darkenlighten Posted March 23, 2010 Posted March 23, 2010 ambros I still think you are confusing the fact that you should get to the same answer with either Maxwell's equations (which include Gauss's, Faraday's and Ampere's with Maxwell's corrections Laws) or Coulomb's and Biot-Savart Law. And with Ampere's Law, you saying it is only gives loops, but what it is saying is more like the flux through that loops (current) and this why Ampere's law and Biot-Savart law are only applicable for steady currents. You can give the full 3-d picture with Ampere's Law. I really don't think you will understand their full power until you either take an Electrodynamics course or read a book on it front to back. Go to a local Barnes and Nobles or what have you and look through an Electrodynamics book, the emphasis will not be on Coulumb's or Biot-Savart Laws, but on all the others.
Amr Morsi Posted March 23, 2010 Posted March 23, 2010 Ambros........ it is important here to mention a Mathematical Theorem which states that any field vector is totally determined if its curl and divergence are both known. That's why we have 4 Maxwell's Equations; 2 for the Electric Field and another 2 for the Magnetic field ....... although the R.H.S.s of these equations are functions of the electric and magnetic fields themselves. The main problem is in solving these differential equations, and in some times they get solved by perturbation theory. In order to get rid of the curl, you get the curl of both sides of the equation and curl of the curl of a field vector gives the grad of the div of the vector minus the laplacian of that vector. By that I think I explained the 2 problems you are confused with; 1. Maxwell's equations are contradicting or not sufficient, 2. How to solve them?.
ambros Posted March 24, 2010 Author Posted March 24, 2010 I can promise you that this uses maxwell's equations and only maxwell's equations. It is a finite element method model, it splits models into small boxes and solves maxwell's equations inside the boxes using the boundary conditions set by the surrounding boxes. It is used for many applications from antenna design for radar systems to novel EM structures at optical frequencies. Instead of promise, can you point some reference? -- Is there any situation where we can use differential form of Maxwell's equations and can you please point any such scenario or experimental setup? NOT SOLVED: Electron moves along x-axis at 25m/s. What is the magnitude of its magnetic field potential in arbitrary direction at distance 'r'? Please explain whether to use 2nd or 4th equation, and solve for B®. Merged post follows: Consecutive posts merged ambros I still think... If you wish to understand any of this you really have to actually TRY to solve the problem: electron moves along x-axis at 25m/s' date=' what is the magnitude of its magnetic field potential in arbitrary direction at distance 'r', solve for B®. Enough talking, any kid can come here and pretend to know something by photocopying pages from some book while not understanding a slightest bit of what is being said. To understand is to be able to demonstrate, to show by an example, can you do that? -- And in the same time I'm still offering to demonstrate every single thing I said here. Anything else at this point is empty argument and hand-waving. Show me the money! [mp']Consecutive posts merged[/mp] Ambros........ it is important here to mention a Mathematical Theorem which states that any field vector is totally determined if its curl and divergence are both known. That's why we have 4 Maxwell's Equations; 2 for the Electric Field and another 2 for the Magnetic field I hope you actually used any of those equations for anything' date=' so please give us the most simple case scenario where we can apply each of these four equations. -- Can you point any scenario or practical setup that can be solved with only 2nd equation - Gauss's law for magnetism? Can you point any example or experiment where we can use these equations in differential form? The main problem is in solving these differential equations, and in some times they get solved by perturbation theory. In order to get rid of the curl, you get the curl of both sides of the equation and curl of the curl of a field vector gives the grad of the div of the vector minus the laplacian of that vector. By that I think I explained the 2 problems you are confused with; 1. Maxwell's equations are contradicting or not sufficient, 2. How to solve them?. You did not really address any of the issues. Obviously this is something that is not very apparent, so for me to be able to make a point it is necessary for you to follow my argument and respond to questions directly. 1.) Do gravity fields have curl? 2.) Solve the above example, B®?
Klaynos Posted March 24, 2010 Posted March 24, 2010 Instead of promise, can you point some reference? -- Is there any situation where we can use differential form of Maxwell's equations and can you please point any such scenario or experimental setup? NOT SOLVED: Electron moves along x-axis at 25m/s. What is the magnitude of its magnetic field potential in arbitrary direction at distance 'r'? Please explain whether to use 2nd or 4th equation, and solve for B®. Merged post follows: Consecutive posts merged This is not a time resolved modeling system so you can't do that, look at something like MEEP. I cannot give you references unless you want to fork out ~£3000 for a license for HFSS so you can read the documentation. I'm not as familiar with MEEP though. You can solve your problem using maxwell's equations with little trouble, I don't have the time right now though.
Amr Morsi Posted March 24, 2010 Posted March 24, 2010 1. The curl of a static gravitational field is zero 2. To solve the example, thanks to refer to the attached file. chap14.pdf
ambros Posted March 24, 2010 Author Posted March 24, 2010 1. The curl of a static gravitational field is zero Ok, but does it ever change? Does it change with the velocity, with acceleration, maybe only when it interacts with another gravity field? What does it take to change the curl of a single gravity field? 2. To solve the example, thanks to refer to the attached file. "Radiating moving charges" does not apply here and is unnecessary complication. I'm talking about the four equations that we call "Maxwell's equations", not some relativistic error corrections and additions. The same four equations Maxwell used to derive the speed of light and 'wave equation' without any "retarded time" corrections, can we concentrate on those four please. 1.) We have only one charge in this example, there is no interaction, no distance we need to account for where "speed of propagation of fields" error might happen - Lienard-Wiechert potentials, which is more of an addition to Coulomb's law anyway, and this effect has not been confirmed experimentally. 2.) I'm talking about constant velocity, no acceleration - no radiation, right? I wonder what is it that electron can radiate anyway, something inside of it? 3.) I'm talking about charges own reference frame, let's make it as simple as possible, ok? -- B®? Can you point any scenario or practical setup that can be solved with only 2nd equation - Gauss's law for magnetism? Can you point any example or experiment where we can use these equations in differential form?
Amr Morsi Posted March 24, 2010 Posted March 24, 2010 1. The curl of the static gravitational field will not change with the velocity nor acceleration of the affected body but with those of the source mass, i.e. it will be dynamic gravitational field. This can be solved using General Relativity. 2. B® is solved in the attached file for the example you give, just put acceleration equal to zero. Exact B® is given and then approximation is made. Time retardation effects mean the properties of the charge at the time the radiations reach a position P...... It is not an approximation. - With respect to radiation; the electron gets accelerated from the external field, and some energy goes to the kinetic energy of the electron (and change in the direction of the velocity) and a small portion goes to the field radiation. - According to uniformly moving charges frame of reference, the magnetic field will be zero, as the charges will be considered motionless, only there will be electric field. Gauss's law for magnetism is an associated law (since the right hand side is zero), it helps in adding to the other laws that the magnetis flux lines are continuous.
ambros Posted March 25, 2010 Author Posted March 25, 2010 1. The curl of the static gravitational field will not change with the velocity nor acceleration of the affected body but with those of the source mass, i.e. it will be dynamic gravitational field. This can be solved using General Relativity. Where do you draw your conclusions from? -- Rotational fields are those where the field *vectors* point away from the source/sink, like tornadoes and magnetic fields. Do you think these field-lines and force-lines of gravity and electric fields ever actually point anywhere else but towards the "source mass"? -- If they did, these fields would not be considered "conservative fields". In short, it is impossible for these radial fields to ever change their rotation from zero, i.e. their field-lines and force-lines will always point directly towards the source, unlike magnetic field-lines or vortexes. Even if there are circular orbits resulting in such fields, that still does not mean the rotation is due to any curl. 2. B® is solved in the attached file for the example you give, just put acceleration equal to zero. Exact B® is given and then approximation is made. Time retardation effects mean the properties of the charge at the time the radiations reach a position P...... It is not an approximation. Maxwell's equations do not apply without relativistic correction? Retardation effect is not experimentally confirmed, so please stick to FOUR EQUATIONS known as "Maxwell's equations", as applied in classical electrodynamics, or at least write down the said equation here so everyone can see it. I have no idea what are you referring to, it's all very ugly. - With respect to radiation; the electron gets accelerated from the external field, and some energy goes to the kinetic energy of the electron (and change in the direction of the velocity) and a small portion goes to the field radiation. If that was true than gravity and electric field would not be conversational. Energy in such fields is exchanged via kinetic and potential energy ONLY, that is the prerequisite for these field to conserve the total system energy. - According to uniformly moving charges frame of reference, the magnetic field will be zero, as the charges will be considered motionless, only there will be electric field. How would you know that from "divB=0"? That equation is seriously missing any information about velocity, about magnetic constant, and about the amount of electric charge. Please try to apply whatever equation you are talking about and see if what you said is actually what equation says. Gauss's law for magnetism is an associated law (since the right hand side is zero), it helps in adding to the other laws that the magnetis flux lines are continuous. Awww, you mean it's useless on its own? Ok, that leaves us with 3rd and 4th equation. -- Can you point any scenario or practical setup that can be solved with only 3rd equation - Faraday's law of induction? Can you point any example or experiment where we can use these equations in differential form?
darkenlighten Posted March 25, 2010 Posted March 25, 2010 Okay so for one, I already solved your problem for the electric field. And I posted the pages so that you would trust my words were just not me talking, but so that I had a legit source. And as I already stated, for this example using Ampere's Law is not the best, nor is it going to be clean. It is best in this situation to use Biot-Savart Law. Which I have posted, the answer you have is an approximation. If you are to read the derivation I posted you would understand why. I might not know everything about Electrodynamics, but I do know what I have been talking about. And for finding magnetic fields, you don't use "Gauss's Law for magnetism" as you like to say, you use Ampere's law. As I said before Biot-Savart and Ampere's law only whole true for steady currents. So anything that has symmetry and a steady current is easily calculated by Ampere's Law, say a coaxial cable or concentric spherical shells, anything (like I said before) with spherical, cylindrical or planar symmetry. I'm out of town right now, so I'll try to solve it using Ampere's Law when I get a chance, but I don't think it'll be that easy considering its not meant for that. Merged post follows: Consecutive posts merged How would you know that from "divB=0"? That equation is seriously missing any information about velocity, about magnetic constant, and about the amount of electric charge. Please try to apply whatever equation you are talking about and see if what you said is actually what equation says. Awww, you mean it's useless on its own? Ok, that leaves us with 3rd and 4th equation. -- Can you point any scenario or practical setup that can be solved with only 3rd equation - Faraday's law of induction? Can you point any example or experiment where we can use these equations in differential form? No, no no....what he means is that "divB=0" is not what you use to solve for the magnetic field, pay attention and read back through, it is the ∇ x B = μoI ⇒ ∫B·dl = μoI(enclosed), not ∇·B = 0
ambros Posted March 26, 2010 Author Posted March 26, 2010 (edited) And for finding magnetic fields' date=' you don't use "Gauss's Law for magnetism" as you like to say, you use Ampere's law. [/quote'] I tried to explain and you thought it was semantics. 1st and 2nd equation are to be used on a single E and B field (single charge/electron), so 1st equation supposedly can be derived in "half" the Coulomb's law, which will evaluate electric field potential in relation to its own source and not related to anything else, no interaction, no induction here - NO FORCE. Similarly, 2nd equation is supposed to be equivalent with Biot-Savart law, but it's obviously not. 3rd and 4th equation are used when what you say the field is "given", which means ANOTHER spatially separate field is there too, at least one more charge/electron, so to have RELATIVE POTENTIAL DIFFERENCE, which leads to attraction/repulsion and movement. Therefore, 3rd equation is supposed to get two halves of the Coulomb's law which then gives us Coulomb's FORCE equation where we have TWO E fields - Q1 and Q2, not any B fields, but 3rd equation is obviously different and that is not how Coulomb's force works, Coulomb's force works like Coulomb's force law says it works. Finally, 4th equation is supposed to be something like Lorentz FORCE equation, where there are actually two B fields - B1 and B2, which it is lacking, as well as geometry and precision, it can hardly describe magnetic force at all. Gravity fields interact only with gravity fields, electric with electric and magnetic with other magnetic fields - no force between two different kinds of fields. *** INDIVIDUAL POTENTIALS RELATIVE TO ITS OWN SOURCE 1. Gauss's law: divE= p/e0 (SHOULD boil down to Coulomb's law: E= q/r^2 2. Gauss's law for magnetism: divB= 0 (SHOULD boil down to Biot-Savart law: B= q*v x 1/r^2 *** INTERACTION/INDUCTION of at least TWO FIELDS -> F O R C E 3. Maxwell–Faraday equation: rotE= - dB/dt (SHOULD boil down to Coulomb's FORCE equation: F= Q1*Q2/r^2 (F= E1*E2/r^2) 4. Ampère's circuital law: rotB= J + dE/dt (SHOULD boil down to Lorentz FORCE equation: F(1-2)= q1(v1 x B2) & F(2-1)= q2(v2 x B1) Can induction be anything else than the effect of interaction of these fields, which can only mean one thing - FORCE - and that can mean only two things - ATTRACTION and REPULSION - and that can mean only one thing - DISPLACEMENT (MOVEMENT), so there is no such thing as "time-varying field", only at large-scale approximation, but in actuality... ...when space-shuttle goes from its orbit to land down on Earth it eventually goes through "time-varying" gravity field, but it is not the gravity field that is being created, induced or anyhow changing or varying, it is only that we are talking about TIME INTEGRALS, so while shuttle is MOVING, then as it passes through TIME and descends, it will automatically be *experiencing* "TIME-VARYING GRAVITY FIELD", but obviously this phrasing is so terrible as it makes people think it's a field that is changing, "pulsating" or something. So anything that has symmetry and a steady current is easily calculated by Ampere's Law, say a coaxial cable or concentric spherical shells, anything (like I said before) with spherical, cylindrical or planar symmetry. You see almost empty glass as a half-full. I would not say "anything", but only certain specific things with high symmetry, such as loops and infinite wires, but that's pretty much it, and everything else is approximation based on either that loop or infinite wire. No, no no....what he means is that "divB=0" is not what you use to solve for the magnetic field, pay attention and read back through, it is the ∇ x B = μoI ⇒ ∫B·dl = μoI(enclosed), not ∇·B = 0 So, we have this important law for magnetism that is not used to solve for the magnetic fields? What then, what is it used for? -- You are giving me that equation for LOOPS, again?!? "No, no, no" to you. There is no induction in our example, there is only one charge/electron there. Are you suggesting the change in electron's own B field induces changes in its own E field, and the other way around? Edited March 26, 2010 by ambros
darkenlighten Posted March 26, 2010 Posted March 26, 2010 I'm going to give this one more shot. Please read this with unbiased attention first and the speculate. I tried to explain and you thought it was semantics. 1st and 2nd equation are to be used on a single E and B field (single charge/electron), so 1st equation supposedly can be derived in "half" the Coulomb's law, which will evaluate electric field potential in relation to its own source and not related to anything else, no interaction, no induction here - NO FORCE. Similarly, 2nd equation is supposed to be equivalent with Biot-Savart law, but it's obviously not. Okay so the 1st equation allows you to find the electric field of a source, including point, lines, surface and volumes charges. And you can use superposition to get the whole story of the other electric fields from other sources, in which you can then use F = qE, where E is the sum of all fields. The second equation, and I stress, is not what is used to find the B field without boundary conditions, once again it is Ampere's Law you use to find the B field of a source. 3rd and 4th equation are used when what you say the field is "given", which means ANOTHER spatially separate field is there too, at least one more charge/electron, so to have RELATIVE POTENTIAL DIFFERENCE, which leads to attraction/repulsion and movement. Therefore, 3rd equation is supposed to get two halves of the Coulomb's law which then gives us Coulomb's FORCE equation where we have TWO E fields - Q1 and Q2, not any B fields, but 3rd equation is obviously different and that is not how Coulomb's force works, Coulomb's force works like Coulomb's force law says it works. Finally, 4th equation is supposed to be something like Lorentz FORCE equation, where there are actually two B fields - B1 and B2, which it is lacking, as well as geometry and precision, it can hardly describe magnetic force at all. Gravity fields interact only with gravity fields, electric with electric and magnetic with other magnetic fields - no force between two different kinds of fields. No not all. The 3rd equation is Faraday's Law, which is about induction of the changing B field, creating an E field. And this B field can be solved for using Ampere's Law. Then this E field can be then added to say a source charge with its own E field, so you would have E(total) = E(source) + E(induced), where E(source) can be a sum of multiple sources. *** INDIVIDUAL POTENTIALS RELATIVE TO ITS OWN SOURCE 1. Gauss's law: divE= p/e0 (SHOULD boil down to Coulomb's law: E= q/r^2 Okay but the point is Gauss's law its much simpler for pretty much everything past a point charge. 2. Gauss's law for magnetism: divB= 0 (SHOULD boil down to Biot-Savart law: B= q*v x 1/r^2 Once again not the correlation to Biot-Savart Law. *** INTERACTION/INDUCTION of at least TWO FIELDS -> F O R C E 3. Maxwell–Faraday equation: rotE= - dB/dt (SHOULD boil down to Coulomb's FORCE equation: F= Q1*Q2/r^2 (F= E1*E2/r^2) 4. Ampère's circuital law: rotB= J + dE/dt (SHOULD boil down to Lorentz FORCE equation: F(1-2)= q1(v1 x B2) & F(2-1)= q2(v2 x B1) The 4th equation does not mean only induction, but is the correction of induction to the B field. Hopefully you can understand that ∇ x B = μoJ is the what is used to find the B field and (μoεo)dE/dt is the additional induction from an external changing E field. So with all of these equations and F = q(E + v x B) you have pretty much everything you need to solve any non-relativistic electrodynamics problem. And of course you can have a time-varying field, what do you think an EM wave is? And that is how induction works, something has to be changing with time. So in your gravity field example, gravity is, of course, the same at a specific point and changes with respect to distance, but it is the shuttle that is moving which causes the "time-varying field", I understand what you mean there. Same thing with induction can happen, but! You can also have a varying current (AC) which will change the field with respect to time and nothing in the system, besides the current, has to move for this to happen. For example a wire with a charged sphere near by, if the current is varying through the wire, the charged sphere does not have to be moving in order to feel the effect of the changing B field. So, we have this important law for magnetism that is not used to solve for the magnetic fields? What then, what is it used for? -- You are giving me that equation for LOOPS, again?!? "No, no, no" to you. There is no induction in our example, there is only one charge/electron there. Are you suggesting the change in electron's own B field induces changes in its own E field, and the other way around? Once again on the loop thing, the loop is describing the area in which a current is passing through the loop, this is the flux that the loop is feeling, which described the B field of the object in question. Similar to the Gaussian surface, where you have a certain charge enclosed in the surface, you have a certain current passing through this Amperian loop. The Amperian loop is not describing your object that you are looking at, but it is describing the the flux of current of that object in that area. And as I stated above, the 4th equation is not just about induction, but about the whole story of the B field. It could almost be two separate equations. One for deriving the B field (∇ x B1 = μoJ) and one for the additional effect of a changing E field (∇ x B2 = (μoεo)dE/dt), where the total B field is B(total) = B1 + B2. Is that any better?
ambros Posted March 27, 2010 Author Posted March 27, 2010 (edited) The second equation, and I stress, is not what is used to find the B field without boundary conditions, once again it is Ampere's Law you use to find the B field of a source. http://en.wikipedia.org/wiki/Biot-savart_law -"The vector field B depends on the magnitude, direction, length, and proximity of the electric current, and also on a fundamental constant called the magnetic constant. The law is valid in the magnetostatic approximation, and results in a B field consistent with both Ampère's circuital law and Gauss's law for magnetism." Your demonstration so far suggests you have not used any of those equations, ever. You need to realize these two sets of equations must be strictly IDENTICAL as they are describing the same fields and same interaction. So, for example, if 2nd Maxwell's equation does not equal to Biot-Savart law, then one of them is wrong or not complete, and you will never realize which one if you do not start USING them. No not all. The 3rd equation is Faraday's Law, which is about induction of the changing B field, creating an E field. And this B field can be solved for using Ampere's Law. Then this E field can be then added to say a source charge with its own E field, so you would have E(total) = E(source) + E(induced), where E(source) can be a sum of multiple sources. Okay but the point is Gauss's law its much simpler for pretty much everything past a point charge. Once again not the correlation to Biot-Savart Law. Q1: Wire W1 positioned along x-axis has steady current of 1 ampere, what is the magnitude of E and B field at some arbitrary distance, solve for E® and B®? The 4th equation does not mean only induction, but is the correction of induction to the B field. Hopefully you can understand that ∇ x B = μoJ is the what is used to find the B field and (μoεo)dE/dt is the additional induction from an external changing E field. Q2: When and what for is the 2nd equation used then, one example please? So with all of these equations and F = q(E + v x B) you have pretty much everything you need to solve any non-relativistic electrodynamics problem. Q3: Wire W1 positioned along x-axis has a steady current of 1 ampere, the second wire W2 has no current or voltage directly applied to it and is always parallel to W1, it can only move along y-axis so to get closer and further away from W1 while them staying perfectly parallel. -- Now, if wire W2 moves with constant velocity of 25m/s from the distance 2.5m to 0.5m towards the wire W1, describe how dB and dE in these two wires vary with the time and solve for the total amount of E and B fields induced in wire W2 during this motion. And of course you can have a time-varying field Nonsense, time is only a consequence of motion. E fields never ever vary, which is why we say electric charge is quantized and constant. The closest thing to what you're saying is that B fields vary with VELOCITY, where the spatial change is the actual causal link, not the time. In any case nothing else varies about these fields, ever, except their relative distance. what do you think an EM wave is? Let's see... when we smash positron and electron together we get photon, and when we smash photons apart we get positron-electron pairs. I already told you how I got "em waves" with Lorentz force and with no boundary conditions, but with INITIAL CONDITIONS. I did not "force" these two charges to twirl and oscillate around each other as transverse waves, that was written in the Coulomb's, Biot-Savart-Law and Lorentz force long time ago, and still is, see for yourself. http://en.wikipedia.org/wiki/Light_polarization It looks exactly like this, except there is one more charge (opposite) whose trajectory mirrors the blue path pictured here, and is actually THE REASON why would any electric fields move like that - up/down and/or left/right - there are actually two of them orbiting each other. Q4: Are you suggesting the change in electron's own B field induces changes in its own E field, and the other way around? What do you think how many separate E and B fields are there in one photon in any single instant in time? Edited March 27, 2010 by ambros
darkenlighten Posted March 27, 2010 Posted March 27, 2010 http://en.wikipedia.org/wiki/Biot-savart_law-"The vector field B depends on the magnitude, direction, length, and proximity of the electric current, and also on a fundamental constant called the magnetic constant. The law is valid in the magnetostatic approximation, and results in a B field consistent with both Ampère's circuital law and Gauss's law for magnetism." Your demonstration so far suggests you have not used any of those equations, ever. You need to realize these two sets of equations must be strictly IDENTICAL as they are describing the same fields and same interaction. So, for example, if 2nd Maxwell's equation does not equal to Biot-Savart law, then one of them is wrong or not complete, and you will never realize which one if you do not start USING them. Q1: Wire W1 positioned along x-axis has steady current of 1 ampere, what is the magnitude of E and B field at some arbitrary distance, solve for E® and B®? Okay lets do this I will solve this for now and get to the other ones later when I have more time:
ambros Posted March 27, 2010 Author Posted March 27, 2010 Please use some printed and readable pictures or plain text and/or symbols. I'd rather you do not do any derivations any more, but simply write down the final equation exactly as required, or copy/paste somewhere from the internet, or point to proper reference. Constants: Ke= 1/4Pi*e0 ; Km= m0/4Pi E®= Ke* (-q+q)/r^2 B®= Km* I/r^2 ======================================== YOUR EQUATION: E®= Ke* I(t)/r ?? What is that red "t", how do I "plug" that in, what is that? Please get out of cylindrical coordinates and tell us if your distance is inverse squared or not? -- There will be no electric field around wire because conductors are macroscopically electrically neutral due to superposition, as there is about equal amount of negative and positive charges in close proximity, so wires have net zero external electric charge, regrades of any current and voltage applied. That's how crazy formulas can make you blind even to the most obvious everyday experience. YOUR EQUATION: B®= Km* I*Fi/r ?? Is that "Fi" for flux, how do I "plug" in that one? I believe this below is what you meant to say, but that is still not Biot-Savart law. http://dev.physicslab.org/Document.aspx?doctype=3&filename=Magnetism_BiotSavartLaw.xml http://dev.physicslab.org/Document.aspx?doctype=3&filename=Magnetism_AmperesLaw.xml
Cap'n Refsmmat Posted March 27, 2010 Posted March 27, 2010 Please use some printed and readable pictures or plain text and/or symbols. I'd rather you do not do any derivations any more, but simply write down the final equation exactly as required, or copy/paste somewhere from the internet, or point to proper reference. For convenience, we also have a LaTeX system that allows you to typeset your equations nicely. There's a tutorial available here.
darkenlighten Posted March 27, 2010 Posted March 27, 2010 YOUR EQUATION: E®= Ke* I(t)/r ?? What is that red "t", how do I "plug" that in, what is that? Please get out of cylindrical coordinates and tell us if your distance is inverse squared or not? -- There will be no electric field around wire because conductors are macroscopically electrically neutral due to superposition, as there is about equal amount of negative and positive charges in close proximity, so wires have net zero external electric charge, regrades of any current and voltage applied. That's how crazy formulas can make you blind even to the most obvious everyday experience. [/Quote] Yea so the equation I derived is a segment of the wire that would have a net charge if you only considered the electrons charge. So yes you are right there should, then, be no electric field around the wire in that case. So that is done. YOUR EQUATION: B®= Km* I*Fi/r ?? Is that "Fi" for flux, how do I "plug" in that one? I believe this below is what you meant to say, but that is still not Biot-Savart law. Well no the [math]\hat{\phi}[/math] is the direction since it is a vector, so that is the correct B field. And believe it (or not), yes that is what you get for an infinite wire, or an approximation for a really long wire or one "looking" very close to the wire. Using Biot-Savart you can get: [math] \frac{\mu_o I}{4\pi s}(sin\theta_2 - sin\theta_1)[/math] and thanks Cap'n Refsmmat
ambros Posted March 28, 2010 Author Posted March 28, 2010 (edited) Ke=1/4Pi*e0 Coulomb's law: E= Ke* (-q+q)/r^2 Km=m0/4Pi Biot-Savart law:B= Km* I/r^2 -simplification without "dlxR", as distance is measured at right angle ================================================== Ok, let's now look at those constants - what in the world is "4Pi" doing there? It seem arbitrary in these equations as they already describe spherical geometry without it, it's an unnecessary scalar in this vector equation, how did it get there? In any case, we should note the whole term "4Pi*r^2" is the description of 'surface area of a sphere', i.e. A= 4Pi*r^2. 1.) ELECTRIC FIELDS 1st: divE= p/e0 3rd: rotE= -dB/dt ------------------ First time you gave us something like Coulomb's law, so please decide and write down what is the final equation for E field you are offering as the solution for this example, I'm not sure if your distance there is inverse squared or not. In any case there is something strange about the 3rd one, where do we see E field depend on the change of B field, and how can this 3rd equation do anything without either magnetic or electric constant? Are there not any examples where we can use this 3rd (and 2nd) equation? 2.) Magnetic fields 2nd: divB= 0 4th: rotB= J + dE/dt --------------------- Where, why and how do we ever use 2nd equation and how can it work without magnetic constant? Anyhow, here is this 4th equation and we finally have some real answers, so let's see if those make any sense... a.) "Are we talking about the same fields?" MAXWELL: B= m0/2Pi * I/r BIOT-SAVART: B= m0/4Pi * I/r^2 "2Pi" is not the same as "4pi" and "r" is not the same as "r^2". What we have here is 'circumference of a circle': C= 2Pi*r, versus 'surface area of a sphere': A= 4Pi*r^2. This again points to "two-dimensionality" of these equations, but most importantly the two formulas are not IDENTICAL, so which one is wrong? b.) "That same old equation for loops, again." - Your equation in its original form actually has some "time-varying" terms in it, so how and why did you pick that one to start with, since we have a 'steady current' in our example? - Did you start with "Formulation in terms of FREE charge and current" or "Formulation in terms of TOTAL charge and current" and how did you make the decision which one suits this example better - are we dealing here with "displacement current: dD/dt", or with "time-varying electric field" dE/dt"? How to obtain the value for "dD/dt" and/or "dE/dt", what is their physical meaning and what do these terms represent in our example? ============================================ BY THE WAY, why is this important? This is exactly what defines the unit of Ampere, that's why, it is actually this magnetic field that goes all the way around and back to bait its tail and define both electricity and magnetism. All this got even more complicated as the units got redefined ("Rationalized") over time and many things became self-referenced and circularly defined. So, electric aka *Coulomb force constant* and magnetic constant lost their physical meaning as experimentally determined values and now it is almost as if they jumped out of Maxwell's equations... EM WAVES: On Physical Lines of Force, by James Clerk Maxwell http://books.google.co.nz/books?id=duyKrTNps_AC&lpg=PA451&dq=%22on%20physical%20lines%20of%20force%22&pg=PA495#v=onepage&q=&f=false - "To find the relation between electromotive force... The ratio of m to mu varies in different substances; but in a medium whose elasticity depend entirely upon forces acting between pairs of particles, this ratio is that of 6 to 5, and in this case E^2= Pi*m ...(108)" http://books.google.co.nz/books?id=duyKrTNps_AC&lpg=PA451&dq=%22on%20physical%20lines%20of%20force%22&pg=PA499#v=onepage&q=&f=false -"To find the rate of propagation of transverse vibrations through the elastic medium of which the cells are composed, on the supposition that its elasticity is due entirely to forces acting between pairs of particles. V^2= m/p ...(132), where 'm' is the coefficient of transverse elasticity, and 'p' is the density. mu= Pi*p ...(133) Pi*m= V^2*mu ...(134) E= V* sqrt(mu) ...(135), and by (108: E^2= Pi*m), In air or vacuum mu=1, and therefore V = E, = 310,740,000,000 millimeters per second ...(136)." What the...? Ratio 6:5?!? -- Where is the "curl of the curl"? Does anyone recognize that equation used to get to the speed of light? - "The speed of propagation of a wave in a string (v) is proportional to the square root of the TENSION of the string (T) and inversely proportional to the square root of the linear mass (μ) of the string (DENSITY)." http://en.wikipedia.org/wiki/Vibrating_string Hmmm, so these are the 'boundary conditions' - "vibrating string"? Funny enough, to me this makes much more sense than how this derivation is interpreted today with "curl of the curl" thing, and I especially like the part about *pairs* of particles, it's as if he is talking about electron-positron pairs too - "dielectric"/"polarized". However, the final calculation... I have no idea how did he get that number and those units - can anyone make sense as what values did he plug in and where did he get those numbers from? Was this the origin of electric and magnetic constant - elasticity and density? Edited March 28, 2010 by ambros
darkenlighten Posted March 28, 2010 Posted March 28, 2010 Ke=1/4Pi*e0 Coulomb's law: E= Ke* (-q+q)/r^2 Km=m0/4Pi Biot-Savart law:B= Km* I/r^2 -simplification without "dlxR", as distance is measured at right angle ================================================== Ok, let's now look at those constants - what in the world is "4Pi" doing there? It seem arbitrary in these equations as they already describe spherical geometry without it, it's an unnecessary scalar in this vector equation, how did it get there? In any case, we should note the whole term "4Pi*r^2" is the description of 'surface area of a sphere', i.e. A= 4Pi*r^2. To start, the reason I (and if you work with these equations) do not use the constant k, is because it does not always appears because some things cancel out the 4 or the pi. This has to do with the geometry of the electric and magnetic fields. And yes what you get is necessary for vector form because it describes the whole picture. 1.) ELECTRIC FIELDS 1st: divE= p/e0 3rd: rotE= -dB/dt ------------------ First time you gave us something like Coulomb's law, so please decide and write down what is the final equation for E field you are offering as the solution for this example, I'm not sure if your distance there is inverse squared or not. The reason it looks different (and the field is different), is because it is due to the geometry of the object. All of the examples I have given have been different scenarios with different geometry. In any case there is something strange about the 3rd one, where do we see E field depend on the change of B field, and how can this 3rd equation do anything without either magnetic or electric constant? Are there not any examples where we can use this 3rd (and 2nd) equation? Here a couple of scenarios: A magnet in motion near a stationary object, causing a change in the B field Or a time-varying current causing a changing B field. The reason you don't "see" any constants is because you can derive the changing B field or you might already know it. Which would be done from Ampere's Law. Take a look: Say you have wire with current [math] I = I_0 cos(\omega t)[/math] what E field is it producing? So [math]\triangledown \cdot \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t}[/math] [math] \Rightarrow \oint \mathbf{E} \cdot d\mathbf{l} = - \int \frac{\partial \mathbf{B}}{\partial t} \cdot d\mathbf{a}[/math] and using Ampere's Law you get [math] \mathbf{B} = \frac{\mu_0 I_0 cos(\omega t)}{2 \pi s} \hat{\phi} [/math] [math] \Rightarrow \mathbf{E} = - \frac{\partial}{\partial t}[\frac{\mu_0 I_0 cos(\omega t)}{4\pi}] \hat{s}[/math] [math] \Rightarrow \mathbf{E} = \frac{\mu_0 I_0 \omega sin(\omega t)}{4\pi} \hat{s} [/math] which makes sense for an infinite wire that E would not depend on distance away 2.) Magnetic fields 2nd: divB= 0 4th: rotB= J + dE/dt --------------------- Where, why and how do we ever use 2nd equation and how can it work without magnetic constant? Anyhow, here is this 4th equation and we finally have some real answers, so let's see if those make any sense... a.) "Are we talking about the same fields?" MAXWELL: B= m0/2Pi * I/r BIOT-SAVART: B= m0/4Pi * I/r^2 "2Pi" is not the same as "4pi" and "r" is not the same as "r^2". What we have here is 'circumference of a circle': C= 2Pi*r, versus 'surface area of a sphere': A= 4Pi*r^2. This again points to "two-dimensionality" of these equations, but most importantly the two formulas are not IDENTICAL, so which one is wrong? The equation you have is wrong, I can show you the derivation from "Introduction to Electrodynamics" if you would like. And as far as the second equation goes. I am unfortunately not experienced with that, from what I've seen it is more of a reason why these equations work the way they do rather than using it to actually solve for the B field. So I do not currently have an example for the 2nd equation that can solve directly the B field, but don't worry we have Ampere's Law mainly for that. b.) "That same old equation for loops, again." - Your equation in its original form actually has some "time-varying" terms in it, so how and why did you pick that one to start with, since we have a 'steady current' in our example? - Did you start with "Formulation in terms of FREE charge and current" or "Formulation in terms of TOTAL charge and current" and how did you make the decision which one suits this example better - are we dealing here with "displacement current: dD/dt", or with "time-varying electric field" dE/dt"? How to obtain the value for "dD/dt" and/or "dE/dt", what is their physical meaning and what do these terms represent in our example? Once again please, please look and understand why we are using loops when solving for B, it shows how the Magnetic Field is behaving. As for why I had a t in there for the electric field for the most recent example was due to that fact the electric field is caused by charges (or a changing B), so if you have a current I that is equal to [math] I = \lambda v[/math], where [math]\lambda[/math] is a line charge. So that was my attempt to get it into terms of charge, since I is Coulomb's per second, the charge in your example for 1 ampere would have been 1 Coulomb. So my equation was like a snapshot or an observation in a certain time interval, since the charge was changing at a rate proportional to current. ============================================ BY THE WAY, why is this important? This is exactly what defines the unit of Ampere, that's why, it is actually this magnetic field that goes all the way around and back to bait its tail and define both electricity and magnetism. All this got even more complicated as the units got redefined ("Rationalized") over time and many things became self-referenced and circularly defined. So, electric aka *Coulomb force constant* and magnetic constant lost their physical meaning as experimentally determined values and now it is almost as if they jumped out of Maxwell's equations... What are you asking about when say "why is this important"? 1
ambros Posted March 29, 2010 Author Posted March 29, 2010 Wire positioned along x-axis has steady current of 1 ampere, solve for E® and B®. MAXWELL: B= m0/2Pi * I/r BIOT-SAVART: B= m0/4Pi * I/r^2 The equation you have is wrong' date=' I can show you the derivation from "Introduction to Electrodynamics" if you would like. [/quote'] What equation is wrong, "Biot-Savart" or "Maxwell"? http://en.wikipedia.org/wiki/Biot-savart If you mean to disagree be specific and write down EXACTLY what you think is the correct solution for this example given by BOTH formulas so we can compare, and yes provide some reference, online preferably. - Meanwhile, I will repeat that this IS the solution (simplified) given by the Biot-Savart law for the B field in relation to electric current and distance from a straight wire, so to be applied to the given example: B®= m0/4Pi * I/r^2 To start, the reason I (and if you work with these equations) do not use the constant k, is because it does not always appears because some things cancel out the 4 or the pi. I was, of course, referring to Biot-Savart and Coulomb's law where these constants are COMPLETELY UNNECESSARY. The point was those constants in Biot-Savart and Coulomb's law are there because of Maxwell's equations, which is to say - for no good reason. ..where do we see E field depend on the change of B field Here a couple of scenarios: A magnet in motion near a stationary object... Take the example above, the one we are already talking about, then take some magnet and move it around that wire any way you want. There will be dB/dt, but what E field do you think would change - where and how would you measure it? I really want to know what is this "E field" you are talking about in terms of measurement, instruments and in what units is that "E field" of yours, especially since we just previously concluded there will be no electric field around the wire due to superposition of positively charged nucleus in the wire, regardless of any change in current or application of voltage, didn't we? Say you have wire with current [math] I = I_0 cos(\omega t)[/math] what E field is it producing? We are already talking about that scenario, with straight wire along x-axis and steady current of 1 ampere, we said there will be no electric field around it due to superposition, so what in the world is "cos(wt)" and what any angles have to do with E field? So [math]\triangledown \cdot \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t}[/math] [math] \Rightarrow \oint \mathbf{E} \cdot d\mathbf{l} = - \int \frac{\partial \mathbf{B}}{\partial t} \cdot d\mathbf{a}[/math] and using Ampere's Law you get [math] \mathbf{B} = \frac{\mu_0 I_0 cos(\omega t)}{2 \pi s} \hat{\phi} [/math] a.) "Fi" is "flux" symbol in these equations, you need to use "dl" to denote the direction of electric current, is your "Fi" a unit vector or variable magnitude? b.) Are you saying it's "m0/2Pi" and not "m0/4Pi"? Distance is not squared? c.) Do you not see that your dB/dt equals to zero, actually, and what does it take for you to realize there will be no E field around the wire regardless of current, voltage or any change in any magnetic fields? [math] \Rightarrow \mathbf{E} = - \frac{\partial}{\partial t}[\frac{\mu_0 I_0 cos(\omega t)}{4\pi}] \hat{s}[/math] [math] \Rightarrow \mathbf{E} = \frac{\mu_0 I_0 \omega sin(\omega t)}{4\pi} \hat{s} [/math] which makes sense for an infinite wire that E would not depend on distance away Ay, caramba! Is that magnetic or electric constant? What field are you talking about, "around the wire" or something else? Wires are made of neutrally charged atoms - superposition of positive and negative charges is what keeps it all electrically neutral regardless of any B or dB/dt and amperes and voltage, only position, i.e DISTRIBUTION of E fields/charges is what matters: (-q +q), and no B fields go into this vector addition calculus, ok? E= Ke* (-q+q)/r*2 What you did is hideous, you completely removed the distance!!?! You have no idea what E filed you are talking about, without the distance what would you measure, where? - Your conclusions are completely devoid of any practical and experimental linkage, you are still yet do differentiate between the basic terms and their physical meaning, like charge, potential, voltage, current, and what "field(s)" have to do with any of that, in real world.
darkenlighten Posted March 29, 2010 Posted March 29, 2010 What equation is wrong, "Biot-Savart" or "Maxwell"? http://en.wikipedia.org/wiki/Biot-savart If you mean to disagree be specific and write down EXACTLY what you think is the correct solution for this example given by BOTH formulas so we can compare, and yes provide some reference, online preferably. - Meanwhile, I will repeat that this IS the solution (simplified) given by the Biot-Savart law for the B field in relation to electric current and distance from a straight wire, so to be applied to the given example: B®= m0/4Pi * I/r^2 I am saying what you have, [math] \mathbf{B}®= \frac{\mu_0 I}{4\pi r^2} [/math], is wrong. You cannot ignore the [math] d\mathbf{l} \times \mathbf{r} [/math]. So I will repeat, that is not the simplified solution. Please refer back to my earlier example showing what the actual solution is. I don't feel like scanning my book again, but trust me it is a legitimate source. Heck it's even what wikipedia has sourced. Take the example above, the one we are already talking about, then take some magnet and move it around that wire any way you want. There will be dB/dt, but what E field do you think would change - where and how would you measure it? I really don't feel like it lol I really want to know what is this "E field" you are talking about in terms of measurement, instruments and in what units is that "E field" of yours, especially since we just previously concluded there will be no electric field around the wire due to superposition of positively charged nucleus in the wire, regardless of any change in current or application of voltage, didn't we? We are already talking about that scenario, with straight wire along x-axis and steady current of 1 ampere, we said there will be no electric field around it due to superposition, so what in the world is "cos(wt)" and what any angles have to do with E field? So the new example I gave had current as [math] I = I_o cos(\omega t) [/math], so therefore this is not a constant current, but it is a steady current. This is what type of current comes out of the wall with a frequency of 60hz, aka alternating current. a.) "Fi" is "flux" symbol in these equations, you need to use "dl" to denote the direction of electric current, is your "Fi" a unit vector or variable magnitude? Okay so it might not be easy to tell, but that is not correct. Flux is actually denoted by capital phi: [math] \Phi [/math] and the lower case phi: [math] \hat{\phi} [/math] is the azimuthal direction in cylindrical coordinates. So in my case it is a unit vector describing a direction. And as I stated before, [math] d\mathbf{l} [/math] is not just a direction, but a vector, just dropping it out and assigning its direction is not the whole story. which is why the equation you gave is wrong for our earlier example with constant current I. b.) Are you saying it's "m0/2Pi" and not "m0/4Pi"? Distance is not squared? Once again it has to do with the [math] d\mathbf{l} [/math] c.) Do you not see that your dB/dt equals to zero, actually, and what does it take for you to realize there will be no E field around the wire regardless of current, voltage or any change in any magnetic fields? Not at all...how do you figure this, I don't know how many times I need to stress this. Do you know what the derivative of [math] cos(\omega t) [/math] is? It is definitely not zero (spoiler it is [math] - \omega sin(\omega t) [/math]). And yes there will be an E field in this scenario since the B field is changing!!! That is the whole point. Ay, caramba! Is that magnetic or electric constant? What field are you talking about, "around the wire" or something else? Wires are made of neutrally charged atoms - superposition of positive and negative charges is what keeps it all electrically neutral regardless of any B or dB/dt and amperes and voltage, only position, i.e DISTRIBUTION of E fields/charges is what matters: (-q +q), and no B fields go into this vector addition calculus, ok? E= Ke* (-q+q)/r*2 What you did is hideous, you completely removed the distance!!?! You have no idea what E filed you are talking about, without the distance what would you measure, where? - Your conclusions are completely devoid of any practical and experimental linkage, you are still yet do differentiate between the basic terms and their physical meaning, like charge, potential, voltage, current, and what "field(s)" have to do with any of that, in real world. If there is changing B, there will be an Electric Field and since the Magnetic Field depends on current, the Electric Field will also. If the current is constant means no electric field (no change), if the current is changing, there will bean electric field. Put it this way ambros, I don't feel that you will really understand what is going on here until you further your studies in vectors, spherical and cylindrical coordinates and integrals. Because I have more than enough shown you when and why Maxwell's equations are extremely useful and that they are also not always useful, and sometimes you need to use Coulomb's or Biot-Savart Laws. But you are lacking if you don't know when to use what and why. I'm sorry I cannot help you further if my explanations do not do it justice. Thank you though. I'm not sure how much more effort I am going to put into this. We will see how much time I have, Spring Quarter is starting tomorrow and I need some sleep 1
ambros Posted March 29, 2010 Author Posted March 29, 2010 (edited) I really don't feel like it lol ... Put it this way ambros, I don't feel that you will really understand... The former is known as 'ignorance', it qualifies the later as 'arrogance'. Even if you derived those equations properly they would still give DIFFERENT results than Biot-Savart and Coulomb's law, just because of *different* constants and distance relation. Wire positioned along x-axis has steady current of 1 ampere, solve for E® and B®. COULOMB vs. "MAXWELL" by darkenlighten: [math] E = {1 \over 4\pi\varepsilon_0}{Q_{net}\over r^2}[/math] -VS- [math]E = \frac{\mu_0 I}{4 \pi}\hat{r} [/math] BIOT-SAVART vs. "MAXWELL" by darkenlighten: [math]B = \frac{\mu_0}{4\pi} \frac{I d\mathbf{l} \times \mathbf{\hat r}}{r^2}[/math] -VS- [math]B = \frac{\mu_0}{2\pi} \frac{I}{r}\hat{r}[/math] E field at point 'r' can change with varying current, change in voltage, or moving magnets around the wire? -- If you think I do not represent Biot-Savart and Coulomb's law correctly for THIS PARTICULAR example and/or if you think I misinterpreted "your" equations, then go ahead and finally write the "correct" solutions already yourself, get rid of the 'Phi' and spherical coordinates so we can COMPARE the equations properly. Merged post follows: Consecutive posts merged I am saying what you have' date=' [math'] \mathbf{B}®= \frac{\mu_0 I}{4\pi r^2} [/math], is wrong. You cannot ignore the [math] d\mathbf{l} \times \mathbf{r} [/math]. So I will repeat, that is not the simplified solution. Stop wasting everyone's time, that's embarrassing. You are making it only worse for Maxwell because you do not have that term in there at all, and I just got it out because it equals to -ONE- for this particular case scenario. - Logically, and obviously from the illustration, in the case with wires the distance vector is always at 90 degrees to wires, so: dl x r = sin(90) = 1 [math]B®= \frac{\mu_0 I d\mathbf{l} \times \mathbf{r}}{4\pi r^2} = \frac{\mu_0 I sin(angle)}{4\pi r^2} = \frac{\mu_0 I sin(90)}{4\pi r^2} = \frac{\mu_0 I * 1}{4\pi r^2} = \frac{\mu_0 I}{4\pi r^2}[/math] So the new example I gave had current as [math] I = I_o cos(\omega t) [/math], so therefore this is not a constant current, but it is a steady current. This is what type of current comes out of the wall with a frequency of 60hz, aka alternating current. Magnitude of E filed at distance 'r' can change with frequency? Okay so it might not be easy to tell, but that is not correct. Flux is actually denoted by capital phi: [math] \Phi [/math] and the lower case phi: [math] \hat{\phi} [/math] is the azimuthal direction in cylindrical coordinates. So in my case it is a unit vector describing a direction. And as I stated before, [math] d\mathbf{l} [/math] is not just a direction, but a vector, just dropping it out and assigning its direction is not the whole story. which is why the equation you gave is wrong for our earlier example with constant current I. Stop hallucinating equations and dreaming up nonsense. We are COMPARING two different sets of equation by trying to apply them on the same scenario and get them in THE SAME FORMAT. -- You have lost all your credibility, I will not consider any more empty arguments from you without some reference provided and equations written in proper and comparable format. And yes there will be an E field in this scenario since the B field is changing!!! If there is changing B, there will be an Electric Field and since the Magnetic Field depends on current, the Electric Field will also. If the current is constant means no electric field (no change), if the current is changing, there will bean electric field. Magnitude of E filed at distance 'r' can change with changing B field? What "E field" are you talking about? Where and how do we measure it? Edited March 29, 2010 by ambros Consecutive posts merged.
darkenlighten Posted March 29, 2010 Posted March 29, 2010 The former is known as 'ignorance', it qualifies the later as 'arrogance'. Even if you derived those equations properly they would still give DIFFERENT results than Biot-Savart and Coulomb's law, just because of *different* constants and distance relation. Call it what you will, doesn't bother me any. Wire positioned along x-axis has steady current of 1 ampere, solve for E® and B®. COULOMB vs. "MAXWELL" by darkenlighten: [math] E = {1 \over 4\pi\varepsilon_0}{Q_{net}\over r^2}[/math] -VS- [math]E = \frac{\mu_0 I}{4 \pi}\hat{r} [/math] Lets start with this. First that is not what I gave for this specific example. If you would read back through, which I feel you fail to do. This was the example I gave for a changing magnetic field, where I was NOT constant. And we already determined for this E = 0 for a wire, due to its net charge, but this is not true if the B field is changing, which was my example. BIOT-SAVART vs. "MAXWELL" by darkenlighten: [math]B = \frac{\mu_0}{4\pi} \frac{I d\mathbf{l} \times \mathbf{\hat r}}{r^2}[/math] -VS- [math]B = \frac{\mu_0}{2\pi} \frac{I}{r}\hat{r}[/math] E field at point 'r' can change with varying current, change in voltage, or moving magnets around the wire? -- If you think I do not represent Biot-Savart and Coulomb's law correctly for THIS PARTICULAR example and/or if you think I misinterpreted "your" equations, then go ahead and finally write the "correct" solutions already yourself, get rid of the 'Phi' and spherical coordinates so we can COMPARE the equations properly. Yes it can, but not the E field that is due to an electrostatic charge, but due to changing B field, hence a changing current or moving magnet. Stop wasting everyone's time, that's embarrassing. You are making it only worse for Maxwell because you do not have that term in there at all, and I just got it out because it equals to -ONE- for this particular case scenario. - Logically, and obviously from the illustration, in the case with wires the distance vector is always at 90 degrees to wires, so: dl x r = sin(90) = 1 [math]B®= \frac{\mu_0 I d\mathbf{l} \times \mathbf{r}}{4\pi r^2} = \frac{\mu_0 I sin(angle)}{4\pi r^2} = \frac{\mu_0 I sin(90)}{4\pi r^2} = \frac{\mu_0 I * 1}{4\pi r^2} = \frac{\mu_0 I}{4\pi r^2}[/math] You are wrong. So lets take a look at the derivation and as to why you are wrong: Taken from "Introduction to Electrodynamics" by David J. Griffiths Page 216-217 Magnitude of E filed at distance 'r' can change with frequency? Looking at Faraday's equation, you can see that an Electric Field can exist if there is a changing B Field. Therefore, in MY example for a changing current [math] I = I_0 cos(\omega t )[/math], there will be an electric field around the wire due to its changing magnetic field. Stop hallucinating equations and dreaming up nonsense. We are COMPARING two different sets of equation by trying to apply them on the same scenario and get them in THE SAME FORMAT. -- You have lost all your credibility, I will not consider any more empty arguments from you without some reference provided and equations written in proper and comparable format. Hate to break it to you but [math] \hat{r} [/math] is a polar coordinate, hence a cylindrical coordinate, so we are in the same format, you just don't see it. Magnitude of E filed at distance 'r' can change with changing B field? What "E field" are you talking about? Where and how do we measure it? Once again due to the changing B in MY example. I have gave another example where an E field exists due to a changing B Field. And once again in YOUR example with constant I, E = 0 .
ambros Posted March 30, 2010 Author Posted March 30, 2010 First that is not what I gave for this specific example. What then' date=' write it down already. You wrote 4-5 different formulas, some of them proved to be wrong and all of them contradicting each other, violate logic and deny common experience, so which one? You failed at simplest example with point charges and now we are talking about the most basic case scenario with infinite wires, what's problem? [b']Q1: Wire positioned along x-axis has steady current of 1 ampere, solve for E® and B®.[/b] *PROVIDE REFERENCE
ambros Posted March 30, 2010 Author Posted March 30, 2010 The reference in my previous post. I'm asking for the reference to the formulas you supposedly derived from Maxwell's equations and you believe are solutions for this PARTICULAR EXAMPLE: Q1: Wire positioned along x-axis has steady current of 1 ampere' date=' solve for E® and B®. [img']http://www.scienceforums.net/forum/latex/img/9cca7d2d3cbb94a9a0238c6a71db0590-1.gif[/img] Do you say this the solution for THIS PARTICULAR EXAMPLE? No? What is it then? Can you solve THIS SIMPLEST EXAMPLE?
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