrarily set at the frequencies at which one of the ratios is either 0.1 or 10.
The five regions may be easily seen in the adjacent graph of velocity versus frequency of a transmission line with a good dielectric such as polyethylene:
From lowest to highest frequency the regions are:
The high frequency regime is most associated with transmission line behavior. It includes Ethernet, most broadcasting, ordinary video, computer buses, the higher portions of the digital telephony spectrum ( HDSL, ADSL, VDSL).
The intermediate frequency regime includes the lower portions of the digital telephony spectrum ( ISDN, HDSL, ADSL, the upper frequencies of music,
The low frequency regime includes voice telephony, the lower frequencies of music,
The very low frequency regime includes
If then there is no near DC regime. This is the case if the dielectric is vacuum.
The near DC regime expressions approach their DC values as frequency approaches zero, except wavelength which approaches infinity.
The near DC regime expressions approach their DC values as frequency approaches zero, except wavelength which approaches infinity.
The following gallery shows the frequency dependence of some of the other secondary parameters.
This involves a slight bit of synthesis from Brenner and Javid. Page 599 gives i2/i1 = 1/n and 1/n = n1/n2 which can be combined by simple arithmetic to give i1n1 = i2n2 or i1n1 - i2n2 = 0.
Hayt & Kemmerly in Engineering Circuit Analysis, 5'th on page 446 state plainly that i1n1 = i2n2, but it doesn't seem worth adding a reference for that.
(i1n1 - i2n2) is the magnetomotive force, using the current reference directions given in the figure in the same section.
First, an analogy. I can compute the velocity of my car by computing the time derivative of the number displayed on the odometer. That doesn’t mean the odometer causes the car’s velocity. The relationship holds because they are both caused by the same thing, which is the motor. Faraday's law of induction (FLI) states that the EMF (path integral of the electric field) in closed loop is proportional to the time derivative of the total flux the enclosed in the loop, including the flux in the core. This is a very useful relationship for designing transformers and predicting their behavior. This doesn’t mean that the flux in the core causes the EMF in the secondary, although it is often taught that way. Most of the time, that is good enough. But, in fact, if the flux in the core actually caused the EMF in the secondary, that would be action at a distance. Feynman makes this point in Volume 2 of the Feynman lectures, chap 15 section 5 in the second paragraph following equation 15.36.
Modern physicists have worked very hard to eliminate action at a distance. The modern formulation is that the currents produce the magnetic vector potential, A, at the wires. A produces a component of the electric field, E in accordance with E = -∂A/∂t (actually E= -∇φ -∂A/∂t, but I am ignoring φ). The line integral of -∂A/∂t over a closed path is the EMF. Faraday’s law of induction (FLI) works because B = ∇ × A; E at the wires has the same cause as B in core. FLI is useful for engineers because they almost always have the transformer connected to a circuit which provides a complete path. However, E = -∂A/∂t, gives the E field at each infinitesimal part of the path.
I am not going to try to put this in the article; it is probably too technical. I’m going for WP:RIGHTGREATWRONGS, but I will try to edit the article so it is not in conflict with the modern formulation. For example, instead of “EMF is caused by the changing flux in the core” I may write “EMF is equal the rate of change of the flux in the core.” The first version is simpler and more direct, but it is a fiction whereas the second version is a correct statement.
Your comments are invited.
Apparently they knew this in 1913
And 1971
Files uploaded by Roy McCammon
By definition, the diameter of #. 36 AWG is 0.005 inches, and # 0000 is 0.46 inches. The ratio of these diameters is 1:92, and there are 40 gauge sizes from #. 36 to # 0000, or 39 steps. The diameter of a # n AWG wire is determined, for gauges smaller than # 00 (36 to 0), according to the following formula:
The gauge can be calculated from the diameter using
In the ideal transformer section it notes that the ideal transformer is lossless, therefore power out = power in. If output volts go down then output current must go up. That’s a conclusion and not an explanation. Unfortunately, the reliable sources tend to write a bunch of equations and conclude that current transforms inversely with the turns ratio. Again it is a conclusion and not an explanation. I have an explanation, but without any reliable sources, it would be WP:OP. I’ll outline it here, hoping that maybe someone else can find a reliable source or determine that it is supportable by the sources already in the article. The gist is this, take a transformer with turns NP and NS and a load on the secondary and try to force a current IP into the primary. If the quantity NP × IP – NS × IS ≠ 0, then you are forcing flux into the nominally infinite (or very large) self-inductance. It responds with an infinite (or very large) voltage seen on both the primary and the secondary. But there is a load on the secondary that would draw an infinite (or very large) current, so you can’t really get an infinite voltage. In fact, the secondary voltage that you can get is just enough to satisfy NP × IP – NS × IS = 0. The transformer, in effect, generates the voltage required to get the secondary current that will satisfy NP × IP – NS × IS = 0. A transformer with an infinite self-inductance is, so to speak, intolerant of NP × IP – NS × IS ≠ 0. You can sort of make a Lenz's law argument that any deviation from NP × IP – NS × IS = 0 would create huge reaction that would oppose the deviation.
The speed of electromagnetic waves in a low-loss dielectric is given by
where
The speed of electromagnetic waves in a good conductor is given by
where
In copper at 60 Hz, . Some sprinters can run twice as fast. As a consequence of
Snell's Law and the extremely low speed, electromagnetic waves always enter good conductors in a direction that is normal to the surface, regardless of the angle of incidence. This velocity is then the speed with which electromagnetic waves penetrate into the conductor and is not the
Drift velocity of the conduction electrons.
I have seven reliable sources of which two use plain language and the others simple formulas to state that the speed of an electromagnetic wave propagating in a good conductor is very much slower than the speed of light.
Plain language
Simple formula
[5]: 142
Rao
[6]: 332 ,(professor of electrical and computer engineering at U. of Illinois at Urbana) Elements of Engineering Electromagnetics page 332 equation 6.81c
Kraus, Electromagnetics, page 450, equation 11
Sadiku, Elements of Electromagnetics, 1989, p446, section 10.6 Plane waves in good conductors. equation (10.51)b
Taking
yields
Two simple formulas
[7]: 50–52
and on page 50 gives for a good conductor
Using the previous values gives
Stratton,(professor of physics emeritus at MIT) Electromagnetic Theory, 1941, McGraw-Hill, page 522
gives the wavelength within a conductor as
and by common knowledge
yielding
Note that Jackson cites Stratton, Harrington, Sadiku, and Kraus
Jackson 2nd page 337 and 3'rd page 354, eq. 8.9 and 8.10 give the phase term for a wave propagating into the conductor as where ξ=depth into conductor and δ=skin depth.
Magnetic current is, nominally, a fictitious current composed of fictitious moving magnetic mono-poles. It has the dimensions of volts. Magnetic currents produce an electric field analogously to the production of a magnetic field by electric currents. Magnetic current density is usually represented by the symbol M, which has the units of v/m² (volts per square meter). A given distibution of electric change can be mathematically replaced by an equivalent distribution of magnetic current. This fact can be used to simplify some electromagnetic field problems. [a] [b]
The direction of the electric field produced by magnetic currents is determined by the left-hand rule (opposite to the right-hand rule) as evidenced by the negative sign in the equation curl E = -M. One component of M is the familiar term ∂B/∂t, which is referred to as the magnetic displacement current or more properly as the magnetic displacement current density. [c] [d] [e]
[11]: 286
[11]: 286
[f]: 291
[g]: 291
As late as 1963, Purcell offered the following low velocity transformations as suitable for calculating the electric field experienced by a jet plane tranvelling in the Earth's magnetic field.
In 1973 Bellac and Levy-Leblond state that these equations are incorrect or misleading because they do not correspond to any consistent Galilean limit. Rousseaux gives a simple example showing that a transformation from an initial inertial frame to a second frame with a speed of v0 with respect to the first frame and then to a third frame moving with a speed v1 with respect to the second frame would give a result different from going directly from the first frame to the third frame using a relative speed of (v0 + v1).
Bellac and Levy-Leblond offer two transformations that do have consistent Galilean limits as follows:
The electric limit applies when electric field effects are dominant such as when Faraday's law of induction was insignificant.
The magnetic limit applies when the magnetic field effects are dominant.
Statement by Germain Rousseaux: "For the experiments of electrodynamics of moving bodies with low speeds, the Galilean theory is the most adapted because it is easier of stake in work from the calculus point of view and does not bring in the kinematics effect of Special Relativity which are absolutely unimportant in the Galilean limit.
[13]: 12 .
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Electromagnetic units are part of a system of electrical units based primarily upon the magnetic properties of electric currents, the fundamental SI unit being the ampere. The units are:
In the electromagnetic cgs system, electric current is a fundamental quantity defined via Ampère's law and takes the permeability as a dimensionless quantity (relative permeability) whose value in a vacuum is unity. As a consequence, the square of the speed of light appears explicitly in some of the equations interrelating quantities in this system.
Symbol [18] | Name of Quantity | Derived Units | Unit | Base Units |
---|---|---|---|---|
I | electric current | ampere ( SI base unit) | A | A (= W/V = C/s) |
Q | electric charge | coulomb | C | A⋅s |
U, ΔV, Δφ; E | potential difference; electromotive force | volt | V | kg⋅m2⋅s−3⋅A−1 (= J/C) |
R; Z; X | electric resistance; impedance; reactance | ohm | Ω | kg⋅m2⋅s−3⋅A−2 (= V/A) |
ρ | resistivity | ohm metre | Ω⋅m | kg⋅m3⋅s−3⋅A−2 |
P | electric power | watt | W | kg⋅m2⋅s−3 (= V⋅A) |
C | capacitance | farad | F | kg−1⋅m−2⋅s4⋅A2 (= C/V) |
E | electric field strength | volt per metre | V/m | kg⋅m⋅s−3⋅A−1 (= N/C) |
D | electric displacement field | coulomb per square metre | C/m2 | A⋅s⋅m−2 |
ε | permittivity | farad per metre | F/m | kg−1⋅m−3⋅s4⋅A2 |
χe | electric susceptibility | (dimensionless) | – | – |
G; Y; B | conductance; admittance; susceptance | siemens | S | kg−1⋅m−2⋅s3⋅A2 (= Ω−1) |
κ, γ, σ | conductivity | siemens per metre | S/m | kg−1⋅m−3⋅s3⋅A2 |
B | magnetic flux density, magnetic induction | tesla | T | kg⋅s−2⋅A−1 (= Wb/m2 = N⋅A−1⋅m−1) |
Φ | magnetic flux | weber | Wb | kg⋅m2⋅s−2⋅A−1 (= V⋅s) |
H | magnetic field strength | ampere per metre | A/m | A⋅m−1 |
L, M | inductance | henry | H | kg⋅m2⋅s−2⋅A−2 (= Wb/A = V⋅s/A) |
μ | permeability | henry per metre | H/m | kg⋅m⋅s−2⋅A−2 |
χ | magnetic susceptibility | (dimensionless) | – | – |
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Testing
Talk:Gyroscope#Another animation
These work.
These do not work. They link to the top of the article.
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Hayt, William; Kemmerly, Jack E. (1993), Engineering Circuit Analysis (5th ed.), McGraw-Hill, ISBN 007027410X
Reitz, John R.; Milford, Frederick J.; Christy, Robert W. (1993), Foundations of Electromagnetic Theory (4th ed.), Addison-Wesley, ISBN 0201526247
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Talk:Telegrapher's equations#Solutions of the Telegrapher's Equations as Circuit Components
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Alt text is useful for the visually impaired. The following equation has alt text.
One of the best usenet discussions on Poynting vector and wires and angular momentum. Some day I'm going to write it up as a dialog between the Tortoise, Achilles and some other characters.
A discussion on usenet about the self discharge time constant for some tpyes of capacitors, including polypropylene.
See [19] [remark 1].
Consider the functions:
In engineering, a sinusoid has a negative phase shift with respect to some other sinusoid, if the peaks of the first sinusoid occurs after the peaks of the second sinusoid.
Using a trig identity, and can be written as:
In most cases, consistantly using the changing the sign of the phase only changes the sign of the imaginary part of the computation. In othere words, the result of using one convention or the other produces results that are conjugates of each other.
One place this shows up is in the definition of the Fourier transform.
The following use the same convention:
The following use the same convention:
I've looked in 11 references and found two ways to write down the equation for a plane wave.
(In all cases I have changed i to j for consistancy.)
The following group use a form for the plane wave that involves such as or .
The following group use a form for the plane wave that involves such as or .
I think this list is enough to establish that there is a group that uses and a group that uses
The first group are physicist. The second group, except for Crawford, are engineers. Kraus is an engineer but says he can use either convention.
So what is the difference? Not much, because at the end of the computation you discard the imaginary part and keep the real part. You wind up with terms of either or which are equal.
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Feynman [20] and Jackson [21] give the following integral equations for calculating the electric scalar potential, and the magnetic vector potential, at point and time from the current density distribution and charge density distribution. is a 3 dimensional vector. The notation differs slightly from both sources.
There are a few notable things about equation for . First, the position of the source point only enters the equation as a scalar distance from to . The direction from to does not enter into the equation. The only thing that matters about a source point is how far away it is. Second, the integrand uses retarded time. This simply reflects the fact that changes in the sources propagate at the speed of light. And third, the equation is a vector equation. In Cartesian coordinates, the equation separates into three equations thus [22]:
where and are the components of and in the direction of the x axis.
In this form it is easy to see that the component of in a given direction depends only on the components of that are in the same direction. If the current is carried in a long straight wire, the points in the same direction as the wire.
not posted
When magnetic effects are dominent, equation 8 can be simplified to:
9.
Consider two long straight zero (or very low) resistance wires extending along the x axis. One carries a sinusoidally varying current that produces a magnetic vector potential that is directed in the same direction (along the x axis). The electric field in the second wire has the opposite direction to the magnetic vector potential. So the current in one long wire tends to produce a current of in the opposite direction in a parallel wire.
Terman [24] "The power factor ... tends to be independent of frequency, since the fraction of energy lost during each cycle ... is substantially independent of the number of cycles per second, over wide frequency ranges."
Terman is using older terminology. Power factor in a capacitor is the same as dissipation factor. The comment also applies to the loss tangent of a dielectric.
Griffiths [25], regarding the calculation of the magnitude of the B field in a toroidal inductor "determining its magnitude is ridiculously easy."
Halliday [26] regarding the calculation of the magnitude of the B field in a toroidal inductor "For a close-packed coil and no iron nearby ..." .
Time-Harmonic Electromagnetic Fields, McGraw-Hill, 1961, Reprinted 1987
Page 63, "From the field theory point of view, this is equivalent to assuming that no EZ or HZ exists. Such a wave is called transverse electromagnetic, abbreviated TEM. This is not the only wave possible on a transmission line, for Maxwell's equations show that infinitely many wave types can exist. Each possible wave is called a mode, and a TEM wave is called a transmission line mode. All other waves, which must have an EZ or an HZ or both, are called higher-order modes. The higher-order modes are usually important only in the vicinity of a feed point, or in the vicinity of a discontinuity on the line."
Page 147, "We therefore conjecture that all wave functions can be expressed as superposition of plane waves".
Electromagnetic Theory, McGraw-Hill, 1941
Page 533, "The transport of energy along the cylinder takes place entirely in the external dielectric. The internal energy surges back and forth and supplies the Joule heat losses."
Dreams of a Final Theory, Pantheon Books, 1992
Chapter 6. Beautiful Theories:
Chapter 7: Against Philosophy
Engineering Electromagnetics, McGraw-Hill, 1989
Chapter 11: The Uniform Plane Wave,
Section 5: Propagation in Good Conductors: the Skin Effect
Page 360, "Electromagnetic energy is not transmitted in the interior of a conductor; it travels in the region surrounding the conductor, while the conductor merely guides the waves. The currents established at the conductor surface propagate into the conductor in a direction perpendicular to the current density, and they are attenuated by ohmic losses. This power loss is the price exacted by the conductor for acting as a guide."
Feynman [27] regarding QED, "...you're not going to be able to understand it. ... my physics students don't understand it either. That's because I don't understand it. Nobody does."
Feynman
[28] regarding The ambiguity of field energy, "... but we must say that we do not know for certain what is the actual location in space of the electromagnetic field energy."
Feynman [29] regarding Examples of energy flow, "As another example, we ask what happens in a piece of resistance wire when it is carrying a current. ... . . There is a flow of energy into the wire all around. It is, of course, equal to the energy being lost in the wire in the form of heat. So our crazy theory says that the electrons are getting their energy to generate heat because of the energy flowing into the wire from the field outside. Intuition would seem to tell us that the electrons get their energy from being pushed along the wire, so the energy should be flowing down (or up) along the wire. But the theory says that the electrons are really being pushed by an electric field, which has come from some charges very far away, and that the electrons get their energy for generating heat from these fields. The energy somehow flows from the distant charges into a wide area of space and then inward to the wire.
... that the energy is flowing into the wire from the outside, rather than along the wire. "
Feynman [30] regarding real fields, "What we really mean by a real field is this: a real field is a mathematical function we use for avoiding the idea of action at a distance."
Feynman [31] regarding real fields, "We have introduced A <magnetic vector potential> because ... it is ... a real physical field in the sense that we described above."
Feynman [31] regarding The vector potential and quantum mechanics, "In our sense then, the A-field is real. ... The B-field in the whisker acts at a distance."
Standard Handbook for Electrical Engineers, 11th Edition, Fink, Donald G. editor, McGraw-Hill
Chapter 2, Section 40,
Page 2-13, "The energies stored in the fields travel with them, and this phenomenon is the basic and sole mechanism whereby electric power transmission takes place. Thus the electrical energy transmitted by means of transmission lines flows through the space surrounding the conductors, the latter (conductors) acting merely as guides.
"The usually accepted view that the conductor current produces the magnetic field surrounding it must be displaced by the more appropriate one that the electromagnetic field surrounding the conductor produces, through a small drain on its energy supply, the current in the conductor. Although the value of the latter (current) may be used in computing the transmitted energy, one should clearly recognize that physically this current produces only a loss and in no way has a direct part in the phenomenon of power transmission."
Ether and the Theory of Relativity, address on May 05, 1920 at University of Leyden p6 "More careful reflection teaches us, however, that the special theory of relativity does not compel us to deny ether. We may assume the existence of an ether; only we must give up ascribing a definite state of motion to it, ...
According to the general theory of relativity space without ether is unthinkable; for in such space there not only would be no propagation of light"
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