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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
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4108:. And also the 'formula using present time' is already given in the article, I added your citation with the clarification that Lab frame time can be used for it and also the reasoning which comes from Lorentz invariance of the term. Lastly, I prefer you rechecked your sources or opened a discussion before you revert reversions. I'll wait a bit for your reply before making any further changes.
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discusses the power radiated from an accelerated charge, but the formulas are different from this article. I don't see how to reconcile them. At the very least I expect the two articles to cross-reference each other and explain the different assumptions that lead to the different formulas. It's also
188:
The derivation given here was first published by J. J. Thomson (discoverer of the electron) in 1907. It is derived for the special case where the final velocity of the particle is zero but the Larmor formula is true for any sort of accelerated motion provided that the speed of the particle is always
1184:
An example is the electric field around an oscillating charge. 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
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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 needs inserting. Thus the total energy carried away by the pulse of radiation is twice that of the previous equation or
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Paradoxes in radiation reaction do not get resolved just because its effect is negligible in experiments or because self force is a retarding force. Neither does your citation make claims of that. You can go through citations in the ALD article for introduction to
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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. Using angle brackets to denote an average over all points on the shell,
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This implies that the last two expressions in the chain of equalities are equivalent – if the last one is wrong, so is the one but last. So that one is then wrong too and should also be removed. But it is clearly equivalent to the one before it, so
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I added a new source, where the formula is actually mentioned. I couldn't find it in "On a dynamical theory of the electric and luminiferous medium", so this hint shows a paper from the right year and the right author, but is a bit misleading.
3594:
I think this last term is wrong and should be removed, as this µ0, stands for something like 1 over ϵ_0 c^3, which I think is meaningless and certainly not the expression of a dipole moment. This is already obvious by checking the (SI) units.
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Divide both sides of this equation by t0, the duration of the particle’s acceleration. The left-hand side then becomes the energy radiated by the particle per unit time, or the power given off during the acceleration: Power radiated
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If electron acceleration is the source of antenna radiation, then at higher frequencies antenna efficiency would increase, which is clearly not the case. One can safely assume that the main thesis of this
Knowledge article is
3414:
The last sentence in "Atomic
Physics" appears to be a serious misunderstanding of the paper of Haus (found in the link to the wikipedia page "Nonradiation condition"), which says that non-accelerating charges do not radiate.
4011:
q^2/cm has the dimension of energy in ergs, So q^2a^2/c^3 has the dimension of power in ergs/sec. q has the dimension of 'statcoulombs', but that doesn't have to be mentioned if q^2/cm is recognized as energy in ergs.
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2821:{\displaystyle P_{\text{Brem article}}={\frac {q^{2}\gamma ^{6}}{6\pi \varepsilon _{0}c}}\left(({\dot {\beta }})^{2}-({\dot {\beta }}^{2})(\beta ^{2})+({\dot {\beta }}^{2})(\beta ^{2})\cos ^{2}\theta \right)}
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932:, 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
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In the non-relativistic limit, the second term in parentheses can be neglected, and the first term reduces to a^2/c^2. Set q = e and gamma = 1 and the formulas become identical. Where's the problem?
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As of Sept 5 2008, this article used \epsilon rather than \varepsilon for the permittivity of vacuum. I've always see \varepsilon used for this constant. Indeed, this is what is used in
2418:{\displaystyle P_{\text{Brem article}}={\frac {q^{2}\gamma ^{6}}{6\pi \varepsilon _{0}c}}\left((1-\beta ^{2}){\dot {\beta }}^{2}+({\vec {\beta }}\cdot {\dot {\vec {\beta }}})^{2}\right)}
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2234:{\displaystyle P_{\text{Larmor article}}={\frac {q^{2}\gamma ^{6}}{6\pi \varepsilon _{0}c}}\left(({\vec {\dot {\beta }}})^{2}-({\vec {\beta }}\times {\vec {\dot {\beta }}})^{2}\right)}
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If all equations depend on the system of units, the sentence about how the power radiated by a single electron is described in either unit system by the same formula is wrong.
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1901:{\displaystyle P={\frac {q^{2}\gamma ^{4}}{6\pi \varepsilon _{0}c}}\left({\dot {\beta }}^{2}+{\frac {({\vec {\beta }}\cdot {\dot {\vec {\beta }}})^{2}}{1-\beta ^{2}}}\right)}
1704:{\displaystyle P={\frac {q^{2}\gamma ^{4}}{6\pi \varepsilon _{0}c}}\left({\dot {\beta }}^{2}+{\frac {({\vec {\beta }}\cdot {\dot {\vec {\beta }}})^{2}}{1-\beta ^{2}}}\right)}
2604:{\displaystyle P_{\text{Larmor article}}={\frac {q^{2}\gamma ^{6}}{6\pi \varepsilon _{0}c}}\left(({\dot {\beta }})^{2}-\beta ^{2}{\dot {\beta }}^{2}\sin ^{2}\theta \right)}
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Advanced and retarded time are both well defined terms in the future and present respectively. They are not arbitrary. Definition of both is given for example here:
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is a completely incommensurate physical quantity and not a constant. It is not referenced in the article and I have no idea why it was mentioned here.) --
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If the direction in which the energy goes is not important, we can average the energy over all directions. Using a mathematical device, introduce a
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2059:{\displaystyle P={\frac {2q^{2}\gamma ^{6}}{3c}}\left(({\vec {\dot {\beta }}})^{2}-({\vec {\beta }}\times {\vec {\dot {\beta }}})^{2}\right)}
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I changed \epsilon to \varepsilon in this article. If this is incorrect, please describe why \epsilon should be used in this equation.
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Interesting. If this is can be finished and cleaned up, it should moved to the article proper. Especially if this is how Larmor did it.
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what is the total amount of energy radiated over a full cycle from a charge oscillating back and forth with a simple sine wave motion?
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3051:{\displaystyle {\frac {dP}{d\Omega }}={\frac {q^{2}}{4\pi c}}{\frac {\sin ^{2}(\theta )\,a^{2}\,{\hat {\mathbf {n} }}}{c^{2}R^{2}}}.}
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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.
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Now since the origin is at the center of the sphere, the average value of x^2 is the same as the average value of y^2 or z^2:
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3188:{\displaystyle \mathbf {S} ={\frac {q^{2}}{4\pi c}}{\frac {\sin ^{2}(\theta )\,a^{2}\,{\hat {\mathbf {n} }}}{c^{2}R^{2}}}.}
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None of this is relevant to the suggested dependence on the system of units. In the literature some texts have a factor
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possible that one of the two articles is flat-out wrong. Someone knowledgeable can please help?? Thanks in advance!! --
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In cgs units, a has the dimension cm/sec^2, c has dimension cm/sec. Then, q^2a^2/c^3 has the dimension q^2/(cm-sec).
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are truly repulsive. If no one objects, I'm going to change the article's notation to use boldface for vectors.
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The electrons in an antenna generally do not move at relativistic speeds, so the gamma factors do not enter.
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3312:{\displaystyle {\frac {dP}{d\Omega }}={\frac {q^{2}}{4\pi c}}{\frac {\sin ^{2}(\theta )\,a^{2}}{c^{2}}}.}
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http://maxwellsociety.net/PhysicsCorner/Transformations/LienardLarmor/Covariance%20of%20the%20Larmor.html
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I don't understand what is meant by "misled interpretation of citation" in the following revision:
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on
Knowledge. If you would like to participate, please visit the project page, where you can join
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658:{\displaystyle x^{2}={\frac {1}{3}}(x^{2}+y^{2}+z^{2})={\frac {1}{3}}R^{2}={\frac {R^{2}}{3}}}
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The $ \mu_0$ there is not meant to be the expression of a dipole moment, and shouldn't be.
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is independent of a specific system of units, so what is the idea behind the parenthesis
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1521:{\displaystyle P={\frac {e^{2}a^{2}}{6\pi \varepsilon _{0}c^{3}}}{\mbox{ (SI units)}}}
353:{\displaystyle {q^{2}a^{2}\sin ^{2}\theta } \over {32\pi ^{2}\epsilon _{0}c^{4}R^{2}}}
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I think that last sentence should be removed because it wouldn't apply to electrns.
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The article lacks in the area of superconducting currents. Cited material please.
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So the average energy per unit volume stored in the transverse electric field is
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Just got to get the equations correct. Wont be too long. Please bear with me!--
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Bremsstrahlung says "The general expression for the total radiated power is
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Section 2 of the citation derives the Larmor formula at the present time.
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http://www.phys.lsu.edu/~jarrell/COURSES/ELECTRODYNAMICS/Chap14/hmwk14.pdf
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ALL of the equations in that section depend on the system of units used.
918:{\displaystyle {{q^{2}a^{2}} \over {48\pi ^{2}\epsilon _{0}c^{4}R^{2}}}}
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I'll change it to the latter to flow with the text before the equation
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Usually I can stomach arrow notation for vectors, but symbols such as
824:{\displaystyle \sin ^{2}\theta ={1-R^{2} \over 3R^{2}}={\frac {2}{3}}}
3781:{\displaystyle {\mathsf {T}}^{{-}3}{\mathsf {L}}^{2}{\mathsf {M}},}
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and R is constant over the whole shell. Combining equations gives
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if I'm not mistaken, in any case another dimension than power. --
3842:{\displaystyle {\mathsf {T}}{\mathsf {L}}^{{-}1}{\mathsf {I}}^{2}}
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1174:{\displaystyle P={\frac {e^{2}a^{2}}{6\pi \epsilon _{0}c^{3}}}}
1091:{\displaystyle E={\frac {e^{2}a^{2}}{6\pi \epsilon _{0}c^{3}}}}
1005:{\displaystyle E={\frac {e^{2}a^{2}}{6\pi \epsilon _{0}c^{3}}}}
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there is an erroneous equation in the derivation 1 section
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and how does it not apply just as well when working in the
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integral from t=0 to t=1 of (4 pi^2 d f^2 sin(2 pi f t) )^2
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The energy per unit volume stored in an electric field is
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and others don't. The formulas on the first line have
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Knowledge level-5 vital articles in
Physical sciences
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Electric_field#Relativistic_effects_on_electric_field
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must be wrong, based on dimensional analysis alone. d
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4076:) for misled interpretation of citation. Discuss in
3551:{\displaystyle \mu _{0}{\frac {q^{2}a^{2}}{6\pi c}}}
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I'll put Larmor in SI units for a better comparison
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Epsilon or varepsilon for permittivity of free space
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1385:However, thats for one unit of time not one cycle
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1376:2 pi^3 d^2 f^3 (4 pi f) = 8 * pi^4 * d^2 * f^4
251:Neglecting the radial component of the field:
4147:Knowledge vital articles in Physical sciences
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1438:The non-relativistic formula in the lede of
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4162:C-Class vital articles in Physical sciences
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4177:C-Class physics articles of Mid-importance
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3061:I believe the correct formulas are either
1268:Applicability to superconducting currents?
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4068:: Manually undid revision 1248417813 by
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3322:as taken from Jackson 3rd edition pg 665
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3362:/dΩ has units of erg s = g cm s, and (
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3904:of power? What are the dimensions of
3718:{\displaystyle 4\pi \varepsilon _{0}}
1358:= 2 pi^3 d^2 f^3 (4 pi f-sin(4 pi f))
7:
3880:Can you explain how the formula for
1240:http://en.wikipedia.org/Permittivity
106:This article is within the scope of
3573:{\displaystyle {\text{(SI units)}}}
2832:Ah, OK, I see, sorry about that. --
1534:Bremsstrahlung#Dipole_approximation
1420:Bremsstrahlung#Dipole approximation
527:{\displaystyle x^{2}=y^{2}=z^{2}\ }
189:much less than the speed of light.
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4038:misled interpretation of citation.
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935:Total energy in electric field =
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126:Knowledge:WikiProject Physics
120:and see a list of open tasks.
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3453:Acceleration and Radiation
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152:project's importance scale
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3390:Original source by Larmor
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930:transverse electric field
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3977:{\displaystyle \mu _{0}}
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1205:What is your source for
1021:Total energy in pulse =
4046:8:17, 30 September 2024
3410:non-radiation condition
2442:{\displaystyle \theta }
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3925:{\displaystyle q,~a}
3908:
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199:
4078:Talk:Larmor formula
3986:vacuum permeability
3615:vacuum permeability
3611:vacuum permittivity
109:WikiProject Physics
3974:
3943:
3922:
3890:
3839:
3778:
3715:
3678:
3613:is related to the
3570:
3548:
3374:has units of g s.
3309:
3282:
3185:
3142:
3130:
3048:
3005:
2993:
2905:Derivation 1 typo?
2880:
2818:
2601:
2439:
2415:
2231:
2056:
1898:
1701:
1518:
1516:
1411:Inconsistent with
1171:
1088:
1002:
915:
821:
729:
655:
524:
462:
304:
241:
45:content assessment
4034:
4018:comment added by
3990:physical constant
3946:{\displaystyle c}
3918:
3893:{\displaystyle P}
3568:
3546:
3433:
3421:comment added by
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2016:
1988:
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1613:
1596:
1515:
1509:
1264:
1248:comment added by
1223:Added references
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1532:The formula in
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43:on Knowledge's
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3460:80.121.121.188
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2477:
2470:
2464:Larmor article
2461:
2438:
2427:
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2413:
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2146:
2142:
2135:
2130:
2126:
2122:
2119:
2112:
2108:
2102:
2098:
2091:
2085:Larmor article
2082:
2068:
2067:
2066:
2054:
2048:
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2037:
2032:
2029:
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2015:
2012:
2006:
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1998:
1994:
1987:
1982:
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1971:
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1456:
1453:
1440:Larmor formula
1416:
1413:Bremsstrahlung
1409:
1408:
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1405:
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1388:
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1199:
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1187:
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1181:
1165:
1161:
1155:
1151:
1147:
1144:
1137:
1133:
1127:
1123:
1116:
1113:
1082:
1078:
1072:
1068:
1064:
1061:
1054:
1050:
1044:
1040:
1033:
1030:
996:
992:
986:
982:
978:
975:
968:
964:
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954:
947:
944:
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148:Mid-importance
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118:the discussion
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101:Physics portal
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73:Mid‑importance
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258:Energy/vol =
257:
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195:Energy/vol =
193:
190:
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175:Light current
168:
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4014:— Preceding
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3397:141.53.32.79
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2625:Brem article
2260:Brem article
1912:Larmor says
1418:
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1250:DanHickstein
1237:
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107:
51:WikiProjects
34:
1717:Art Carlson
1395:Just granpa
1318:Just granpa
1294:Just granpa
1244:—Preceding
4131:Categories
3582:cgs system
3567:(SI units)
1514:(SI units)
1277:Kmarinas86
1225:Complexica
180:TEMP HOME
3957:(I think
3902:dimension
3727:dimension
3376:Zueignung
2892:Zueignung
39:is rated
4058:contribs
4028:contribs
4016:unsigned
3419:unsigned
3329:Jhmadden
1258:contribs
1246:unsigned
169:Untitled
4085:Alfa137
4070:Alfa137
4020:Alfa137
3998:Lambiam
3865:Alfa137
3851:Lambiam
3586:Lambiam
3476:Alfa137
3439:Alfa137
668:since,
150:on the
123:Physics
114:Physics
70:Physics
41:C-class
3992:. The
3458:wrong.
47:scale.
4101:that.
3790:power
3584:? --
3490:Units
3470:wabi
2834:Steve
1425:Steve
1192:linas
28:This
4118:talk
4089:talk
4074:talk
4055:talk
4024:talk
3988:, a
3932:and
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3601:talk
3480:talk
3464:talk
3443:talk
3427:talk
3401:talk
3380:talk
3333:talk
2896:talk
2838:talk
2429:Let
1721:talk
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1429:talk
1399:talk
1322:talk
1298:talk
1254:talk
1215:Talk
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402:1
398:=
387:2
345:2
341:R
335:4
331:c
325:0
315:2
293:2
283:2
279:a
273:2
269:q
237:2
232:|
227:E
219:0
211:2
207:/
203:1
154:.
53::
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