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 1st November 2011, 04:31 PM #4361 W.D.Clinger Illuminator     Join Date: Oct 2009 Posts: 3,300 a simple derivation of magnetic reconnection, part 1 So long as Michael Mozina continues to wallow in the pit of denial he's dug for himself, we might as well finish up the derivation of magnetic reconnection in the experiment he's been running away from for most of the past year. By giving up on Michael Mozina, we free ourselves to use freshman-level math and physics that lie far beyond his knowledge and capability. Simpler demonstrations of magnetic reconnection have already been presented in this or related threads, includingThe Man's demonstration using refrigerator magnets videos derived directly from Maxwell's equations and recommended by Tim Thompson The purpose of this derivation is to show how we can get from Maxwell's equations to Dungey's figures, the first half of Yamada et al's figure 3, and Wikipedia's animation using no mathematics beyond freshman calculus. The derivation proceeds along the outline suggested by the five equations I quoted from Jackson's Classical Electrodynamics. Although that is hardly a freshman-level textbook, equivalents of those particular equations appear within Purcell's Electricity and Magnetism and other introductory textbooks. Equation 1 (Ampère's law with Maxwell's correction) $ $\nabla \times \hbox{{\bf H}} - \frac{\partial \hbox{{\bf D}}}{\partial t} = \hbox{{\bf J}}$$That's one of the four Maxwell's equations. By conducting the experiment in a vacuum and changing the magnetic field slowly, we can make Maxwell's correction as small as desired. (Changing the magnetic field more slowly makes magnetic reconnection happen more slowly, so you might be afraid this demonstration will be like watching grass grow. Never fear: We can compensate by using time-lapse animation to view the reconnection.) We can simplify our math by making Maxwell's correction negligible and dropping it from the equation to obtain Ampère's original law: $ $\nabla \times \hbox{{\bf H}} = \hbox{{\bf J}}$$ Equation 2 (relationship between H and B) Ampère's law is stated using the H-field. For our derivation, we need to use the B-field. In a vacuum, converting from the H-field to the B-field involves a change of units. The conversion factor µ0 is known as the magnetic constant: $ $\hbox{{\bf H}} = \frac{\hbox{{\bf B}}}{\mu_0}$$Substituting for H in Ampère's original law, we get $ $\nabla \times \hbox{{\bf B}} = \mu_0 \hbox{{\bf J}}$$ Equation 3 (applying the Kelvin-Stokes theorem) Let S be any smooth compact 2-dimensional surface, and let C (a 1-dimensional curve) be the boundary of S. Applying the Kelvin-Stokes theorem (which is a corollary of the fundamental theorem of calculus in n dimensions) to the equation above, we get $ $\oint_C \hbox{{\bf B}} \cdot d \hbox{{\bf l}} = \int_S \nabla \times \hbox{{\bf B}} \cdot \hbox{{\bf n}} \; da = \mu_0 \int_S \hbox{{\bf J}} \cdot \hbox{{\bf n}} \; da$$ Equation 4 (magnetic field around a current-carrying rod) For our experiment, we can use long rods and perform all of our measurements of the magnetic field in the vicinity of the rods' centers. Under those conditions, the magnetic fields we measure will be the same (to within experimental error) as the magnetic fields around infinitely long rods. We need to start by calculating the magnetic field around a single current-carrying rod. By symmetry, the magnetic field will look the same in every plane that intersects the rod at a right angle. Taking S to be a disk of radius R in one of those planes with the rod at its center, we find that the integral of B along the boundary of that disk is equal to the total current flux through the disk. By Ampère's law, the magnetic field is tangent to that boundary at every point (with direction determined by the right hand rule). By symmetry, the magnitude of the field is the same at every point on the circle. Denoting the current through a single rod at time t by I(t), the current flux through S is I(t). Hence $ $2 \pi R | \hbox{{\bf B}} | = \mu_0 I(t)$$whence $ $| \hbox{{\bf B}} | = \frac{\mu_0}{2 \pi} \frac{I(t)}{R}$$which is a simplification of Jackson's equation. (His equation illustrated the Biot-Savart law, which we managed to avoid by appealing to symmetry.) (We have now answered one of Reality Check's critical questions that Michael Mozina was unable to answer.) Equation 5 (superposition) Superposition is so simple that many textbooks don't even bother to state it as an equation. Jackson stated superposition as part of the equation that tells how to convert the B-fields through media of different permeability into the composite H-field: $ $H_\alpha &= \sum_{\beta} \mu_{\alpha \beta}^\prime B_\beta$$By conducting our experiment in a vacuum, transforming from component notation to vector notation, and translating the left-hand side of that equation into the equivalent B-field, we get the unadorned and uncomplicated equation for superposition of magnetic fields: $ $\hbox{{\bf B}} = \sum_{\beta} \hbox{{\bf B}}_\beta$$(Yes, the Greek letter that confused Michael Mozina has disappeared altogether. Imagine that.) To be continued... Last edited by W.D.Clinger; 1st November 2011 at 05:39 PM. Reason: corrected a minor mistake (while leaving a more serious error untouched)
 1st November 2011, 04:32 PM #4362 Reality Check Penultimate Amazing   Join Date: Mar 2008 Location: New Zealand Posts: 21,356 Originally Posted by Michael Mozina By your logic both of Clinger's books also support God and astrology too because neither author mentions them. Holy cow! Yep, this is *EXACTLY* like arguing with creationists. Wrong again. The logic is really simple. Fresh-man level textbooks describe the theory of electromagnetism (Maxwell's equations, etc.). It is the theory of electromagnetism that supports magnetic reconnection. If you knew or understood EM theory then you would agree but you do not have that knowledge: Michael Mozina's ignorance of high school science (the right hand rule). __________________ NASA Finds Direct Proof of Dark Matter (another observation) (and Abell 520) Electric comets still do not exist!
 1st November 2011, 04:33 PM #4363 Michael Mozina Banned   Join Date: Feb 2009 Posts: 9,361 Originally Posted by Reality Check Wrong again. The logic is really simple. Fresh-man level textbooks describe the theory of electromagnetism (Maxwell's equations, etc.). Maxwell's equations don't say a DAMN THING about "reconnection".
 1st November 2011, 04:35 PM #4364 Reality Check Penultimate Amazing   Join Date: Mar 2008 Location: New Zealand Posts: 21,356 MM: Can you answer sol invictus's question about magnetic field lines and Gauss' law Originally Posted by Michael Mozina Yep, it's *EXACTLY* like arguing with creationists. Denial, denial, dodge, denial. Wrong: it's *EXACTLY* like arguing with a typical physics cranks: Ignorance, ignorance, dodge, denial, straw man, return to ignorance. For example, you continue to dodge: MM: Can you answer sol invictus's question about magnetic field lines and Gauss' law first asked by sol invictus on 27 October 2011 __________________ NASA Finds Direct Proof of Dark Matter (another observation) (and Abell 520) Electric comets still do not exist!
 1st November 2011, 04:38 PM #4365 Michael Mozina Banned   Join Date: Feb 2009 Posts: 9,361 Originally Posted by W.D.Clinger By conducting the experiment in a vacuum and changing the magnetic field slowly, we can make Maxwell's correction as small as desired. (Changing the magnetic field more slowly makes magnetic reconnection happen more slowly,.... BS! That permeability factor that you're running like hell from describes *INDUCTANCE* per unit length, not *RECONNECTIONS* per unit length! http://en.wikipedia.org/wiki/Equivocation Your entire argument is based on a fallacy. You've simply redefined the term "inductance" to "reconnection"! Last edited by Michael Mozina; 1st November 2011 at 04:41 PM.
 1st November 2011, 04:41 PM #4366 Reality Check Penultimate Amazing   Join Date: Mar 2008 Location: New Zealand Posts: 21,356 Originally Posted by Michael Mozina Maxwell's equations don't say a DAMN THING about "reconnection". Originally Posted by Reality Check Wrong: it's *EXACTLY* like arguing with a typical physics cranks: Ignorance, ignorance, dodge, denial, straw man, return to ignorance. How ignorant of you MM. Maxwell's equations don't say a DAMN THING about magnetic reconnection. They also say nothing aboutdouble layers plasma Alfvén waves whistler waves every other EM process in the universe ! EM processes like magnetic reconnection and double layers are based on Maxwell's equations. For MHD we also add fluid mechanics to the mix. __________________ NASA Finds Direct Proof of Dark Matter (another observation) (and Abell 520) Electric comets still do not exist!
 1st November 2011, 04:45 PM #4367 Reality Check Penultimate Amazing   Join Date: Mar 2008 Location: New Zealand Posts: 21,356 Michael Mozina's delusion about "*RECONNECTIONS* per unit length" Originally Posted by Michael Mozina BS! That permeability factor that you're running like hell from describes *INDUCTANCE* per unit length, not *RECONNECTIONS* per unit length! Double BS. Firstly W.D. Clinger is not running away from permeability. The equations he has cited have permeability in them (one equation is the definition of permeability!). ETA: The only reason that he has permeability is so that he can use H instead of B for a while. As in his post above, he then transforms back to B and permeability vanishes! The main idiocy in your post is the delusion that the equations have to have a mythical "*RECONNECTIONS* per unit length" in them. __________________ NASA Finds Direct Proof of Dark Matter (another observation) (and Abell 520) Electric comets still do not exist! Last edited by Reality Check; 1st November 2011 at 05:16 PM.
 1st November 2011, 05:04 PM #4368 Reality Check Penultimate Amazing   Join Date: Mar 2008 Location: New Zealand Posts: 21,356 Michael Mozina's delusion that permeability is inductance Originally Posted by Michael Mozina BS! That permeability factor that you're running like hell from describes *INDUCTANCE* per unit length, not *RECONNECTIONS* per unit length! The second delusion in this post (see Michael Mozina's delusion about "*RECONNECTIONS* per unit length" for the first one) is the delusion that permeability is inductance just because permeability has the SI units of henries per meter and inductance has the SI units of henries. MM: FYI, I could measure permeability in cgs units and inductance in SI units and all of a sudden permeability is not inductance according to your twisted logic ! Perpetual Student's post is the best explanation Originally Posted by Perpetual Student Inductance is a property of a circuit element (an object like a coil, an inductor) -- it's a measure of its ability to store energy in a magnetic field, whereas, Permeability is the ability of a material to support a magnetic field (the degree of magnetization that can be supported) which is why some object's permeability can be seen as inductance per unit length (henry per meter). A device that is made of a material that has x permeability will have an inductance (henries) based on its size and construction. It only takes a little logic and rudimentary mathematics to understand the difference. Note that inductance is the measure of the property of an object; permeability is the measure of the property of a material. __________________ NASA Finds Direct Proof of Dark Matter (another observation) (and Abell 520) Electric comets still do not exist! Last edited by Reality Check; 1st November 2011 at 05:09 PM.
 1st November 2011, 07:08 PM #4369 W.D.Clinger Illuminator     Join Date: Oct 2009 Posts: 3,300 ETA: I might as well make another correction to that equation! Originally Posted by Michael Mozina This conversation is *EXACTLY* like arguing with creationists. You guys NEVER actually read or respond to the materials and you make stuff up as you go. No RC, "reconnection" is trivially *IMPOSSIBLE* in basic theory because magnetic lines have no beginning and no ending and no ability to "disconnect" or "reconnect". Congratulations, Michael Mozina. You have just confirmed (for the umpteenth time) what I wrote here: Originally Posted by W.D.Clinger You will have no right to judge anyone until you read and understand the basic concepts of freshman-level electromagnetism. For example: You have been denying the relevance of $ $\lim_{\delta \rightarrow 0} \frac{1}{8 r \delta^3} \oint_{S_\delta(r,\theta,z)} \hbox{{\bf B}} \cdot d \hbox{{\bf A}} = 0$$ What part of that equation do you not understand? Last edited by W.D.Clinger; 1st November 2011 at 07:17 PM. Reason: added the previously omitted factor of 1/r
 1st November 2011, 07:59 PM #4370 Reality Check Penultimate Amazing   Join Date: Mar 2008 Location: New Zealand Posts: 21,356 Missed this: Originally Posted by Michael Mozina No RC, "reconnection" is trivially *IMPOSSIBLE* in basic theory because magnetic lines have no beginning and no ending and no ability to "disconnect" or "reconnect". ...'kinetic energy' gliiberish snipped... MM, repeating your ignorance about magnetic reconnection is is not wise. Magnetic reconnection is trivially *POSSIBLE* in basic EM theory. There are no magnetic field lines beginning and ending in magnetic reconnection. The magnetic fields lines are not cut. No ends of magnetic field lines are glued together. See MHD reconnection N.B. The curator of this Scholarpedia article is Eric R Priest. __________________ NASA Finds Direct Proof of Dark Matter (another observation) (and Abell 520) Electric comets still do not exist!
 2nd November 2011, 12:54 AM #4371 tusenfem Master Poster     Join Date: May 2008 Posts: 2,165 Originally Posted by Michael Mozina IMO you're underestimating the energy conditions inside the pinch during a flare. Something sure is releasing gamma radiation during some types of flare events. Apparently, like in every paper you read, you have not understood the processes said paper was talking about. This is a paper about curvature radiation, the emitted frequency is specifically given for this process. Try to get that to work in a solar flare, really do the math! Naturally, there are other mechanisms to create gamma radiation, but those are not in the paper as they were unimportant in the physics of neutron star magnetospheres. __________________ 20 minutes into the future This message is bra-bra-brought to you by z-z-z-zik zak And-And-And I'm going to be back with you - on Network 23 after these real-real-real-really exciting messages (Max Headroom) follow me on twitter: @tusenfem, or follow Rosetta Plasma Consortium: @Rosetta_RPC
 2nd November 2011, 03:10 AM #4372 Belz... Fiend God     Join Date: Oct 2005 Location: In the details Posts: 71,789 Originally Posted by Michael Mozina Yes, I know. Finally. __________________ Master of the Shining Darkness
 2nd November 2011, 03:11 AM #4373 Belz... Fiend God     Join Date: Oct 2005 Location: In the details Posts: 71,789 Originally Posted by Michael Mozina __________________ Master of the Shining Darkness
 2nd November 2011, 05:22 AM #4374 W.D.Clinger Illuminator     Join Date: Oct 2009 Posts: 3,300 a simple derivation of magnetic reconnection, part 1 (erratum) This is the more serious error I didn't correct when editing my post last night. As you can see, it won't affect our derivation in any way. Originally Posted by W.D.Clinger Equation 5 (superposition) Superposition is so simple that many textbooks don't even bother to state it as an equation. Jackson stated superposition as part of the equation that tells how to convert the B-fields through media of different permeability into the composite H-field: $ $H_\alpha &= \sum_{\beta} \mu_{\alpha \beta}^\prime B_\beta$$ No, that equation does not express superposition. It's on page 14 of Jackson's Classical Electrodynamics, third edition, in the section immediately following the section on linear superposition, but I misread the equation. As written, it's the equation for translating from B to H in a medium of non-uniform permeability, and there is no superposition. It appears that Jackson never bothers to write down the equation for superposition. Since that's the equation we need, however, I'll continue to refer to the following as our equation 5: Originally Posted by W.D.Clinger ....we get the unadorned and uncomplicated equation for superposition of magnetic fields: $ $\hbox{{\bf B}} = \sum_{\beta} \hbox{{\bf B}}_\beta$$ Last edited by W.D.Clinger; 2nd November 2011 at 05:23 AM. Reason: elided redundant phrase
 2nd November 2011, 07:18 AM #4376 Michael Mozina Banned   Join Date: Feb 2009 Posts: 9,361 Originally Posted by tusenfem Apparently, like in every paper you read, you have not understood the processes said paper was talking about. This is a paper about curvature radiation, the emitted frequency is specifically given for this process. Try to get that to work in a solar flare, really do the math! Naturally, there are other mechanisms to create gamma radiation, but those are not in the paper as they were unimportant in the physics of neutron star magnetospheres. The other important mechanism is a plasma pinch. Somewhere I posted a Chinese paper related to gamma radiation from plasma pinches. I'll see if I can find it later for you.
 2nd November 2011, 07:23 AM #4377 GeeMack Banned   Join Date: Aug 2007 Posts: 7,235 Originally Posted by Michael Mozina I don't understand where the million degree plasmas come from at two ZERO points in a couple of magnetic fields. To suggest a lack of understanding the current state of solar physics somehow validates an otherwise wholly unsupported conjecture would be an argument from ignorance.
 2nd November 2011, 07:27 AM #4379 Michael Mozina Banned   Join Date: Feb 2009 Posts: 9,361 Originally Posted by GeeMack To suggest a lack of understanding the current state of solar physics somehow validates an otherwise wholly unsupported conjecture would be an argument from ignorance. Yes, and since you've never bothered to read Cosmic Plasma or Peratt's book in all the YEARS that we've discussed these topics, you've personally made a CAREER out of arguing from pure ignorance.
 2nd November 2011, 07:30 AM #4380 Michael Mozina Banned   Join Date: Feb 2009 Posts: 9,361 Originally Posted by Reality Check The second delusion in this post (see Michael Mozina's delusion about "*RECONNECTIONS* per unit length" for the first one) is the delusion that permeability is inductance just because permeability has the SI units of henries per meter and inductance has the SI units of henries. MM: FYI, I could measure permeability in cgs units and inductance in SI units and all of a sudden permeability is not inductance according to your twisted logic ! Irony overload. You folks are the ones who are DESPERATELY trying to redefine INDUCTANCE as "reconnection". Your entire argument is based on a logical fallacy called equivocation.
 2nd November 2011, 11:53 AM #4383 Belz... Fiend God     Join Date: Oct 2005 Location: In the details Posts: 71,789 Originally Posted by Michael Mozina The "funny" (well "sad") part of your participation in this thread is that you've made absolutely no attempt to check out the validity of the statements RC or anyone else is making *BEFORE* jumping into the conversation. The sad part in your response to my participation in this thread is that you think that every participant should do so in order to check out the validity of anyone's statement. My comment was relevant, you just don't like it. __________________ Master of the Shining Darkness
 2nd November 2011, 12:11 PM #4384 Reality Check Penultimate Amazing   Join Date: Mar 2008 Location: New Zealand Posts: 21,356 Originally Posted by Michael Mozina Your personal attacks aren't working Clinger, not in any scientific sense anyway. I've learned a LOT from noting the questions that you REFUSE to address. It is not a personal attack: I tis a conclusion dram from your display of ignorance, e.g. Michael Mozina's ignorance of high school science (the right hand rule). He had given references for his claim (any textbook on electromagnetism) which is that you can demonstrate MR using EM. You have no references - just delusions about them: Michael Mozina's fantasy about Anthony Peratt's definition of electrical discharge! 13th January 2011: Dungey's and Peratt's definition of discharge are different Originally Posted by Michael Mozina You refuse to really spend any time at all addressing my questions about changing materials and changing *INDUCTANCE* per distance unit. You are lying: he stated what you should know - the permeability of air is different from the permeability of free space. And as you see above - there is no permeability in the equations when we get back to B. There is no *INDUCTANCE* per distance unit: Michael Mozina's delusion that permeability is inductance! __________________ NASA Finds Direct Proof of Dark Matter (another observation) (and Abell 520) Electric comets still do not exist!
 2nd November 2011, 12:55 PM #4385 Reality Check Penultimate Amazing   Join Date: Mar 2008 Location: New Zealand Posts: 21,356 MM: Induction = solar flares take a million years to happen (31st December 2009) Originally Posted by Michael Mozina Irony overload. You folks are the ones who are DESPERATELY trying to redefine INDUCTANCE as "reconnection". Your entire argument is based on a logical fallacy called equivocation. Ignorance overload. We folks are the ones who are FOLLOWING WHAT THE SCIENCE DOES: defining magnetic reconnection as .... magnetic reconnection! Your entire argument of magnetic reconnection = inductance is based on a logical fallacy called argument from ignorance or maybe a new fallacy which I will call argument from delusion. You continue to ignore the physics that the energy released from solar flares would take a million years if released through induction ! Magnetic Reconnection Redux V (31st December 2009) Originally Posted by Tim Thompson The conversion of magnetic energy into a current always operates on a time-scale characteristic of the system, and that time scale is controlled by the ability of the magnetic field to move through the conductor, in order to create a dB/dt term from which the current is generated. That time-scale in a plasma is rather different than it is for a fixed conductor. Here we find the real deal once again in Priest & Forbes:"In space physics the distinction between ideal and non-ideal processes is important because simple estimates imply that magnetic dissipation acts on a time-scale which is many orders of magnitude slower than the observed time-scale of dynamic phenomena. For example, solar flares release stored magnetic energy in the corona within a period of 100 s. By comparison, the time-scale for magnetic dissipation based on a global scale length of 105 km is of the order of 106 yrs." Priest & Forbes, page 6 All of this occurs in the first few pages of the book, but evidently Mozina has not even bothered to look at it. Why bother to suggest books & papers when the evidence suggests that Mozina will never consult them anyway? __________________ NASA Finds Direct Proof of Dark Matter (another observation) (and Abell 520) Electric comets still do not exist!
 2nd November 2011, 01:23 PM #4386 Reality Check Penultimate Amazing   Join Date: Mar 2008 Location: New Zealand Posts: 21,356 Originally Posted by sol invictus Specifically, they can evolve as shown in this video http://www.youtube.com/watch?v=oKTyf...74A6AD&index=2 . That link is a play list of 5 videos. The easiest one to understand in the context of our discussion is Simulation of Magnetic Reconnection in a Dusty Plasma - DENISIS which shows the magnteic field lines curving into the null point at the center of the plasma to form an X and then reconnecting. __________________ NASA Finds Direct Proof of Dark Matter (another observation) (and Abell 520) Electric comets still do not exist!
 2nd November 2011, 06:08 PM #4387 W.D.Clinger Illuminator     Join Date: Oct 2009 Posts: 3,300 a simple derivation of magnetic reconnection, part 2 In the first part of this derivation and an erratum, we used 5 equations to derive the magnetic field B around a current-carrying rod. In this part of the derivation, we will express that magnetic field in both cylindrical and Cartesian coordinates. In part 3, we will show that the magnetic field around four current-carrying rods reproduces both of the figures in Dungey's 1958 paper, figure 3a in the survey paper by Yamada et al, and the still figure in Wikipedia's current article on magnetic reconnection. In part 4, I will describe a simple variation of the experiment I've been suggesting to Michael Mozina and prove that the topology of the magnetic field changes during that experiment. As Yamada et al explain in their appendix, that change in the topology of the magnetic field is what we mean by magnetic reconnection. Notation for B When we write ∇∙B, we're thinking of B as a function of points in 3-space. When we write dB/dt or ∂B/∂t, we're thinking of B as a function of time. As will become painfully clear if you read Michael Mozina's posts, that contextual overloading of B can confuse people. Let's take a minute to review the notation. We usually speak of B as the magnetic field, which means it's a function from points in 3-space (which we write as R3) to vectors of magnetic flux density (which we also write as R3). In that kind of context, B is a function from R3 to R3, and it would be correct to writeB ∈ (R3 ➝ R3)where (R3 ➝ R3) is the set of all functions from R3 to R3. When we speak of B as a function from time to magnetic fields, it would be correct to writeB ∈ (R ➝ (R3 ➝ R3))We may also regard B as a function of four variables (x, y, z, and t), so it would be correct to writeB ∈ ((R3 × R) ➝ R3)Because (R ➝ (R3 ➝ R3)) is isomorphic to ((R3 × R) ➝ R3), these last two meanings for B are consistent. I'll continue to use the traditional notation (instead of lambda calculus, which would be more precise), but everyone should keep in mind that context determines whether we're thinking of B as a function of space or time. From part 1, here are the equations we'll need as we move forward: Equation 3 (integral form of Ampère's law) $ $\oint_C \hbox{{\bf B}} \cdot d \hbox{{\bf l}} = \int_S \nabla \times \hbox{{\bf B}} \cdot \hbox{{\bf n}} \; da = \mu_0 \int_S \hbox{{\bf J}} \cdot \hbox{{\bf n}} \; da$$ Equation 4 (magnitude of magnetic field around a current-carrying rod) In cylindrical coordinates: $ $| \hbox{{\bf B}} | = | \hbox{{\bf B}} (r, \theta, z, t) | = | \hbox{{\bf B}} (t) (r, \theta, z) | = \frac{\mu_0}{2 \pi} \frac{I(t)}{r}$$where those first two equalities illustrate the context-dependent overloading of B. Equation 5 (superposition) $ $\hbox{{\bf B}} = \sum_{i} \hbox{{\bf B}}_i$$ Magnetic field around a single rod (cylindrical coordinates) From equations 3 and 4, the magnetic field around a single current-carrying rod positioned at r=0 is $ $\hbox{{\bf B}} = \hbox{{\bf B}} (r, \theta, z, t) = \hbox{{\bf B}} (t) (r, \theta, z) = \frac{\mu_0}{2 \pi} \frac{I(t)}{r} \hbox{{\bf e}}_\theta$$where eθ is the unit vector in the θ direction. Magnetic field around a single rod (Cartesian coordinates) In part 3, we'll derive the magnetic field for two and then four current-carrying rods. They won't all be positioned at r=0. To derive the magnetic field around rods positioned elsewhere, Cartesian coordinates will be more convenient. From the equation above for cylindrical coordinates, the magnetic field around a single current-carrying rod positioned at the origin of a Cartesian coordinate system is  \begin{align*} \hbox{{\bf B}} &= \hbox{{\bf B}} (x, y, z, t) = \hbox{{\bf B}} (t) (x, y, z) \\ &= \frac{\mu_0}{2 \pi} \frac{I(t)}{\sqrt{x^2+y^2}} \left( - \frac{y}{\sqrt{x^2+y^2}} \, \hbox{{\bf e}}_x + \frac{x}{\sqrt{x^2+y^2}} \, \hbox{{\bf e}}_y \right) \\ &= \frac{\mu_0}{2 \pi} \frac{I(t)}{x^2+y^2} \left( - y \, \hbox{{\bf e}}_x + x \, \hbox{{\bf e}}_y \right) \end{align*}where ex and ey are the unit vectors in the x and y directions. Everything we've done so far is found within standard textbooks on electromagnetism. In part 3, we'll go beyond freshman-level textbooks by reproducing the magnetic fields shown in Dungey's figures and in Yamada et al's figure 3a.
 2nd November 2011, 06:18 PM #4388 Reality Check Penultimate Amazing   Join Date: Mar 2008 Location: New Zealand Posts: 21,356 Originally Posted by W.D.Clinger As Yamada et al explain in their appendix, that change in the topology of the magnetic field is what we mean by magnetic reconnection. The existence of the Yamada et. al. does emphasis a problem that Michael Mozina seems to have: he is so convinced that his fantasies are correct that he ignores the actual science and any citations to the actual science. Yamada et al were first cited in this thread on 27th January 2011 by tusenfem and there is no sign that MM has even looked at the paper . __________________ NASA Finds Direct Proof of Dark Matter (another observation) (and Abell 520) Electric comets still do not exist!
 2nd November 2011, 07:16 PM #4389 Michael Mozina Banned   Join Date: Feb 2009 Posts: 9,361 Originally Posted by W.D.Clinger In the first part of this derivation and an erratum, we used 5 equations to derive the magnetic field B around a current-carrying rod. In other words, just like any good creationist, you absolutely, positively refuse to provide ANY kind of published work to support your OUTRAGEOUS claims, instead you just keep handwaving away and tossing around formulas related to INDUCTANCE per distance unit, not RECONNECTION. You also refused to answer any of my related questions about kinetic energy at two zero points in a magnetic field. You just keep flailing away, and trying to use completely unrelated work inside of ELECTRICAL DISCHARGE PLASMAS to support your case (Dungey/Yamada). Wow. Evidently you never intend to address those permeability questions or electrical discharge questions (Dungey) in any meaningful way. Last edited by Michael Mozina; 2nd November 2011 at 07:31 PM.
 2nd November 2011, 07:26 PM #4390 Michael Mozina Banned   Join Date: Feb 2009 Posts: 9,361 Originally Posted by Reality Check The existence of the Yamada et. al. does emphasis a problem that Michael Mozina seems to have: he is so convinced that his fantasies are correct that he ignores the actual science and any citations to the actual science. Huh? Let see. Clinger has name dropped four names now, Purcell, Jackson, Dungey and Yamada in support of his personal "reconnection experiment", two of which NEVER EVEN MENTIONED reconnection. The other two papers he keeps referring to (Dungey/Yamada) occur in PLASMAS, include ELECTRICAL DISCHARGES/Discharge chambers, and have NOTHING whatsoever to do with Clinger's personal 'experiment'. Would Clinger like to throw in Jesus and Einstein too as MR proponents? They never mentioned "magnetic reconnection" either, but that clearly doesn't seem to stop him from trying to use them to support his case. Last edited by Michael Mozina; 2nd November 2011 at 07:28 PM.
 2nd November 2011, 07:35 PM #4391 Michael Mozina Banned   Join Date: Feb 2009 Posts: 9,361 Originally Posted by Belz... The sad part in your response to my participation in this thread is that you think that every participant should do so in order to check out the validity of anyone's statement. My comment was relevant, you just don't like it. http://books.google.com/books?id=e63...dungey&f=false I think it's reasonable to be asking yourself who's telling you the truth and who isn't. RC is in pure denial of the fact that both Dungey and Peratt described "electrical discharges" in plasmas. In fact Dungey (and Giovanelli before him) specifically linked flares to "electrical discharges" and Dungey specifically links "discharges" to "reconnection" events. The sad part is that you simply don't care to find out who's telling the truth.
 2nd November 2011, 07:38 PM #4392 Michael Mozina Banned   Join Date: Feb 2009 Posts: 9,361 Originally Posted by Reality Check That link is a play list of 5 videos. The easiest one to understand in the context of our discussion is Simulation of Magnetic Reconnection in a Dusty Plasma - DENISIS which shows the magnteic field lines curving into the null point at the center of the plasma to form an X and then reconnecting. Oh, science by pretty "looks like a reconnection bunny" pictures. Where does the kinetic energy come from at two ZERO points in two magnetic fields RC? Dungey used ELECTRICAL DISCHARGES.
 2nd November 2011, 07:38 PM #4393 Reality Check Penultimate Amazing   Join Date: Mar 2008 Location: New Zealand Posts: 21,356 Originally Posted by Michael Mozina In other words, just like any good creationist, ..usual rant.... In other words, just like any honest person, W.D. Clinger is trying (obviously in vain) to educate you about the basic EM theory that the experiment I've been suggesting to Michael Mozina uses. You continue to lie about his claim: W.D. Clinger'sclaim is that you can use freshman-level EM to describe magnetic reconnection. His 2 'simple derivation' posts so far have used freshman-level EM to describe the magnetic field around a current carying rod. FYI: Maxwell's equations are introduced to physics students in their first (freshman) year. You continue to lie about his references: W.D. Clinger has cited at least one freshman-level EM textbook, one book on magnetic reconnection and one magnetic reconnection paper (a 2010 review). He refused to answer your 'kinetic energy at two zero points in a magnetic field' question becuase the question isGibberish Nothing to do with his proposed experiment (no plasma = no particles = no kinetic energy). Now try reading his posts again: a simple derivation of magnetic reconnection, part 2 Quote: In the first part of this derivation and an erratum, we used 5 equations to derive the magnetic field B around a current-carrying rod. In this part of the derivation, we will express that magnetic field in both cylindrical and Cartesian coordinates. In part 3, we will show that the magnetic field around four current-carrying rods reproduces both of the figures in Dungey's 1958 paper, figure 3a in the survey paper by Yamada et al, and the still figure in Wikipedia's current article on magnetic reconnection. So far this is definitely freshman EM: Maxwell's equations plus a bit of calculus. __________________ NASA Finds Direct Proof of Dark Matter (another observation) (and Abell 520) Electric comets still do not exist!
 2nd November 2011, 07:41 PM #4394 Michael Mozina Banned   Join Date: Feb 2009 Posts: 9,361 Originally Posted by Reality Check In other words, just like any honest person, W.D. Clinger is trying (obviously in vain) to educate you about the basic EM theory that the experiment I've been suggesting to Michael Mozina uses. An "honest" man would provide a PUBLISHED REFERENCE that was DIRECTLY RELATED to his actual experiment, he'd explain where the kinetic energy comes from, and he'd answer my questions about permeability and INDUCTANCE per unit length. Last edited by Michael Mozina; 2nd November 2011 at 07:55 PM.
 2nd November 2011, 07:43 PM #4395 Michael Mozina Banned   Join Date: Feb 2009 Posts: 9,361 Originally Posted by Reality Check So far this is definitely freshman EM: Maxwell's equations plus a bit of calculus. You're right, but all of it relates to INDUCTANCE and not a single bit of it relates to "reconnection". Purcell never even mentioned "reconnection", but I'm sure he explained permeability and INDUCTANCE in his book.
 2nd November 2011, 07:47 PM #4396 Michael Mozina Banned   Join Date: Feb 2009 Posts: 9,361 Clingers use of circuit theory is quite ironic, particularly in current carrying plasma (like Yamada and Dungey) where Alfven's double layer paper makes MR theory OBSOLETE.
 2nd November 2011, 07:48 PM #4397 Reality Check Penultimate Amazing   Join Date: Mar 2008 Location: New Zealand Posts: 21,356 Originally Posted by Michael Mozina Oh, science by pretty "looks like a reconnection bunny" pictures. Oh, science by plug the laws of physics into a completer simulation and see what we get - pretty pictures that illustrate the science ! This is not your very ignorant 'I see bunnies in the clouds' logic where you ignore the science in favor of your fantasies, e.g.'electrical discharges' in a tokamak the delusional nature of Michael Mozina's fantasy about the TRACE RD 171A movie! (debunked by simple physics) the delusional nature of Michael Mozina's fantasy about the Kosovichev movie! (debunked by Dr. Kosovichev) __________________ NASA Finds Direct Proof of Dark Matter (another observation) (and Abell 520) Electric comets still do not exist!
 2nd November 2011, 07:53 PM #4398 Reality Check Penultimate Amazing   Join Date: Mar 2008 Location: New Zealand Posts: 21,356 Originally Posted by Michael Mozina An "honest" man would provide a PUBLISHED REFERENCE that was DIRECTLY RELATED to his actual experiment, he'd explain where the kinetic energy comes from, and he'd answer my question about permeability and INDUCTANCE per unit length. An honest man would not lie about what W.D. Clinger has stated. He has never stated that the proposed experiment is in a PUBLISHED REFERENCE. You have been cited many PUBLISHED REFERENCES on magnetic reconnection experiments that are DIRECTLY RELATED to his actual experiment. He does not have to answer gibberish that is unrelated to his proposed experiment. He does not have to cater to your delusions: Michael Mozina's delusion that permeability is inductance! __________________ NASA Finds Direct Proof of Dark Matter (another observation) (and Abell 520) Electric comets still do not exist!
 2nd November 2011, 07:55 PM #4399 Reality Check Penultimate Amazing   Join Date: Mar 2008 Location: New Zealand Posts: 21,356 Originally Posted by Michael Mozina You're right, but all of it relates to INDUCTANCE and not a single bit of it relates to "reconnection". None of it relates to INDUCTANCE (and never will) and not a single bit of it relates to magnetic reconnection - yet. Michael Mozina's delusion that permeability is inductance! __________________ NASA Finds Direct Proof of Dark Matter (another observation) (and Abell 520) Electric comets still do not exist!
 2nd November 2011, 07:56 PM #4400 Michael Mozina Banned   Join Date: Feb 2009 Posts: 9,361 Originally Posted by Reality Check None of it relates to INDUCTANCE Everywhere you see a permeability variable in his equations it's a measure of INDUCTANCE per unit distance, not RECONNECTIONS!

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