Work Done is given by the formula :-

W= -Q [ integral ] (E.dl)

The plate A is falling in the field produced by the surface charge i.e. uniform field, directed perpendicular to the plates A & B. This will definitely cause some work done, but at the same time the plate A is falling in the gravitational field, which will also cause its own work done. These two work done possibly cancel each other, to result in no net work done, I feel. 

Max,

When you slide plate A away from above B, you will do work. The two are attracted to each other - and they are finite. B is *not* in an equipotential field - the plates are finite are they not?

>Is there an equation that proves that Energy is always Conserved?

For it not to be would require Newton's third law (integrated, to yield energy from momentum) to be broken. Which is akin to breaking Galilean (and Lorentzian) frame transformations.

It cannot be done - at least in any self-consistent universe that holds to the very simplest principles.

I agree with James Garry. The sliding of plate A away from B is not without work done.

In general, conservation of energy is the first law of thermodynamics. (If you factor in relativity, you have to view mass also as a form of energy, and then there is conservation of mass-energy.). My feel is that it is more fundamental than Newton's laws, its really a very basic and very trustworthy basis, and if you find any experiment that seemingly violates it, there is most likely a mistake.

Best Regards,

Henri

The only way work can be done is if your saying the electric field lines on a flat plane are not perpendicular to it. The only charges interacting with plate A are the charges directly opposite it on plate B. The charges it has passed on the far side as you move it are not affecting it. We are moving plate A through an electric equipotential therefore we do no work.

Max,

Your statement is not true. Think of the problem as two point charges - you are attempting to move one away from the other, fighting the electrostatic force of attraction.

You are doing work in order to separate them.

Now, extend the analogy into an array of lots of point charges - and so you can turn a point into an extended object, like a flat plate.

The same argument now applies to all of the pairs that form these plates.

You are *still* doing work.

Max and James,

- It is true that the only way work can be done, is if the field lines are not perpendicular to it : Agree !, Correct !.

- It is true that the field lines are perpendicular to the flat plate. The flat plate is an equipotential object, and as a result, the field lines are perpendicular to it : Agree !. Correct !.

- However, the flat plate has also an edge, the place where the plate ends. It happens that there are field lines that terminate at the edge, and they are not perpendicular to the plate (It is the edge, the plate stops to exist there !.), and the work is done by the field lines that terminate at the edge, and do not 'see' the equipotential flat plate.

Best Regards,

Henri.

On the Earth  due to the effects of gravity, air resistance and  friction energy is rarely conserved.

Conservation only takes place between  subatomic particles.

As in all the classical perpetual motion machines, there is a defect in your thought experiment. Your assumption that the parallel motion is equipotential is only valid if the  plates are infinite. For finite plates the electrical potential changes around their boundaries, where the approximation of parallel electrical field is no longer valid. Thus, a work is required when the plate A moves parallely surpassing the boundary of plate B.

I hope this helps to clarify your doubt.

For you Max, there is the first law of thermodynamics.

And, since you want to claim patents on various versions of perpetuum mobile, you might also want to consider the second law. There is also a third law, but I cannot imagine it will be necessary for you to worry about.

As I have pointed out on another thread, it is simple to create some extra energy --- just by tickling the universe to expand a little faster :=D. I will not protest if Max makes a patent claim on that! He really deserves to be rewarded in some way for his relentless searches.

I am sure you can patent a perpetuum mobile. After all, the paper is patient. It accepts anything you write on it. However, when it comes to actually built one, then your search is pretty much a waste of time. The first law of thermodynamics (the law of the conservation of energy, or - with relativity factored in - the law of conservation of mass-energy) is very strong principle. Also, the second law is quite strong. The second law postulates that heat energy can only flow from high temperature to low temperature. If you want to reverse the flow, and make heat flow from low temperature to high temperature, you need to add some extra high-quality energy (like eg electricity or mechanical energy), which, in the process, is degraded to lower quality energy (eg heat at low or high temperature.)

Both these laws are fundament of thermodynamics, and, so far, they always hold. You cannot defeat them by simple experiments, and, also, not by complicated experiments. You are of course free and welcome to try, and challenge us, the more experimented people, to find the mistake. This will in the end lead to a better understanding of science for all of us. However, if your goal is to built a perpetuum mobile, either by defeating the first law or the second law, I am afraid you are losing your time.

Best Regards,

Henri.

Energy is a fundamental entity, and conservation of energy if a fundamental principle, which has no direct proof. Energy shall be conserved so long as you factor in all the conservative and non-conservative forces. At a higher level of application, for example the nuclear energy production, the mass energy relation must be factored in.  To say Energy is always conserved without these per-conditions shall be misleading.

What exactly means "always"?

What you mentioned can be represented by the law of conservation of energy (i.e., the first law of thermodynamics). That is, energy cannot be destroyed but can be converted from one form to another.

Hope this helps answer your question.

Professor Yehia Khalil

Yale University

USA

Assuming very thin plates the curved electric fields at the ends are almost zero.

If you could try to calculate the work done to remove plate A from the curved electric fields at the ends its not more than the energy I got from its fall.

Keep in mind that once out of the electric field I can place plate A as high as I want without expending any energy but the angle of the curved electric fields at the ends are constant so the energy to pull plate A out is constant. This means the work got from the fall can definitely be more than pulling plate A out of the curved electric fields at the ends.

Max,

As you are so sure, may I suggest that you actually either:

a) Build an experiment

b) Contract an FEA study to clarify the matter

c) Build an analytical model

Discussion here appears to be worthless as you are unwilling, seemingly, to understand the nature of what it is that you are proposing.

(are you now conversant with the concept of the Hamiltonian?)

Max,

The electric field at the end is not almost zero. This is a very wrong assumption.

If you have a curved object, the electic field emanating from it, is inversely proportional to the curvature radius. This effect is eg used in spontaneous electron emitters (devices that emit electrons in vacuum without heating) to create the very large electrical fields to let the electrons escape from the metal. (with relatively low voltage, of course.)

With the very thin electrical plate, the curvature ratio is obviously very small, and the electrical field is very large at the edges. An infinite thin electrical plate, would get an infinite high electrical field, meaning dielectric breakdown at the thin edge of the plate.

In doing so, you see, that even if the edge of the plate is very small, due to the very large electrical field there, the work done is significant.

This effect (the electrical field being inversely propotional to the curvature radius), is the result of one of Maxwells law (The electric flux leaving a volume is proportional to the charge). I am sure Remi would be able to produce all the formulas, but let me give you an example. Take a globe with a certain charge on it. Now, surround this cylinder with a surface, and calculate the electric flux going through this surface. Assuming the electric field to be constant, it is equal to the electric field strength times the area of the surface.

Now, here comes the curvature ratio. It happens for some surfaces, the surface area of an object surrounding it does not vary much with distance (eg a infinite flat plate - if you surround it with an object, the area remains constant, regardless the distance), for others, the surface area goes up very quickly with the distance. The parameter determining this most, is the curvature ratio. Hence, the electric field near an object with very small curvature ratio is very high, dissipating quickly with distance to a low value, while for a 'flat' object, the electric field is more or less constant.

Best Regards,

Henri.

Max and James,

Please do not shoot the pianist. Be professional, and answer the questions, dont shoot the messenger. If you dont like the discussion, stay away.

Henri.

Henri,

The discussion is fine - what I find challenging to my (normally placid) demeanour is the unwillingness of the student to go and learn the foundations of their chosen discipline. And, when given advice, their (seeming) refusal to heed it.

I applaud your patience and will strive to retain a similar attitude.

Max,

This is not a personal vendetta - indeed, your gedanken experiments are useful tools for teaching. But I would strongly advise personal study first and foremost. Research Gate is not a school. And what you need to do is not 'research' (ie, uncover new data and ideas) but 'study' (absorb the wisdom of the ancients that is known to be true)

The following examples and proves exit

1. The total energy of the harmonic oscillation is constant.

https://www.boundless.com/physics/textbooks/boundless-physics-textbook/waves-and-vibrations-15/periodic-motion-123/energy-in-a-simple-harmonic-oscillator-433-7945/

2. Total energy of a body falling from a height is constant.

http://physics.stackexchange.com/questions/77373/proof-of-conservation-of-energy

James

I do not agree !.

This is a quite pertinent question. The student sees a contradiction between the conservation of energy, and Maxwell's laws governing electricity, and thinks he can create a perpetuum mobile out of it.

Of course there is a mistake, the mistake being that at the discontinuity of the plate (the edge), there is a discontinuity in the electic field. (it becomes essentially infinite), and he did not know that a discontinuous electrical field is possible. So, we explain him.

This behavior, when finding a contradition in your mind, to research and ask, is very scientific. It becomes unscientific when rejecting the basis of science, in this case, refusing to accept an explanation based on Maxwell's laws.

In a certain way, Researchgate is a school. I mean, asking questions on fundamental things like this, is fine. What I dont like (you are free to disagree), is that many people seem to take their homework to Researchgate - questions like 'how can I do XYZ in Matlab', where there is no intend to understand why and how to come to the solution in Matlab.

Note that there is plenty to challenge in science, but I am afraid the energy conservation law (the first law of thermodynamics), and the energy degradation law (the second law of thermodynamics) are not part of that. (I dont believe the second law is broken, and I cannot find the article on it that it is. There is just some journalist 'hearsay', which does not have the detail of the experiment.)

Some examples of things that should not be taken for granted (I am sure there are plenty others.)

- Cold fusion (fusion of deuterium to helium during electrolisis of water)

  (I dont say it is possible. I say it is not proven to be impossible.)

  (If you like free energy.)

- My preferred one: the compatibility of science with existence of a god. My point here is that is not possible to prove god does not exist, so then why does everybody want us to accpt this ?  On my website here on Researchgate there is an article on this: "The universe is a quantum computer".

Greetings,

Henri.

Henri> I dont say it is possible. I say it is not proven to be impossible

In a way cold fusion is possible! Muon catalyzed cold fusion works as long as the muon lasts. Which, perhaps unfortunately, is for less than 10 reactions on average. So, you only have to find a way to make the muon stable -- or a very energy efficient way to produce muons, and collect the energy back when they decay :-)

Henri> "The universe is a quantum computer"

And we are but instances of a primitive class running on that computer...

It is necessary to have a balance between the bravery and reflection, especially for students. One must have the basic education for research activity. Without it there will be just a bunch of false statements and self-evident errors. There is a class of people - "physical freaks" - they design perpetuum mobile, "new physics" with elementary mathematics (they don't know other), etc. It is near a mental desease and it is necessary to prevent this degenerative way for students.  

Henri,

I largely agree, thank you for stressing the issue of abusing RG and other platforms for letting others make the homework.

IMHO, the (non-)existence of god is outside science. Cusanus claimed that god is one and the same everywhere and at all times, hence, space and time are homogeneous and isotropic. Such kind of heuristics is fine for me.

In contrast, religion is a psychological phenomenon.

Thank you,

Peter

Forgive my curiosity but I feel there may be a loop hole like in this thought experiment about charge induction.

Consider two conductor bodies A and B.

A is positively charged and it stores electrostatic energy of 10J.

A is then brought close to B that is neutral. A then induces charge separation between the positive and negative charges in B.

Assuming all the electric fields produced by A are interacting with B it means these charge separations have equal magnitude with charges in A.

The negative charges on B are closer to A while the positive charges are at the far side. When I Earth the positive far side of B I will get 10J of electric energy.

After the Earthing I remain with positively charged A and the negative charge on B. With A in the same position, I then connect A directly to B and electric current of 10J flows.

So I charged my body using 10J and now I have got 20J out of Earthing and connecting the two bodies together.

Peter,

God is not outside science. Take Evolution Theory. There is no doubt that 99.9 % of all evolution of species can be explained from this theory, but the theory now is used to 'prove' that 100 % of evolution can be explained by it, and then the conclusion is drawn that life originated by itself. This implies the assumption of no god.

For the study of evolution of life (where it comes from, where it goes to), the presence or absence of god is very important, as it may influence evolution mechanism.

'The Universe is a quantum computer' is in a way a study as to what mechanics the Universe is subjected to, it is not religion. There are 3 types of mechanics: newtonian mechanics, relativistic mechanics and quantum mechanics, and they differ eg in how time goes forward: For newtonian mechanics, it always goes forward, for relativistic mechanics, it slows down, but still goes forward, and for quantum mechanics, its not causal. Time goes forward and backward at the same time.

Now, usually only small systems are subject to quantum mechanics. One exception is the quantum computer, or any quantum mechanically coherent system. Then I make the  reflection that also the universe may be a quantum mechanically coherent system, and then, when you look at the results of that, the conclusions are really weird.

Regards,

Henri.

I assumed electric field lines of parallel plates where always perpendicular. Since I was wrong then that first thought experiment cannot work. The last one at the question top is giving me more problems.

Max,

For the case of only electrical field, there are 2 Maxwell laws that determine the behavior :

(1). For any surface, the electrical flux through this surface is proportional to the electrical charge contained.

(2). If in any electrical field, you move a charge over a closed trajectory, the net energy needed for this is zero. (this is not true in the presence of a changing magnetic field. We are not dealing with that here, however.)

The second law implies conservation of energy. You can built 'electrical machines' that convert between electrical and mechanical power, using the electrical field (not common, like you propose), or using the magnetic field (quite common), but there is ALWAYS conservation of energy. For electrical field, its right in Maxwells laws, for combined fields, its more complex.

Best Regards,

Henri.

Thanks Henri,

the problem here is we have Earthed the system and got back the energy we used to charge it. But we come to realize that we can still get more electric energy flowing in different parts of the system due to the presence of the same charge.

So little electric potential energy in the central sphere say 10J is giving rise to say 100J electric energy flow.

Emmy Noether’s theorem proves that for a physical system having differentiable (i.e. smooth, continuous) symmetries experiencing an action has a corresponding conservation law. The action is an integral of the Lagrangian (L=T-V) function, for systems which can be modeled through the Lagrangian alone (or for that matter the Hamiltonian, H = T+V). Consequentl, the equations can be shown to lead to the principal of least action, i.e. implicitly a potential energy (V) minimum. In short, the answer to your question is yes, there is a proof. Returning to your question, the thing to note is that the symmetry of your spheres isn’t continuous.