# Paradox or miscalculation ?

1. Sep 12, 2007

### tabchouri

Paradox or miscalculation ??

Hello everybody,

First of all, let me say that I am an computer science engineer, and that i had relatively deep physics courses. That is to say, I know (more or less) what I am talking about :)

Well, my dilemma is: several years ago, I modeled a macroscopicphysical system based on static electrical charges. Those charges, assumed to be pontual and encapsulated in a non conducting material, are fixed in a certain manner within the physical system.
The system itself might be made of any solid material.
The thing is, the configuration of the system (rotation tying of its different parts) and the disposition of the charges implies a perpetual rotation of a central rod (on wich some charges are attached).

I have reviewed my calculations several times (wich are pretty simple that is), and my programming. I have run several simulations, and all come with the same result : there is always a tork force on the rod directed in the same direction, making it turn perpetually.

The system does not consume any internal or external energy of any type.

I have abondoned the idea, because this is just contradictory with the basic physical principles : the energy outcome (entering and exiting) in a closed system is equal to 0.

I reviewed that modelling lately, and I was thinking about it's feasability with permanent magnets, as it is not parctically feasable to have electrical charges.
The magnetic forces computations are pretty tricky to achieve for permanent magnets in motion, as there are no direct ways to do them.

So this is my dilemma, before plunging in those compolicated magnetic computations, can someone tell me in my process in physically possible, or did I make a big mistake somewhere ?

Thank you very much

2. Sep 13, 2007

### tabchouri

Hello again,

To make it more clear, I have taken into account the electric fields, and the magnetic fields generated by the movement of the charges.
The total forces applied to a charge X is the sum of the electrical force exerted by the other charges, and the magnetic force due to the magnetic filed (generated by the movement of other charges) and the movement of X.

I'm pretty confused here,
Can someone tell me please if this system is possible ?
Is it feasable to have such a configuration of a system that perpetually generate energy in the forme of rotation of a rod ?

Thank you very much.

3. Sep 13, 2007

### genneth

One should never have to ask if perpetual power generation is possible: it's never. End of story. Any violation of energy conservation or 2nd law of thermodynamics is an automatic fail as a physical theory.

4. Sep 13, 2007

### f95toli

I am not sure what the problem is here. From what I understand you are saying that the rod just rotates, this is NOT the same thing as power generation so there is no violation of the 2nd law.
If there is no mechanism for dissipation in your model (e.g. friction) the total energy will just be conserved and if the initial conditions are such that the rod moves it will just continue to move.

It is a bit like a mass hanging from a spring, if you set up a model for this and then use initial conditions that specify that the spring is initally displaced from its equilibrium position the mass will just continue to move forever; in order for it to ever slow down you need to put a friction term into the equation.

Since this is a rotating electrical system there will always be losses due to e.g. eddy currents; are these losses included in your model?

5. Sep 13, 2007

### tabchouri

Sorry i have not been clear on this point.
The rotation of the rod is not just due to the initial conditions.
In fact, my calculations lead to a total torque ( Newton.Meter ) having the same sign on the rod, thus making it rotate, and might produce work.

no, i have not included eddy losses is my model. What if the structure is made of non conductive materials ?

6. Sep 13, 2007

### olgranpappy

The answer must, of course, be "miscalculation" because there are no paradoxes, only apparent paradoxes.

7. Sep 13, 2007

### tabchouri

I'm pretty confused, I'm well aware of thermodynamics law of energy conservation.
But then, my system is really simple, involving moving charges (so only electric and magnetic forces) and physical coupling at non relativistic speed.
I'm sure of the force calculations and torque coupling.

If my considerations are incomplete, can you guys point me to some elements i did not take into account, that might explain my mistake ? should I consider other elements or energy losses or anything else that might legitimate this ?

thank you

8. Sep 13, 2007

### f95toli

So you are saying that the rod is speeding up with time in your calculations?
In that case there is something wrong. The only available energy in the system(if the rod is initially at rest) is the electrostatic potential energy.

9. Sep 13, 2007

### tabchouri

Yes, the rod is speeding up as my calculations lead to a torque with the same sign and non null magnitude in the full revolution.
I did not follow the simulation to a much extented steps, but the magnetic field would grow in strenght, and the implied forces on the charges would oppose the rotation.

Last edited: Sep 13, 2007
10. Sep 13, 2007

### olgranpappy

you haven't showed us your calculations. it's hard to diagnose exactly where the error is if we don't know what you did already. Obviously there is an error somewhere because there can not be torque on the rod always in the same direction causing it's angular velocity always to increase. There must be something external to the system which you have not taken into account, or your calculation is simply incorrect.

11. Sep 13, 2007

### f95toli

You shouldn't need any other effects if your calculations are correct. Eddy currents, friction etc will cause to system to slow down with time (since it losses energy) but you don't need to include them to CONSERVE energy.

From what I understand you are basically using Newtonian mechanics with some classical electrodynamics. Now, all equations of motion in classical physics automatically conserve energy (you never get more energy out than you put in), so if the amount of energy in your system increases there must be something wrong with your calculations. It is as simple as that.

Have you tried just calculating the total energy of your system? I. the kinetic energy of the rod+the electrostatic energy as a function of time. The sum of these two should be a time-independent constant, otherwise there is something wrong.

12. Sep 13, 2007

### Loren Booda

Perhaps you did not apply the symmetries of the electric and magnetic field correctly. Where in your equations do you find anything but an radial electric force and an energy that conserves? When you integrate the field at the boundary of the system, does your source charge agree?

13. Sep 13, 2007

### tabchouri

Thank you for the replies

The system contains cetain charges (enclosed) attached to physical parts.
Here is an attempt to explain what i have calculated :
- compute the Electric field at each center of a charge $$q_{i}$$ (cased by other charges $$q_{j}$$, j$$\neq$$i) : $$E_{i} = \Sigma_{j \neq i} \stackrel{\rightarrow}{C_{j}C_{i}}. q_{j} / (4.\Pi.\epsilon_{0}.C_{j}C_{i}^{3})$$
Where $$C{i}$$ is the center of charge i.

- compute the Magnetic field at each center of a charge $$q_{i}$$ (cased by other moving charges $$q_{j}$$, j$$\neq$$i) : $$B_{i} = \Sigma_{j \neq i} (\stackrel{\rightarrow}{v_{j}} \wedge {\stackrel{\rightarrow}{C_{j}C_{i}}}). \mu_{0}.q_{j} / (4.\Pi.C_{j}C_{i}^{3})$$
Where $$\stackrel{\rightarrow}{v_{j}}$$ is the velocity of charge j.

- then compute the forces on each charge, given by $$F_{i} = q_{i} (\stackrel{\rightarrow}{E_{i}} + \stackrel{\rightarrow}{v_{i}} \wedge \stackrel{\rightarrow}{B_{i}})$$

- the troques are then computed with these forces.
There is a coupling of torque with clockworks, transferring a torque from periperal rods to the central rod with a ratio
$$TORQUE_{central} / TORQUE_{perip} = - R_{perip} / R_{central}$$.

that's about all the calculations

Last edited: Sep 13, 2007
14. Sep 13, 2007

### Loren Booda

tabchouri
Are these statements mutually compatible?

15. Sep 13, 2007

### tabchouri

Well, that might explain why i get magnetic force really weak (negligible compared to electric forces).

But i wanted to include all parameters that i am aware of, in order to avoid any inconsistencies.

16. Sep 13, 2007

### ezfzx

Maybe this is "obvious" and maybe it's not, but things don't just rotate without consequences. There is angular momentum to consider, and more importantly, rotational kinetic energy (proportional to the square of the angular velocity).

Don't think in terms of torque. Think in terms of energy. A thorough accounting of all your energy usually reveals everything.

Also, you cannot hand wave out the "non-relativistic speeds", because the very nature of magnetic fields is that they are purely a relativistic expression of electric fields. Plus, the strength of the E field is such that even at slow speeds, relativity has a hand. (You don't have to have a very high current in a wire to get a magnetic field.)

17. Sep 13, 2007

### olgranpappy

it takes energy to separate the charges out into the initial arrangement. This energy can be converted into motion of the charges (the rods start spinning or whatnot), but *you* were the one who provided the energy by setting the charges up.

Consider, for example, two positively charged point charges sitting one meter apart; I set them there, one meter apart, and am holding them. Now I let go. The charges will indeed move away from each other, and will increase their kinetic energy, but the sum of their kinetic and potential energy is conserved.

18. Sep 13, 2007

### tabchouri

i agree with that,

But then, the physical system, as designed and as calculations yield, implied a perpetual rotation of the rod (if we assume no friction).
I guess that the angular velocity cant grow indefinitely (due to magnetic field breaking the rotation).
Then could it be at that max velocity, all the potential energy (of most of it) that i did to assemble the system has been transformed to kinetic ?
When we excert external work on the system to stop the rotation, then it acquires again its potential energy.

would that be an answear ?

Last edited: Sep 13, 2007