Author Topic: Coulomb's law and a voltage frame of reference  (Read 25232 times)

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Offline RIS

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Re: Coulomb's law and a voltage frame of reference
« Reply #25 on: April 27, 2016, 10:21:55 am »
to say that the field does not exist because it has no effect on electron inside is ridiculous
and yes the charge of the cage can be detected from inside
your just need a good hammer,not for breaking but to measure the energy oscillations.
 

Offline Zeranin

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Re: Coulomb's law and a voltage frame of reference
« Reply #26 on: April 27, 2016, 12:14:53 pm »
to say that the field does not exist because it has no effect on electron inside is ridiculous
and yes the charge of the cage can be detected from inside
your just need a good hammer,not for breaking but to measure the energy oscillations.

Actually, an electric field is defined in terms of the force it exerts on a charged particle.

No electrostatic force on electron means no electric field, end of story.

If you disagree then it might be best if we agree to disagree, and let others here judge for themselves.
 

Offline RIS

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Re: Coulomb's law and a voltage frame of reference
« Reply #27 on: April 27, 2016, 12:54:36 pm »
I agree with this philosophical issues.
but if we put man at the center of gravity the it will not be a philosophical issue,it will be a matter of life and death.
These are just my rough thoughts.
 

Offline John HeathTopic starter

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Re: Coulomb's law and a voltage frame of reference
« Reply #28 on: April 28, 2016, 11:22:23 am »
I like you model better. Let us make it clearer by floating in the middle of space somewhere. Stray capacity is no longer an issue. I will replace gravity with a spring on the gold leaf. If charged the leaf spring opens. Take the charge away and the leaf closes. Both us as observers from a distance and the ones that live on this gold leaf apply Coulomb's law as an accounting issue of literally counting the number of + charges and _ charges , protons / electrons , and applying Coulomb's law accordingly. This resolves the conflict between the distant observer and the one that lives on the gold leaf as they will now arrive at the same answer for the gold leaf.

I do not mean to be a trouble maker here but there is one fly left in the soup. Replace the spring gold leaf with a Faraday cage that has 0 charge. We place one electron in the middle somewhere. As the cage has 0 charge then Q X Q / R^2 or 0 X 1 electron = 0 force. The electron is free to float around not effected by a Coulomb force.  I am going to throw a wrench in the works by sprinkling some electrons on the Faraday cage. let us say the cage now has a charge of -1 and the electron floating inside has a charge of -1 just to give it a number. If Q X Q / R^2 is true then the electron should stay in and exact center of the cage as R^2 means closer to any side of the cage will increase the Coulomb force repelling it. The problem is the electron could care less and will still just float around indifferent to R^2 Coulomb force from the sides of the Faraday cage. This was demonstrated in the video by Professor Eric Rogers ironically using the inverse law R^2 to explain it. Maybe I misunderstood it.

He hints that it is similar to gravity at the center of the world where one weighs 0 pounds. That can be understood. However if the earth were a egg shell and we were inside the egg shell gravity would not pull one towards the shell just like the 1 electron floating around in a positive charged Faraday cage for this example would not feel a Coulomb force to the cage walls . How can an electron not want to go to a positive charged Faraday wall? In an oscilloscope the electron will go toward a positive deflection plate but not in the Faraday cage despite R^2.

I think we are getting close to complete resolution. The question is, if you charge up a Faraday cage, meaning the cage has an excess charge, then why does an electron inside see no force, at ANY position within the cage. Professor Rodgers explained this, but you may have missed his point.

Assume for simplicity that the cage is spherical. At the centre of the cage, we know from symmetry there can be no force on the electron. You might think intuitively that if you move the electron off centre and closer to the inside wall, the net Coulomb force would increase, as it gets closer to the charged wall, especially as the force goes as 1/R^2.

The trick is to realize that the electron is being pulled literally in EVERY direction, and these forces always cancel just as long as the inverse square law is true. Look again at the video. If you move the electron off centre, then you still have to consider ALL the Coulomb forces, not just the forces from the part of the wall nearest to the electron, which is what you are doing. If you cleverly divide the inside surface of the sphere into little ‘patches’, you find that the ‘patches’ on the wall where the wall is nearest to the electron have less area, in inverse proportion to R^2, compared to the larger ‘anti-patches’ on the part of the wall that is further away. The force from any such patch is proportional to it’s area, and therefore inversely proportional to it’s distance R from the electron. Each patch area scales as R^2, but the Coulomb force scales inversely as 1/R^2, with the result that the magnitude of the Coulomb force is the same for every patch, but the forces cancel out because each pair of patches pull in an opposite direction. It’s messy to explain verbally, but if you look again at the video then I’m sure it will be clear, not to mention rather nifty.

You can reach the same conclusion trivially easily by application of Gauss’s Law to an imaginary Gaussian closed surface, chosen to be a concentric sphere inside the spherical Faraday shell. As there is no charge enclosed in the spherical Gaussian surface, the electric field must be zero everywhere on this surface, and thus everywhere inside the spherical Faraday shell. If there is no electric field, then there is no force on an electron, as it is an electric field (units Newtons/Coulomb) that provides electrostatic force on charges. However, this explanation is cheating because you have to take Gauss’s Law on trust, whereas Rodger’s explanation in the video is intuitive and understandable by anyone. Although spherical Faraday cages are easiest to analyse, in fact the electric field is zero everywhere inside ANY closed, conducting shape. For a sphere, the charge excess charge distributes itself evenly on the surface, as it must from symmetry considerations. For other shapes, the surface charge density is not constant, but distributes itself in such a way that the E-field is everywhere zero inside, and it turns out that in order to do so, the charge density is much higher at corners and edges.

Yet another way we know that the E-field must be zero inside a hollow conductor, is to note that the entire conductor must be equipotential, at the same voltage. This we know from Ohm’s Law. At DC, any two point on a conductor are at the same voltage, unless there is a current flowing, which there is not in an electrostatic problem. If every point on the inside surface is at the same voltage, then intuitively one can see that there can be no electric field created, units of V/m. You can’t produce volts per meter, unless you have voltage difference(s), and there can be no voltage differences anywhere on a closed equipotential surface.

Quicky getting back to your intuitive feeling that the electron would see a stronger Coulomb force when nearer to the inside wall, consider the case of an electron above a large, charged flat plate. You may intuitively think that Coulomb force of attraction to (or repulsion from) the plate would be stronger at closer distance to the plate, yet in fact the force is a constant, independent of distance, because as the electron moves further from the plate (force dropping off as R^2), it ‘sees’ more of the plate, increasing by R^2.

Enough raving. I enjoy solving mysteries and paradoxes, or at least trying to, so keep them coming.

Sorry for the delay. Had to watch some videos on Gauss's law to wake up some distant college memories. I see your point. Can not have a voltage gradient within a closed Faraday cage for evenly distributed charges on the Faraday walls. Will set the net Faraday cage charge at +1 . On the outside the electric field will fall off at R^2 but uniform inside the cage. Will now place 1 electron at the center of the Faraday cage . Mr Electron's -1 charge should fall off at R^2 from within the Faraday cage being a single point charge , yes/no? If the electron were very close to one of the Faraday walls it will run into infinity problems with R^2 for electron - Coulomb force causing it to stick to the Faraday walls. I could make the same argument for gravity. Say the earth is an egg shell and we are inside this egg shell. The gravity gradient inside is 0 in the same way the voltage gradient in the Faraday cage is 0. However I am a single point mass generating my gravity field that should drop off at R^2 from within the egg shell. I should stick to the inside of the egg shell much like the - electron should stick to the + Faraday wall. 

I am confident everything I said is false , incorrect. The question is what went wrong and can anything be leaned from this? I will toss one in your court for consideration.

A] Coulomb force comes from the properties of the vacuum around the electron only not the Faraday cage walls. The implication of this is an electron accelerating in a CRT gun is pulling on a vacuum not the positive charge of the second HV anode. To conserve momentum the vacuum must have accelerated in the other direction. The TV as a total must move backwards while the electron is accelerating forward to conserve momentum. Can the vacuum around the accelerating electron pull on the TV set or do we have to wait for the electron to hit the phosphor to settle the score? NASA has ion accelerators to propel space ships using a Coulomb force so apparently the vacuum around an accelerating electron can pull a TV set backwards.  Not sure if this is going anywhere , just brain storming.



 

Offline Zeranin

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Re: Coulomb's law and a voltage frame of reference
« Reply #29 on: April 29, 2016, 12:24:13 am »
Sorry for the delay. Had to watch some videos on Gauss's law to wake up some distant college memories. I see your point. Can not have a voltage gradient within a closed Faraday cage for evenly distributed charges on the Faraday walls. Will set the net Faraday cage charge at +1 . On the outside the electric field will fall off at R^2 but uniform inside the cage. Will now place 1 electron at the center of the Faraday cage . Mr Electron's -1 charge should fall off at R^2 from within the Faraday cage being a single point charge , yes/no? If the electron were very close to one of the Faraday walls it will run into infinity problems with R^2 for electron - Coulomb force causing it to stick to the Faraday walls. I could make the same argument for gravity. Say the earth is an egg shell and we are inside this egg shell. The gravity gradient inside is 0 in the same way the voltage gradient in the Faraday cage is 0. However I am a single point mass generating my gravity field that should drop off at R^2 from within the egg shell. I should stick to the inside of the egg shell much like the - electron should stick to the + Faraday wall. 

I am confident everything I said is false , incorrect. The question is what went wrong and can anything be leaned from this? I will toss one in your court for consideration.

A] Coulomb force comes from the properties of the vacuum around the electron only not the Faraday cage walls. The implication of this is an electron accelerating in a CRT gun is pulling on a vacuum not the positive charge of the second HV anode. To conserve momentum the vacuum must have accelerated in the other direction. The TV as a total must move backwards while the electron is accelerating forward to conserve momentum. Can the vacuum around the accelerating electron pull on the TV set or do we have to wait for the electron to hit the phosphor to settle the score? NASA has ion accelerators to propel space ships using a Coulomb force so apparently the vacuum around an accelerating electron can pull a TV set backwards.  Not sure if this is going anywhere , just brain storming.

Hmm. I thought my previous posting showed clearly that when viewed from any angle, a electron inside a Faraday cage will not be attracted to the cage wall.

Can not have a voltage gradient within a closed Faraday cage for evenly distributed charges on the Faraday walls.

Absolutely correct. You can’t have a voltage gradient (imposed from outside the cage) within a Faraday cage, period, because the inside surface is equipotential. You can set up non-symmetric charge distributions with resultant voltage gradients outside the cage if you wish, yet still you will not create any voltage gradient (AKA electric field) inside the cage, because the inside surface is equipotential. This is the principle of electrostatic shielding. Of course, you can set up electric fields within the cage if you wish, by placing charged particles or electrodes inside the cage.


On the outside the electric field will fall off at R^2 but uniform inside the cage.

You say the electric field inside is ‘uniform’, but the correct description is that the field inside is ZERO.


Mr Electron's -1 charge should fall off at R^2 from within the Faraday cage being a single point charge , yes/no?

Yes, but after that your reasoning goes astray. To calculate the electrostatic force on said electron, we multiply the electron’s charge in Coulombs, by the strength of the E-field (units N/C, or V/m, they are the same unit) in absence of the electron. As I think we agree, the E-field strength in the absence of Mr electron is zero, and thus the force on the electron is zero. Period. The field strength is zero right up to the inside wall, and even inside of the wall, so the force on the electron is zero, right up to the wall. I can’t make it any clearer. ?

The implication of this is an electron accelerating in a CRT gun is pulling on a vacuum not the positive charge of the second HV anode.

That is not correct. The reaction force is most certainly on the electrostatic structure that created the electric field, and thus accelerates the electron. The simplest accelerating structure is a charged sphere, and you KNOW that there is an electrostatic force between two charges, one being the mechanically fixed sphere and the other an electron. Coulomb’s law is symmetric, and automatically predicts the same force on both the charges. As a practical example of this, we design and manufacture ion-thrusters for NASA, for interplanetary space craft. These nifty ‘rocket engines’ work by accelerating charged ions out the back of the engine. If your proposal was correct, these ion-thrusters would not work. The reason ion-thrusters are used is twofold. Firstly, the power for the engine can come from solar panels. Secondly, we need to get the maximum possible amount of thrust per unit mass of ejected fuel, because we can’t afford to carry ridiculous masses of fuel. This means we need the highest possible exhaust velocity. With an ion-thruster, we can achieve exhaust velocities approaching the speed of light, far higher than is possible with a conventional fuel-burning rocket. As described, the spacecraft would charge up, so we developed a ‘helicon double layer’ design where the ions and electrons are both ejected into the exhaust. Getting back to your TV set, if we take the case of accelerating a single electron, then while the electron is being accelerated, the TV and electrons accelerate in opposite directions, from the equal and opposite force. When the electron eventually hits the phosphor, the ‘score is settled’, and both end up with no velocity. In reality we have a continuous beam of electrons, so the forces are at all time balanced.

I enjoy your ideas, and you really exercised my brain on the topic of why an electroscope will not register that a sphere is charged, when placed inside the sphere. I initially though I knew that an electroscope simply measured excess charge, but was forced to think more carefully. My excuse is that I don’t use electroscopes, so had never thought deeply about what they actually measure.
« Last Edit: April 29, 2016, 03:09:40 am by Zeranin »
 

Offline John HeathTopic starter

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Re: Coulomb's law and a voltage frame of reference
« Reply #30 on: April 29, 2016, 05:15:37 am »
I have an analogy that tracks Q X Q /  R^2. Will replace the vacuum with a 2D matrix of 100 1 M resistors somewhat like a screen door. Will solder a copper wire along the outside of the matrix of the resister grid. This will be the Faraday cage walls. Now it works. If I place 1 electron in the middle of this matrix of resistors it will have no reason to move up , down , left or right as there is no voltage gradient in the matrix to cause the electron to move even if it is almost touching the Faraday wall. A vacuum is an insulator not a resistor so it is not the best analogy but at least it is tracking Coulomb's law inside a sphere.

Yes I can see how an ion accelerated to .99 c would give you a big bang for your buck for fuel mass. .99 c would be a mass increase of 7 . There are some tiny satellites they plan to launch using laser photons to accelerate them to our neighboring galaxy. That would be 0 fuel mass , ha.

As to your pondering on a possible absolute 0 voltage frame of reference. I have given that very question some considerable thought. I have a 1 foot square Faraday cage that I charge up to 10 K volts then back down to ground every 10 seconds. While that is going on a fiber cable is sampling a 10 MHz clock inside the cage but the frequency counter is outside the cage.  The 10 MHz oscillator is in a difference voltage frame of reference than the frequency counter. I believe the key to measuring a change caused by a different voltage frame of reference is to not be in the frame of reference when measuring. The predicted target is 50 uHz faster per second for a 10 MHz oscillator. To put that in perspective a GPS clock would be faster by 5 mHz. That is not as bad as it sounds as the oscillator only has to be stable for 10 seconds. Noise and jitter is a problem but net average stability for a 10 second period seems okay. 10 mHz is about as close as I can get so far. Need 3 more zeros of resolution. I sometimes wonder if there is a better way to do this. In any event a measurable change caused by a change in a voltage frame of reference could point to the direction of what is an absolute 0 voltage frame of reference.
 

Offline Zeranin

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Re: Coulomb's law and a voltage frame of reference
« Reply #31 on: April 29, 2016, 10:53:50 am »
I have an analogy that tracks Q X Q /  R^2. Will replace the vacuum with a 2D matrix of 100 1 M resistors somewhat like a screen door. Will solder a copper wire along the outside of the matrix of the resister grid. This will be the Faraday cage walls. Now it works. If I place 1 electron in the middle of this matrix of resistors it will have no reason to move up , down , left or right as there is no voltage gradient in the matrix to cause the electron to move even if it is almost touching the Faraday wall. A vacuum is an insulator not a resistor so it is not the best analogy but at least it is tracking Coulomb's law inside a sphere.

Yes!

Your analogy is smack on the money, and more valid and powerful than you could imagine. What you are describing is known as FEA, Finite Element Analysis. Of course, while you describe a 2D array of 'resistors', the full solution is a 3-D matrix of such 'resistors', AKA finite elements. As you say, a vacuum is not literally resistive, but it turns out that the math for solving the electric potential at all points in space, for any structure of conductive objects in 3D space, is identical as if you were solving the voltage at every point in the situation where the vacuum is occupied by a solid resistive material such as carbon, which in turn is (in effect) modelled as a matrix of resistors, exactly as you describe. As you would realize, solving for the voltage at every node in a huge 3D array of resistors, where there could be millions of nodes, is computationally intensive, though conceptually simple. 

The FEA method is extraordinarily powerful. I invented and developed it 25 years ago for solving magnetic problems, writing my own FEA code to run on the first 8086 PC's, years before commercial magnetic modelling applications were generally available. I developed an iterative algorithm for efficiently solving the huge matrices, being the FEA 'engine', and then added a (primitive by today's standards) graphical user interface so I could view the 3D model from any angle, and display 2D slices on any plane. My application at that time was for designing ultra-high-efficiency brushless electric motors, and my FEA software allowed me to calculate the flux density at every point within an electric motor consisting of windings, magnetic materials and air. By observing the change in flux as the armature is rotated, one can calculate torque, speed, efficiency etc. The fantastic thing about FEA is it's complete generality, so soon I was using the same software to model and design complex systems of magnetic coils used in physics research.

Next I modified the code to solve electrostatic problems as well, exactly as you describe, and went on to design all manner of 'ion optics' for physics research, specialized electron guns, ion lenses and accelerators and so on. The commercial electrostatic FEA modelling package was (and still is) called SIMION, with similar capabilities. As FEA gives you the electric potential at every point in 3D space, it also gives you the E-field at every point in space, being just the difference in potential at 2 points on the matrix, divided by the distance between these 2 points. Then I added to capability for 'ray tracing' of charged particle(s), which is actually quite easy, as the force on the particle at any point is just the E-field times the charge, so it is just a matter of iteratively applying Newton's laws of motion to trace out the path of a charged particle(s). With Simion, the user inputs a particular physical design of electrodes, and can then ray-trace to observe the result. The user can then manually modify the design check the result, and repeat so as to hone and optimize the design, a slow and laborious process. I added more code to my FEA application to automate that process, so that many thousands of designs can be tried with the design being progressively optimized automatically, a process that would take hundreds of man years with the commercially available software. As a result, I have designed some of the most perfect ion imaging lenses ever built for the physics research group that I work with. FEA is a lot of fun.

FEA can solve almost any 3D field problem, or any similar problem where a physical quantity 'flows' as a result of a driving force. Another example where I have applied my code to good effect is thermal modelling. The math for all this FEA stuff is essentially the same, its just a matter of adding different front ends to the FEA engine to solve different types of problem. I can model any arrangement of thermal materials, define the heat sources, and then calculate and display the temperature at every point in the model, a lot of fun.

Another application is calculating the resistance of any arbitrary 3D shape, consisting of any number of different materials. I collaborate with electronic manufacturers on lots of stuff, one very large resistor manufacturer is interested in my code for calculating the resistance of complicated shapes of resistive foil, for example in the very large shunt that they built for me. At present, they 'guestimate' the effect of square bends etc in the zig-zag shape, then fine tune the design later to get exactly the right resistance. With FEA, you can accurately calculate the resistance of ANY shape.

Another really big application is calculation of stress and strain in mechanical engineering structures, and it goes on and on.

Some of your ideas may not work out, but your 'resistor matrix' ides is more relevant and powerful than you could have imagined.  :-+ 
 

Offline John HeathTopic starter

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Re: Coulomb's law and a voltage frame of reference
« Reply #32 on: April 29, 2016, 02:17:56 pm »
This is indeed good news. It has been nothing but good news from the time I came to this group only a few months ago. Have received a wealth of information on precise frequency counting from fine minds that have been there done that. Then to find out that you are a specialist in 3D metric tensors. I have a pile of questions. Off to work.
 

Offline John HeathTopic starter

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Re: Coulomb's law and a voltage frame of reference
« Reply #33 on: April 30, 2016, 10:55:15 am »
I have a 1 cubic meter of vacuum on my kitchen table . It is 8.8 p farad by 1.2 Henry for a propagation speed of c  and impedance of 376 . If I tap this 1 meter cube of vacuum it should resonate at about 50 MHz. I like to pace around this cube to better understand it. In the middle of this cube there is a sun that spits out bursts of charged particles now and then moving freely outward through the vacuum. You see the problem? The vacuum is both a insulator and conductor of charges at the same time ? Both can not be true. We have to say that a vacuum is a conductor of charges with low resistance. Mr copper wire bathed in our conducting vacuum just got a lot more complicated. Electrons are free to move inside copper and they are free to move in a vacuum. This means it is the transition between copper and a vacuum that is an insulator not the vacuum itself as both copper and the vacuum conduct electrons. The only reason to bring this up is to say your use of a resistor matrix to represent the vacuum inside a Faraday cage is justified as the vacuum should act this way being a conductor of charged particles.

My questions. What does a 1 K resistor measure in a X , Y  2 dimensional matrix that goes off into infinity? Secondly how do I terminate the outside of this resister matrix so that it appears to go off into infinity. The outside resisters would have to be lower than 1 K to make it seem to be continuous yes / no ?. Thirdly have you tried inducters Henry and condensers Farad matrix for a vacuum then terminate the outside with resisters. That to myself would be the ultimate vacuum model so you must have entertained this at some point. 
 

Offline Zeranin

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Re: Coulomb's law and a voltage frame of reference
« Reply #34 on: April 30, 2016, 01:45:57 pm »
I have a 1 cubic meter of vacuum on my kitchen table . It is 8.8 p farad by 1.2 Henry for a propagation speed of c  and impedance of 376 . If I tap this 1 meter cube of vacuum it should resonate at about 50 MHz. I like to pace around this cube to better understand it. In the middle of this cube there is a sun that spits out bursts of charged particles now and then moving freely outward through the vacuum. You see the problem? The vacuum is both a insulator and conductor of charges at the same time ? Both can not be true. We have to say that a vacuum is a conductor of charges with low resistance. Mr copper wire bathed in our conducting vacuum just got a lot more complicated. Electrons are free to move inside copper and they are free to move in a vacuum. This means it is the transition between copper and a vacuum that is an insulator not the vacuum itself as both copper and the vacuum conduct electrons. The only reason to bring this up is to say your use of a resistor matrix to represent the vacuum inside a Faraday cage is justified as the vacuum should act this way being a conductor of charged particles.

My questions. What does a 1 K resistor measure in a X , Y  2 dimensional matrix that goes off into infinity? Secondly how do I terminate the outside of this resister matrix so that it appears to go off into infinity. The outside resisters would have to be lower than 1 K to make it seem to be continuous yes / no ?. Thirdly have you tried inducters Henry and condensers Farad matrix for a vacuum then terminate the outside with resisters. That to myself would be the ultimate vacuum model so you must have entertained this at some point.

These are not simple questions.


The only reason to bring this up is to say your use of a resistor matrix to represent the vacuum inside a Faraday cage is justified as the vacuum should act this way being a conductor of charged particles.

The use of a 'resistor matrix' is certainly justified, but not for the reason you give. The first step is to convince yourself that a 'resistor matrix' is a valid way to model and solve for the voltages and current at all points inside a block of electrically conductive material, such as carbon, with metal surfaces/shapes/electrodes at fixed potentials embedded in the carbon. That said, what we ACTUALLY want to model is to find the electric potential at all points in space, where the carbon is actually vacuum, and in this REAL case there is nothing physical that actually 'flows'. That said, if you look at the equations relating permittivity, electric flux, electric flux density, electric field and potential, you find an exact mathematical analogy. The math and the method is therefore identical, and it's just a matter of re-naming the familiar quantities such as electrical resistance in terms of the equivalent electrostatic quantity. In the same way, you find an exact mathematical analogy with magnetic quantities, so you can equally well do magnetic modelling, essentially just by renaming the quantities (eg resistance and EMF) into the equivalent magnetic quantities (eg reluctance and magneto-motive-force)


What does a 1 K resistor measure in a X , Y  2 dimensional matrix that goes off into infinity?
I don't exactly understand the question, though maybe my answer to your next question covers it.


Secondly how do I terminate the outside of this resister matrix so that it appears to go off into infinity. The outside resisters would have to be lower than 1 K to make it seem to be continuous yes / no ?.
Yes, this is an important point in electrostatic or magnetic FEA. In theory, you should build your 3D FEA model out to infinity, but of course that is not practical. Alternatively, you can model out 'well beyond' the volume of interest, with the result that you will get 'near enough' to the right answer in the volume of interest. However you look at it though, your FEA model stops at a 'boundary', and you ask exactly the right question, how do you fudge this boundary to get the most accurate results, by making the boundary behave as if the resistors extended out to infinity. For starters, you need to assign a potential (voltage) at the boundary, else the matrix is insoluble. If you use the same resistance value at the boundary as elsewhere, then that is equivalent to having the vacuum extend outward, terminating at an equipotential surface, and in many cases that is exactly what you want - you are modelling inside of a shielding can. However, if you want to model vacuum out to infinity, then by choosing the boundary resistor values 'just right' then the matrix behaves as if it extended out to infinity. The 'just right' value of resistance is higher than the other resistors representing the vacuum, and the optimum value depends on the overall size of the model, the further out you model empty space, the larger the optimum resistor value. My program lets the user choose they type of boundary, fixed potential, infinite resistance, or 'magic elements' that behave as if the matrix extended forever. When I last looked at the commercial SIMION package, it did not have this level of sophistication, and gave erroneous results near the model boundary as a result, when modelling vacuum out to infinity.   


Thirdly have you tried inducters Henry and condensers Farad matrix for a vacuum then terminate the outside with resisters. That to myself would be the ultimate vacuum model so you must have entertained this at some point.
That is similar to how you model a transmission line, but not for solving electrostatic problems.

Wonder if anyone else is interested in this stuff? The link to metrology is getting ever more tenuous.  :)

 

Offline John HeathTopic starter

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Re: Coulomb's law and a voltage frame of reference
« Reply #35 on: April 30, 2016, 09:37:14 pm »
At 1000 views in just 5 days it is safe to say this Metrology group has an interest in what you are saying. The only difference between Metrology and FEA is 2D measurement vs 3D measurement. Cern particle detectors , basically FEA , is the leading edge of the limits of measurements made in our day. To dip your toes in those waters would be a dream come true for a Metrology nut.

In ion len shape modeling does FEA adjust for ion mass? In other words would a proton charge +1 and a gold atom with charge + 1 end up in the same place at the same time or does FEA account for this mass difference?





 

Offline Zeranin

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Re: Coulomb's law and a voltage frame of reference
« Reply #36 on: May 01, 2016, 08:20:11 am »
In ion len shape modeling does FEA adjust for ion mass? In other words would a proton charge +1 and a gold atom with charge + 1 end up in the same place at the same time or does FEA account for this mass difference?

A good question. Strictly speaking, the FEA finds the electric potential and E-field at all points in space, while modelling the movement of charged particles through this space is a separate subsequent process.

So to your question, electrostatic systems produce ion trajectories that are mass independent, provided all the particles have the same KE, which is usually the case, and provided the particles have the same charge of course. In ion-optic systems, usually all charged particles are accelerated to the same energy, because all are accelerated through the same voltage, the gain in energy given by the charge multiplied by the change in potential. Therefore your proton and positively charged gold atom will follow exactly the same trajectory through any ion-optic system, and end up at the same place, though not at the same time, because the heavier particles will be travelling slower for the same energy. The reason that different masses follow the same path is as follows. At first glance it may seem as if the heavier particle would be deflected less, because the electrostatic deflecting force is the same, but the heavier particle 'takes more' to deflect. However, the heavier particle is travelling slower as discussed, so the electrostatic deflecting force has longer to act on the particle, with the net result that the path taken is mass independent. Cute, eh? In my program, and SIMION, you can of course specify the particle mass, and even set up a variety of masses, and then observe all the masses to take identical paths, but different transit times. By contrast, different masses DO take different paths through magnetic fields. In general, electrostatic fields change the particles energy, and of course deflect the particle, while magnetic fields deflect but do not change the energy, because the magnetic force is always at right angles to the velocity, so no work is done.

Maybe I'll attach some screen shots from the program, showing an electrostatic or magnetic structure, with the associated field strength displayed as coloured contours and the field direction displayed as arrows. These coloured contour plots are often quite beautiful and artistic, independently of the information they convey.
   
 

Offline John HeathTopic starter

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Re: Coulomb's law and a voltage frame of reference
« Reply #37 on: May 01, 2016, 07:21:52 pm »
I would like to see some windows screen shots. If memory servers you said the first version use a 100 bus system so it must have been a printout of numbers armed only with CPM and the brand new Dr John G. Kemeny's BASIC programming language. Liberated from machine code at last. I am old enough to remember flipping those switches for a cold cold boot.

The magnetic field force is at right angles to the movement of the charge therefore no energy. That is a profound statement. I see your point. If I place an electron charge next to a magnet it will have no effect or force. It is only when the electron is moving or the strength of the magnetic field changers that a force is seen. Brings to mind the first paragraph of the electrodynamics of moving bodies where a distinction is made between a moving wire and a moving magnet. The distinction can not be made as movement of the wire or movement of the magnet is a relative concept depending on the wire's point of view or the magnet's point of view. The wire and the magnet can not have different laws therefore Maxwell must be wrong. If a magnet were to accelerate a charge it would be in clear violation of energy conservation laws as I could simply place a permanent magnet to accelerate charges. However the notion that the magnetic force on a moving charge is at right angles therefore no energy is a new way of thinking of it. Must stew on this some more.
 

Offline Zeranin

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Re: Coulomb's law and a voltage frame of reference
« Reply #38 on: May 03, 2016, 04:48:23 am »
Here is a screen shot from my ancient 3D FEA magnetic modelling program. This is about the simplest model I could make, being a cubic NdFeB permanent magnet (orange) sitting in empty space (olive). The magnet is 13x13x13mm, while the modelling boundary is a cube measuring 40x40x40. The grid spacing is 1mm, and each FEA ‘element’ is a 1x1x1 mm cube, chosen here to be coarse so you can see the individual elements. The boundary is shown in dark blue, and the permeability of the boundary is less than that of free space (vacuum), to make the model behave as if the boundary was at infinity, as discussed in previous posting.

The view is a 2D slice through the 3D model, with the magnet being magnetized in the vertical direction. The direction of the field at every point is space is shown by a tilted line inside every element. As you see, the FEA shows the classic magnetic field lines for a permanent magnet, often illustrated by placing the magnet under a piece of paper, on top of which is sprinkled iron filings.

Although not visible in the screen shot, in the real program, the user can move the cursor anywhere on the model, and the (x,y,z) coordinates and magnetic values are displayed at the bottom of the screen. For example, looking at the bottom of the screen reveals that when this screen shot was taken, the cursor was at (20,27,20), which is centrally just above the top pole piece of the magnet. As shown, at this point the cursor is in ‘air’, the flux density is 0.4701 Tesla, and the relative permeability at this position (air) is 1.0. By moving the cursor, and changing which 2D slice is being viewed, one can therefore read out the flux density (or any one of a number of other magnetic quantities) at any point within the 3D model. FYI, the flux density is higher in the centre of the magnet (0.783 tesla), while vertically above the magnet, at the boundary, the field has dropped off to only 0.053 Tesla.

Alternatively, one can produce coloured contour plots of any magnetic quantity, on any chosen 2D slice, and overlay the vectors if desired. These are often quite pretty.  I’ll follow up with another posting showing the coloured contour plots of mod(B), Bx, By, Bz and magnetic potential, on the same 2D slice. One can include in the model current carrying coils, and permeable magnetic materials (eg steel), and can also handle ‘real’ non-linear magnetic materials providing the B-H curve is known. Even this very simple model of 8000 elements takes about half a second to solve, so for large, complex models the processor is kept very busy indeed.

All lots of fun, if you are into this sort of stuff.
« Last Edit: May 04, 2016, 11:39:35 pm by Zeranin »
 

Offline CatalinaWOW

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Re: Coulomb's law and a voltage frame of reference
« Reply #39 on: May 03, 2016, 05:14:36 am »
It is quite difficult to solve these problems on intuition.  Newton and Leibnitz developed the calculus to better define and understand gravitational problems.  Gauss, Maxwell, Hilbert and others developed other mathematical tools to concretely describe what is going on.  If you want to understand Faraday cages, field shielding and other related things in detail you will need to spend quite a bit of time developing your math skills.  These tools are quite accurate and provide great insight, but work best on a limited set of geometries.  Things like spheres and rectangular boxes.

Finite element methods are a brute force method of solving differential and integral equations.  They work for any geometry you are willing to set up, though they have limitations at corners and some other types of discontinuities.   The computer science course I took in the early 70s described how to do this and there were homework assignments.  The fact that these tools were widely known fifty years and more ago does not in any way detract from the achievement of applying these solutions to particular problem fields, adapting them to the relatively limited capabilities of early personal computers and particularly in generating graphical interfaces as a way to present the enormous amounts of data involved.  The peculiarities of boundary conditions and various non-linearities in different problem fields makes any particular implementation a work of great merit.
 

Offline John HeathTopic starter

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Re: Coulomb's law and a voltage frame of reference
« Reply #40 on: May 03, 2016, 11:23:12 pm »
Here is a screen shot from my ancient 3D FEA magnetic modelling program. This is about the simplest model I could make, being a cubic NdFeB permanent magnet (orange) sitting in empty space (olive). The magnet is 20x20x20mm, while the modelling boundary is a cube measuring 40x40x40. The grid spacing is 1mm, and each FEA ‘element’ is a 1x1x1 mm cube, chosen here to be coarse so you can see the individual elements. The boundary is shown in dark blue, and the permeability of the boundary is less than that of free space (vacuum), to make the model behave as if the boundary was at infinity, as discussed in previous posting.

The view is a 2D slice through the 3D model, with the magnet being magnetized in the vertical direction. The direction of the field at every point is space is shown by a tilted line inside every element. As you see, the FEA shows the classic magnetic field lines for a permanent magnet, often illustrated by placing the magnet under a piece of paper, on top of which is sprinkled iron filings.

Although not visible in the screen shot, in the real program, the user can move the cursor anywhere on the model, and the (x,y,z) coordinates and magnetic values are displayed at the bottom of the screen. For example, looking at the bottom of the screen reveals that when this screen shot was taken, the cursor was at (20,27,20), which is centrally just above the top pole piece of the magnet. As shown, at this point the cursor is in ‘air’, the flux density is 0.4701 Tesla, and the relative permeability at this position (air) is 1.0. By moving the cursor, and changing which 2D slice is being viewed, one can therefore read out the flux density (or any one of a number of other magnetic quantities) at any point within the 3D model. FYI, the flux density is higher in the centre of the magnet (0.783 tesla), while vertically above the magnet, at the boundary, the field has dropped off to only 0.053 Tesla.

Alternatively, one can produce coloured contour plots of any magnetic quantity, on any chosen 2D slice, and overlay the vectors if desired. These are often quite pretty.  I’ll follow up with another posting showing the coloured contour plots of mod(B), Bx, By, Bz and magnetic potential, on the same 2D slice. One can include in the model current carrying coils, and permeable magnetic materials (eg steel), and can also handle ‘real’ non-linear magnetic materials providing the B-H curve is known. Even this very simple model of 8000 elements takes about half a second to solve, so for large, complex models the processor is kept very busy indeed.

All lots of fun, if you are into this sort of stuff.

Nicely done ! I can see the lines tilting just like iron filings on paper. You said you pinched off  the blue boundary permeability to a little less than a vacuum to simulate infinity so the Tesla net numbers near the outside should be about as real as you can get.

On looking at the screen shot my mind wonders to what a forced mono pole would look like ? By forced mono pole I mean gluing a bunch of magnets together forcing all south poles to face center therefore all north poles facing out in the shape of a golf ball. That is about as close as we are going to get to a mono pole. I would like to run this golf ball on your program just to get a intuitive feel of what mono pole would look like. Could your simulation multitask two such mono poles at the same time? Would the two identical mono poles repel each other just like two positive charges? Is a mono pole magnet the true nature of a charge? If it walks like a duck and sounds like a duck then maybe it is a duck. Your simulator would know if two identical golf ball mono poles are sounding and walking like two + charges. If so then flipping a down quark to a up quark could take on a whole new meaning.   
 

Offline Zeranin

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Re: Coulomb's law and a voltage frame of reference
« Reply #41 on: May 04, 2016, 01:45:30 am »
Nicely done ! I can see the lines tilting just like iron filings on paper. You said you pinched off  the blue boundary permeability to a little less than a vacuum to simulate infinity so the Tesla net numbers near the outside should be about as real as you can get.

On looking at the screen shot my mind wonders to what a forced mono pole would look like ? By forced mono pole I mean gluing a bunch of magnets together forcing all south poles to face center therefore all north poles facing out in the shape of a golf ball. That is about as close as we are going to get to a mono pole. I would like to run this golf ball on your program just to get a intuitive feel of what mono pole would look like. Could your simulation multitask two such mono poles at the same time? Would the two identical mono poles repel each other just like two positive charges? Is a mono pole magnet the true nature of a charge? If it walks like a duck and sounds like a duck then maybe it is a duck. Your simulator would know if two identical golf ball mono poles are sounding and walking like two + charges. If so then flipping a down quark to a up quark could take on a whole new meaning.


Before moving on to magnetic monopoles, I'll send more screen shots of the rectangualr bar magnet, being coloured contour plots of |B|, Bx,By,Bz and magnetic potential.

Then I'll build you a 'monopole'. A spherical monopole as you describe would be a pain to model, but I can very easily do just as well, by building you a 'monopole cube', where each of the 6 faces is magnetized through the thickness of the face, with every face having the south pole on the outside surface. I’ll make each face something like 20x20x5 mm, so they will be magnetized in the 5mm direction. I’ll make ‘em in NdFeB, so they’ll be nice and powerful, too. Of course I can make two of them if you want, but suggest we build one first.

How could this NOT behave as a monopole, you ask? Every exterior face is a south pole, no denying that. As Catalina said, the results for this type of problem are not always intuitive, but it’s always fun to model it and see what happens.
 

Offline Zeranin

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Re: Coulomb's law and a voltage frame of reference
« Reply #42 on: May 04, 2016, 03:41:26 am »
Looking first at image Bar_modB, this is a plot of the magnitude of the flux-density vector, AKA modB or |B|, sometimes called the magnetic field strength. As in the plot in the previous posting, the magnetization is in the vertical direction, that from here on I will refer to as the Y-direction. There is a vertical  ‘colour-key’ on the RH side of the plot, so bright yellow represents the highest flux density, fading out to black at zero flux density. It is seen that the flux density is higher inside the magnet than outside. Perhaps counterintuitively, the highest flux density is not in the centre of the magnet, but at the edges of the magnet.  Outside of the magnet, the flux density is seen to fall off rapidly, first showing as a dim red halo, then fading into black at the model boundary. The operator can ‘zoom’ the colour sensitivity, to bring out the detail in areas of low field strength, in which case the magnet would ‘saturate’ in bright yellow.


Image Bar_modB_plan_view is a plan view, in the X-Z plane, with the 2D slice taken at the vertical centre of the magnet, Y=20mm. Here it is seen that the flux density is highest of all at the vertical edges of the cubic magnet, again, not an intuitive result. This screen shot was taken with the cursor exactly at the centre of the screen, at (20,20,20), as displayed at the bottom left. The permeability (relative to air) is always displayed at the cursor position, here showing a value of 1.069, this being the relative permeability of this grade of NdFeB. It is counterintuitive that a magnetic material should have such a low permeability, almost the same as vacuum, but such is the case for NdFeB. 

Next posting will show the coloured plots for Bx and magnetic potential, then I’ll move on to building something more exciting, a magnetic monopole.
 

Offline Zeranin

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Re: Coulomb's law and a voltage frame of reference
« Reply #43 on: May 04, 2016, 08:54:31 am »
Image file Bar_Bx shows the strength of the X-component of the flux density vector, where the X-direction is left-to-right, and the magnetization is vertical. Observe two black ‘bars’ passing through the center of the model, one horizontal and one vertical, indicating that the X-component of the field is zero here, or put another way, the field is vertical. If you look back to the first plot a few postings back, showing the field direction at all points in this plane as tilted lines, then you will observe that the field is indeed vertical along these black ’bars’. There is nothing unexpected or exceptional about this plot - I included it mainly because it is rather pretty. Call me strange, but I happen to think that models are often very pretty, and I certainly enjoy playing with them. The fact that I get paid for mucking around with pretty models is icing on the cake.

Image file Bar_mag_potential is a plot of the “magnetic potential’ AKA magneto-motive-force, a concept possibly not familiar to most. It is the magnetic analog of electro-motive-force, the magnetic driving force that drives the magnetic flux (Webers) around the magnetic circuit, and is in units of ampere-turns. A permanent magnet is modelled as a large number of ampere-turns, distributed along the length of the magnet in the direction of magnetization. As with potentials in general, we are really only interested in potential differences, and can choose the point of zero magnetic potential for our convenience. The horizontal black ‘bar’ across the centre of the model indicates zero magnetic potential, and the potential built up by the magnet is +ve above the magnet, and symmetrically –ve below it. The colours represent only magnitude, so the coloured plot looks identical above and below the dark bar where the potential is zero. In the screen shot, the cursor was placed just above the top pole piece of the magnet where the potential is greatest, and you can see from the readout at the bottom of the screen that the magnetic potential at this point is 2275 ampere-turns (AT). Just below the lower face of the magnet, the potential is -2275 AT, so the equivalent total number of ampere turns for this physically small (13x13x13mm) NdFEB magnet is an astonishing 2275x2 = 4550 ampere turns. There is no way that you could build a single turn 13x13mm current carrying coil that could carry 4550 amps, so the conclusion here is that at least in smaller sizes, NdFeB permanent magnets will easily outperform any electromagnet than you can build, which is why they are used.  :blah: :blah: :blah:

Surely the OP must be bored by now?   :=\
« Last Edit: May 04, 2016, 11:38:20 pm by Zeranin »
 

Offline John HeathTopic starter

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Re: Coulomb's law and a voltage frame of reference
« Reply #44 on: May 05, 2016, 02:22:50 am »
Nicely done ! I can see the lines tilting just like iron filings on paper. You said you pinched off  the blue boundary permeability to a little less than a vacuum to simulate infinity so the Tesla net numbers near the outside should be about as real as you can get.

On looking at the screen shot my mind wonders to what a forced mono pole would look like ? By forced mono pole I mean gluing a bunch of magnets together forcing all south poles to face center therefore all north poles facing out in the shape of a golf ball. That is about as close as we are going to get to a mono pole. I would like to run this golf ball on your program just to get a intuitive feel of what mono pole would look like. Could your simulation multitask two such mono poles at the same time? Would the two identical mono poles repel each other just like two positive charges? Is a mono pole magnet the true nature of a charge? If it walks like a duck and sounds like a duck then maybe it is a duck. Your simulator would know if two identical golf ball mono poles are sounding and walking like two + charges. If so then flipping a down quark to a up quark could take on a whole new meaning.


Before moving on to magnetic monopoles, I'll send more screen shots of the rectangualr bar magnet, being coloured contour plots of |B|, Bx,By,Bz and magnetic potential.

Then I'll build you a 'monopole'. A spherical monopole as you describe would be a pain to model, but I can very easily do just as well, by building you a 'monopole cube', where each of the 6 faces is magnetized through the thickness of the face, with every face having the south pole on the outside surface. I’ll make each face something like 20x20x5 mm, so they will be magnetized in the 5mm direction. I’ll make ‘em in NdFeB, so they’ll be nice and powerful, too. Of course I can make two of them if you want, but suggest we build one first.

How could this NOT behave as a monopole, you ask? Every exterior face is a south pole, no denying that. As Catalina said, the results for this type of problem are not always intuitive, but it’s always fun to model it and see what happens.

The square is fine . In only 3 generations of distance from the center the square will be a golf ball. A surprisingly fast transition from square to a circle but I have empirical evidence that this will happen. If you measure I B I Tesla diagonally 2 pi will jump off the page and bite you on the nose. This comes from the Dave spirit of " don't talk about it , build it and measure ".



Pay close attention to the last 1/3 of the video where 2 pi is right in your face from a decidedly square matrix. How cool is that !

 You have put too much on the table to respond to your other posts. Prefer to read with the benefit of time before responding. Do not want to push my luck but we need either the right or left blue boundary impedance to a magnetic field set very low to simulate a fridge wall. It is a given that two monopoles will act like two + charges but if it sticks to a fridge all is lost. The monopole must not stick to a fridge. Would not ask you to compromise your scientific integrity however there is a possibility I could jump off my balcony if the simulated monopole sticks to a fridge. It's only the second floor but hey I could sprain an ankle.
 

Online IanB

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Re: Coulomb's law and a voltage frame of reference
« Reply #45 on: May 05, 2016, 03:12:10 am »
This is a long and wordy thread, and very difficult to read and comprehend everything that has been said. However, if I may jump in at the end, and forgive me if this has already been said, but I see one presumption which I think is (or may be) wrong. The presumption is that an electrometer indicates charge. It doesn't, it indicates a electric field gradient. Under prescribed circumstances an electrometer may be used to measure charge, but that's not what it indicates.

By analogy, consider a spring scale for measuring weight (or force). The pointer on the scale indicates displacement of the spring, which we hope measures the weight (mass) of the thing being weighed, but only under appropriate circumstances. If you hang a 1 kg weight on the scale it will indicate 1 kg, but if you submerge the weight in a bucket of water it will no longer indicate 1 kg. The mass of the weight hasn't changed, but the indication on the scale has.

So coming back to the analogy, if we take a gold leaf electrometer in free space and apply a charge to it, the charge will produce a non-uniform electric field around the device, and the field gradient will cause the electrometer leaves to separate. However, if we bring the surroundings to the same potential as the electrometer there will no longer be a field gradient and the electrometer will indicate nothing.

This I think is the solution to the conundrum. The electrometer can indicate the local electric field gradient produced if the electrometer has a different potential from its surroundings. The difference in potential can be produced by adding or removing charge from the electrometer, but the charge itself is just the agent of change, it is not itself the thing that is indicated.
 

Offline Zeranin

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Re: Coulomb's law and a voltage frame of reference
« Reply #46 on: May 05, 2016, 05:26:53 am »
This is a long and wordy thread, and very difficult to read and comprehend everything that has been said. However, if I may jump in at the end, and forgive me if this has already been said, but I see one presumption which I think is (or may be) wrong. The presumption is that an electrometer indicates charge. It doesn't, it indicates a electric field gradient. Under prescribed circumstances an electrometer may be used to measure charge, but that's not what it indicates.

By analogy, consider a spring scale for measuring weight (or force). The pointer on the scale indicates displacement of the spring, which we hope measures the weight (mass) of the thing being weighed, but only under appropriate circumstances. If you hang a 1 kg weight on the scale it will indicate 1 kg, but if you submerge the weight in a bucket of water it will no longer indicate 1 kg. The mass of the weight hasn't changed, but the indication on the scale has.

So coming back to the analogy, if we take a gold leaf electrometer in free space and apply a charge to it, the charge will produce a non-uniform electric field around the device, and the field gradient will cause the electrometer leaves to separate. However, if we bring the surroundings to the same potential as the electrometer there will no longer be a field gradient and the electrometer will indicate nothing.

This I think is the solution to the conundrum. The electrometer can indicate the local electric field gradient produced if the electrometer has a different potential from its surroundings. The difference in potential can be produced by adding or removing charge from the electrometer, but the charge itself is just the agent of change, it is not itself the thing that is indicated.

Great to have you in on the discussions. Just to be clear about what you are saying, do you mean the electric field gradient, in units of V/m/m, or do you mean the electric potential gradient, AKA the electric field, in units of V/m?

Regardless, I maintain that fundamentally a gold-leaf electroscope measures the excess charge in Coulombs on each leaf, and that the repulsive force between the leaves is proportional to Q1xQ2/R^2, as per Coulomb's Law, where Q1 and Q2 are the excess (equal) charge on each leaf, and R is the leaf separation.

That said, your way of looking at it is really just the same thing, for you cannot have excess charge on the leaves without an electric field extending outward from the leaves. We are talking about 2 sides of the same coin.

You refer to the electroscope being at a different potential to it's surroundings in order to deflect, but in one sense that is not true. If the electroscope was the only object in the Universe, in which case there are no physical 'surroundings', the electroscope will still operate correctly, and it will indicate excess charge on the leaves, just as it always does. That said, there will also be an electric field surrounding the electroscope, dropping off as 1/R^2 at distances large compared to the dimensions of the electroscope, but most people (me included) would say that this field is a consequence of the electroscope having excess charge.

If there are physical surroundings at a particular potential (volts) with respect to the electroscope, then the excess charge on the electroscope is given by Q=CV, where C is the capacitance between the electroscope and the surroundings. Then, the force on the leaves can be calculated from Coulomb's law, knowing this excess charge. Yet again, it seems to me that what is fundamentally creating the force on the leaves is the excess charge on the leaves, which in this case has been 'pushed' there by the potential difference between electroscope and surroundings.

Keep in mind that we can create electric fields and field gradients by all manner of electrostatic apparatus, such as the accelerating stack in a CRT, or a particle accelerator. You can place an electroscope smack in the middle of such a field or field gradient, but it won't register anything unless there is excess charge on the leaves, adding weight to my argument that fundamentally the force on the leaves is as a result of excess charge on the leaves.

Mostly, you and I are looking at 2 sides of the same coin, but you may prefer looking at the other side of the coin. Are we in agreement?   
« Last Edit: May 05, 2016, 06:06:49 am by Zeranin »
 

Offline Zeranin

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Re: Coulomb's law and a voltage frame of reference
« Reply #47 on: May 05, 2016, 06:56:09 am »
OK JohnHeath, it’s time to build (inside my PC) your magnetic monopole, by creating a cube, where each face is a NdFeB permanent magnet, magnetized with the South pole facing outward on every face, evidently producing a magnetic monopole.

First though, I need to talk to you sternly about the Law. It seems to me that you are a habitual Law Breaker, or at least you try your best to be. You need to know that if you break the Law, then there will be consequences. As you probably know, there is a Law against creating magnetic monopoles, actually one of Maxwell’s Laws. You have convinced me to try to beak this Law, so we should expect consequences. Perhaps the FEA program will crash, or perhaps grind on forever trying to reach a solution. Or maybe my PC will explode in a ball of fire, or disappear in a puff of smoke. Or maybe the program will correctly model the monopole, but the result will be unlike what you expect. I have never before attempted to model a magnetic monopole, but I’m expecting trouble, as every Law breaker should.

As a precursor to creating the cube, I have modelled a single face of the cube, so we can see how much magnetic flux emanates from this single face. Then I’ll assemble 6 such faces to form our monopole cube.

The face is 2mm thick (2 grid squares), magnetized in the direction of the 2mm. The attached image file is a 2D slice through this face, so you can see it is indeed 2mmm thick, and 23mm across. The edges are beveled so that the 6 faces can fit together to form a cube.

The plot is exactly what you would expect, with the magnet driving the magnetic flux upwards, with the flux then spreading out and eventually returning to the bottom of the magnet. At a distance 2mm above the top surface, the average flux density is about 0.12 Tesla. Keep that number in the back of your mind. For a successful monopole, we need to have a magnetic flux of this order emanating outward from every face of the cube.

This evening I’ll model the full cube, and set the FEA program running. Assuming no injury from an exploding PC, I’ll then report the result back here. I also look forward to viewing the infinite resistor matrix video that you attached.
« Last Edit: May 05, 2016, 06:57:48 am by Zeranin »
 

Offline John HeathTopic starter

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Re: Coulomb's law and a voltage frame of reference
« Reply #48 on: May 05, 2016, 12:15:42 pm »
I see. Build one side first then add the other sides later. This way if the program freezes you can always remove one side of the monopole to see what went wrong. There is a trick I used solve Koide formulas that can often freeze windows.

Set timer to 100

On timer end program

This way you do not have to reset your compute if Mr monopole runs into infinity problems. Look forward to your test results and thanks for taking the time for this.
 

Offline monkeysuncle

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Re: Coulomb's law and a voltage frame of reference
« Reply #49 on: May 05, 2016, 01:28:31 pm »
Lots of great discussion of the physics here. I wanted to share a philosophical thought.

The OP wanted to know if there was such a thing as a  "voltage frame of reference," analogous to a relativistic frame of reference for motion.

My father, who was a physics professor at an engineering college, once looked at me very darkly when I asked him a similar question. "Analogy has no place in science," he told me.

I objected that that wasn't true. Everyone who has taken freshman physics knows that an LC tank circuit is analogous to a mass-spring system.

He explained that that "analogy" works only because the dynamic equations that describe the two systems happen to have identical form. If you want to assert that two physical systems are analogous, you must be absolutely clear what you are asserting in mathematical terms. Otherwise you haven't asserted anything that has any physical meaning.

With respect to the current discussion, it is true that a physical system will have the same behavior if the potential of the entire system is raised or lowered by an arbitrary amount (relative, let us say, to zero at infinity). That includes not only the potentials on the components of the system, but also the potential function that exists in space surrounding the components.

The principle at work here, however, is not the principle of relativity, but the principle of linear superposition.
 
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