The copper wire was magnetized? If you mean that after the experiment, it still retained magnetic alignment - awesome, but I don't think that is what you mean. Did the copper loop behave differently than a magnet in place of it would? I don't think so. If anything, this means that your 'corrected' formula is not correct.
Also, what is d^2 F? Don't you just mean df as the force on the wire element dl or current element di?
It could also be that the force between two elements is more complex? There are two or three angles that can be considered. The first angle is the cosine of the dot product of the two current elements. The second is the angle between one of the current elements and the vector pointing to the second current element. the third is the angle between the current element not in the same plane as the connecting vector and one of the elements. The Grassmann's formula on p31 of "Newtonian Electrodynamics" predicts that two parallel current element (i.e. dot product of dl1 . dl2 = |dl1| |dl2| is constant with angle = 0) can either be attractive or repulsive depending on their relative spacial displacement with a functional dependence of (2-3 cos^2 alpha) in the angle. This means that current elements +/- 30 degrees to the front or back are repulsive, while current elements spacialy to either side are attractive as would be expected by parallel wires. This formula predicts a longitudinal repulsive force inside the wires. Is it possible that maybe using a more general force law may predict these results?
I think that Grassmann's formula is derived from experiment, as Lorentz force law. Because experiment cannot isolate elements of current, it is impossible to derive correct law from old experiments. I have proposed the magnetised wire effect to explain force between perpendicular currents but later I have figured out the way how this force works, but I have still to derive the analytic formula.
For experiment that will verify the force between current elements, I propose to measure the force between 2 rectangular coils for many angular relative positions and to solve the linear system made by the measured force. Each side is a current element. Like this:
Force x and y= Force x and y on (sides 1 + sides 2 + side 3 + side 4 ) Force x and y between side i and j =I1*I2*(Sum (p*sin(ang ij)+q*cos(ang ij)) This equation is to be repeated for each couple of side i (coil 1) and j (coil 2)
We build a linear system using the measured force x and y for many angular position of the coil 1 with respect to coil 2 and solve for force on each side. This way we can find the correct force on current elements.
To explain this here is too complex. I will show this in detail one day.
I have found an interesting formula derived by Charles W Lucas in his paper "Derivation of the Universal Force Law - Part 2", it is very similar to your equation but with an extra term that decays more quickly, as your experiments seem to indicate. It is derived from Ampiers law, Faradays law, Gausses law, Lenz's law, and Galilean transform, and is consistent with Newtons 3rd law, Mach's principal and based on the Grassmann force law. It is
where r_ is the position vector, and the dl[i] and dl[j] are the current element vectors. It appears to describe the magnetization of wire phenomenon you have described. The normal dot product force decays as 1/r^2, but the second term decays as 1/r^4, much more quickly.
I am very interested in what you are doing, I believe you are on the right track. It would be fascinating if your experiments do in fact validate such a theory. The implication are tremendous! I have been doing experiments in alt-science for many years now, very interesting, love to hear more about your linear system of measurments.
Correction, I was thinking those were unit vectors, but there were actually full length vectors, so both terms decay as 1/r^2. The second dot product terms only change the direction of the force vector.
Thanks for your formular. Effectively, the magnetised wire effect should be of the order of 1/r^3. This will be interesting for those who want to dig deeper into this phenomenon. As it decays very quickly, it does not affect Lorentz force which is the object of my proposition of experiment.
In fact, the advantage the linear-system-solving experiment is to be able to measure the force on real elements of current that are the sides of a small coil. I think that no experiment involving real elements of current has ever been done before. Because the Lorentz's force formula is so strong in predicting EM force for closed coils that no one has seriously tried to derive an experiment with real current elements. But this must be done because Lorentz force have to respect Newton's third law on elementary level and because strong experimental evidences are necessary to convince people that EM theory must be corrected.
To simplify this experiment, I propose to first use an equilateral triangular coil and a long straight wire. This is equivalent to the interaction between 3 current elements and a long wire. As we are able to derive an analytical formula of the force between 1 current element and a long wire, we will only have a system of 2*3=6 linear equations to solve, that is, global x and y force and the torque or, x and y forces on each of the 3 sides. The long wire is in the plane of the triangular coil so that the z force is zero.
2 force sensors will be placed in the center of the coil to measure the global x and y forces. One will be placed on a tip of the coil to measure the global torque. The first measurement will be done when a side is parallel to the long wire. This will give us 3 measured quantities: x and y global forces and 1 global torque. Then we rotate the coil to another angle with respect to the long wire, for example 90°. Then the measurement will give us 3 more forces and torque. So we have the needed 6 linear equations that we will solve.
In fact, the parallel position will give zero y force and zero torque. This makes the system down to 4 equations.
If you have equipment to carry this experiment, then you will be able to determine forces on real current elements that nobody has done ever.
This is only a quick thought. I have to make a more careful design and mathematical derivation.
I do not have such fancy equipment either, these experiments are only my hobby. Actually if I was to carry out such experiments I would do them the way your are doing them now. Having a low friction pivot point with (mecury or balanced nail) to conduct the electricity, and measure the angle with respect to gravity is probably the most accurate way to measure such a torque with a long lever arm, even today. Some times the old fashion way of doing things is the best, unfortunately it takes time, because each torque experiment must be created individually, and just takes hard work and time, but all things worth doing, do.
Probably designing a zero torque experiment for one theory that has a torque in another theory is good way to rule out false theories, but creating the perfect experiment is always most of the battle.
I just wanted to mention that the final torque equation in the paper was given as a triple cross-product and is said to be consistent with Newtons 3 law, Ampiers law and Gauses Law, and conservation of energy. It includes more terms not included in the above equation, and is the preferred equation of this author. Maybe this, if plugged in to your theory will correctly predict the magnetization of the wire?
F[i j] = dl[i] x dl[j] x r_[i j]/ (c |r[i j]|^3)
It also reduces (with vector identity Ax(BxC) = B(A.C)-C(A.B) )to your equation with the dot products of the currents and an extra term with a dot product of the radial vector and current element. It would be interesting if your experiments are in agreement with this theory, since they also have derive a possible connection to the Gravitation force through Electromagnetism using this equation.
To make the scientific community change their mind is very difficult, if not impossible. So many brilliant scientists have died before their discovery gets recognition. Not only they have to predict quantitatively new phenomena with new theory and verify by experiments, they first have to make their new theory read by ruling scientists of the time. For alternative theorists, as the latter thinks EM theory is the correct theory, they do not even care to read challenging papers.
So, for now, the most important thing to do is to carry out more experiments that show the flaw of the classical EM theory, that show things that classical theory does not predict, phenomena that are contrary to classical theory, such as presence of force or torque where the classical theory predicts zero. This is the object of my experiments with the 2 m long solenoid, the tangential force motor, tangential force in earth’s and round magnet magnetic field, etc.
It will be great if you are willing to carry out such experiments because until now I’m the only one who does so. More experimenters bringing up more experimental evidence will make the flaw of the classical EM theory more credible. Only when sufficiently many physicists discuss this subject that it can get enough attention. Otherwise, this subject will stay ignored.
So, it is OK that you do not have equipment for precisely measuring force, I do not have neither. Let us just do experiments which clearly show force there should not be.
The copper wire was magnetized? If you mean that after the experiment, it still retained magnetic alignment - awesome, but I don't think that is what you mean.
ReplyDeleteDid the copper loop behave differently than a magnet in place of it would? I don't think so.
If anything, this means that your 'corrected' formula is not correct.
Also, what is d^2 F? Don't you just mean df as the force on the wire element dl or current element di?
This magnetisation is only a hypothesis to explain the perpendicular force that I did not predict.
DeleteIt could also be that the force between two elements is more complex? There are two or three angles that can be considered. The first angle is the cosine of the dot product of the two current elements. The second is the angle between one of the current elements and the vector pointing to the second current element. the third is the angle between the current element not in the same plane as the connecting vector and one of the elements. The Grassmann's formula on p31 of "Newtonian Electrodynamics" predicts that two parallel current element (i.e. dot product of dl1 . dl2 = |dl1| |dl2| is constant with angle = 0) can either be attractive or repulsive depending on their relative spacial displacement with a functional dependence of (2-3 cos^2 alpha) in the angle. This means that current elements +/- 30 degrees to the front or back are repulsive, while current elements spacialy to either side are attractive as would be expected by parallel wires. This formula predicts a longitudinal repulsive force inside the wires. Is it possible that maybe using a more general force law may predict these results?
ReplyDeleteDr Jaynes
I think that Grassmann's formula is derived from experiment, as Lorentz force law. Because experiment cannot isolate elements of current, it is impossible to derive correct law from old experiments. I have proposed the magnetised wire effect to explain force between perpendicular currents but later I have figured out the way how this force works, but I have still to derive the analytic formula.
DeleteFor experiment that will verify the force between current elements, I propose to measure the force between 2 rectangular coils for many angular relative positions and to solve the linear system made by the measured force. Each side is a current element. Like this:
Force x and y= Force x and y on (sides 1 + sides 2 + side 3 + side 4 )
Force x and y between side i and j =I1*I2*(Sum (p*sin(ang ij)+q*cos(ang ij))
This equation is to be repeated for each couple of side i (coil 1) and j (coil 2)
We build a linear system using the measured force x and y for many angular position of the coil 1 with respect to coil 2 and solve for force on each side. This way we can find the correct force on current elements.
To explain this here is too complex. I will show this in detail one day.
I have found an interesting formula derived by Charles W Lucas in his paper "Derivation of the Universal Force Law - Part 2", it is very similar to your equation but with an extra term that decays more quickly, as your experiments seem to indicate. It is derived from Ampiers law, Faradays law, Gausses law, Lenz's law, and Galilean transform, and is consistent with Newtons 3rd law, Mach's principal and based on the Grassmann force law. It is
DeleteF[i j] = - (A I I')/2 * r_ * { (2/r_^3) (dl[i] . dl[j]) - (3/r_^5) *{ (dl[i] . r_ ) * (dl[j] . r_)},
where r_ is the position vector, and the dl[i] and dl[j] are the current element vectors. It appears to describe the magnetization of wire phenomenon you have described. The normal dot product force decays as 1/r^2, but the second term decays as 1/r^4, much more quickly.
I am very interested in what you are doing, I believe you are on the right track. It would be fascinating if your experiments do in fact validate such a theory. The implication are tremendous! I have been doing experiments in alt-science for many years now, very interesting, love to hear more about your linear system of measurments.
Dr. Jaynes
Dr Jaynes
Correction, I was thinking those were unit vectors, but there were actually full length vectors, so both terms decay as 1/r^2. The second dot product terms only change the direction of the force vector.
DeleteDr. Jaynes
Thanks for your formular. Effectively, the magnetised wire effect should be of the order of 1/r^3. This will be interesting for those who want to dig deeper into this phenomenon. As it decays very quickly, it does not affect Lorentz force which is the object of my proposition of experiment.
DeleteIn fact, the advantage the linear-system-solving experiment is to be able to measure the force on real elements of current that are the sides of a small coil. I think that no experiment involving real elements of current has ever been done before. Because the Lorentz's force formula is so strong in predicting EM force for closed coils that no one has seriously tried to derive an experiment with real current elements. But this must be done because Lorentz force have to respect Newton's third law on elementary level and because strong experimental evidences are necessary to convince people that EM theory must be corrected.
To simplify this experiment, I propose to first use an equilateral triangular coil and a long straight wire. This is equivalent to the interaction between 3 current elements and a long wire. As we are able to derive an analytical formula of the force between 1 current element and a long wire, we will only have a system of 2*3=6 linear equations to solve, that is, global x and y force and the torque or, x and y forces on each of the 3 sides. The long wire is in the plane of the triangular coil so that the z force is zero.
2 force sensors will be placed in the center of the coil to measure the global x and y forces. One will be placed on a tip of the coil to measure the global torque. The first measurement will be done when a side is parallel to the long wire. This will give us 3 measured quantities: x and y global forces and 1 global torque. Then we rotate the coil to another angle with respect to the long wire, for example 90°. Then the measurement will give us 3 more forces and torque. So we have the needed 6 linear equations that we will solve.
In fact, the parallel position will give zero y force and zero torque. This makes the system down to 4 equations.
If you have equipment to carry this experiment, then you will be able to determine forces on real current elements that nobody has done ever.
This is only a quick thought. I have to make a more careful design and mathematical derivation.
I do not have such fancy equipment either, these experiments are only my hobby. Actually if I was to carry out such experiments I would do them the way your are doing them now. Having a low friction pivot point with (mecury or balanced nail) to conduct the electricity, and measure the angle with respect to gravity is probably the most accurate way to measure such a torque with a long lever arm, even today. Some times the old fashion way of doing things is the best, unfortunately it takes time, because each torque experiment must be created individually, and just takes hard work and time, but all things worth doing, do.
DeleteProbably designing a zero torque experiment for one theory that has a torque in another theory is good way to rule out false theories, but creating the perfect experiment is always most of the battle.
I just wanted to mention that the final torque equation in the paper was given as a triple cross-product and is said to be consistent with Newtons 3 law, Ampiers law and Gauses Law, and conservation of energy. It includes more terms not included in the above equation, and is the preferred equation of this author. Maybe this, if plugged in to your theory will correctly predict the magnetization of the wire?
F[i j] = dl[i] x dl[j] x r_[i j]/ (c |r[i j]|^3)
It also reduces (with vector identity Ax(BxC) = B(A.C)-C(A.B) )to your equation with the dot products of the currents and an extra term with a dot product of the radial vector and current element. It would be interesting if your experiments are in agreement with this theory, since they also have derive a possible connection to the Gravitation force through Electromagnetism using this equation.
Dr. Jaynes
I’m back. Thanks for keeping commenting.
DeleteHappy New Year.
To make the scientific community change their mind is very difficult, if not impossible. So many brilliant scientists have died before their discovery gets recognition. Not only they have to predict quantitatively new phenomena with new theory and verify by experiments, they first have to make their new theory read by ruling scientists of the time. For alternative theorists, as the latter thinks EM theory is the correct theory, they do not even care to read challenging papers.
So, for now, the most important thing to do is to carry out more experiments that show the flaw of the classical EM theory, that show things that classical theory does not predict, phenomena that are contrary to classical theory, such as presence of force or torque where the classical theory predicts zero. This is the object of my experiments with the 2 m long solenoid, the tangential force motor, tangential force in earth’s and round magnet magnetic field, etc.
It will be great if you are willing to carry out such experiments because until now I’m the only one who does so. More experimenters bringing up more experimental evidence will make the flaw of the classical EM theory more credible. Only when sufficiently many physicists discuss this subject that it can get enough attention. Otherwise, this subject will stay ignored.
So, it is OK that you do not have equipment for precisely measuring force, I do not have neither. Let us just do experiments which clearly show force there should not be.