# Two different electrostatic charges in rotation

It's a theoretical problem. I mean I drawn a circle and I consider this circle exist.

I would like to understand how works this device composed of a circle and two charges:

Two charges fixed on a circle, one positive, one negative turn at the same angular velocity. The circle is free to move or rotate.

Each charge will give a magnetic field and this field will interact with the other charge.

Does the device moves in linear velocity ?
Does the device rotates in another axis ?
Does the device be in a stable position or vibrates ?

I need a little help for understood how a charge can interact with the other.

The velocity of the charge is $30000 km/s$ and the radius of the circle is $1e-22 m$. I choose value for cancel the centrifugal force with the electrostatic force. So, the charge is $1.6e-19C$ and the mass is around $2.5e-21kg$. Maybe it's possible to choose anothers datas, just cancel the centrifugal force and the electrostatic force. But, if it's possible I would like to study this device like that.

• Your model isn't complete. Due to the given distance the charges have to be electron and positron? Commented Jun 14, 2015 at 16:17
• Your circle could not exist due to your dimension, so there has to be or a nucleus or the charges will not move around and fly away. Commented Jun 14, 2015 at 16:20
• I added some datas. I forgot to say that centrifugal force is canceled by electrostatic force
– L X
Commented Jun 14, 2015 at 17:12
• There are too much presumptions. First at all it is not possible to produce such a constellation. How to force an electron and a positron to revolve into the same direction? Using magnetic field, the will revolve in opposite directions (clockwise and anticlockwise). I'm pointing out this moment because a forced circular motion led to photon emission and the circle get smaller and smaller. Commented Jun 15, 2015 at 4:45

There are two aspects of this question,one charge part and the other mass part. If you consider charge part,we see that magnetic force on + ball due to -ve ball and on -ve ball due to +ve ball both act upward,so the torque gets canceled and since these forces are internal, they will not make any change in momentum of system. The attractive forces of charges are acting along radius and thus will also not produce any momentum. Now coming to mass aspect, since the external force on system is zero and angular momentum is also constant, therefore it would also not make any change in momentum and thus the device will not rotate on any axis nor will it have any linear velocity. Take care:-)

• I think your directions for the magnetic forces are wrong. Both of the charges exert attractive magnetic forces on the other. The magnetic force exerted can't be along the direction of motion (since magnetic forces are always at right angles to the motion), and it can't be perpendicular to the plane of rotation (since that's the direction of the magnetic fields themselves.) So the magnetic forces must be radial. Commented Jun 14, 2015 at 13:19
• When two particles like electron, proton or their antiparticles interact, their magnetic dipole moments get aligned and they will attract each over. One have to look on this process on the level of particles, because magnetism is from the magnetic dipole moments only. Commented Jun 14, 2015 at 16:30
• But if electrons etc. get deflected their intrinsic spin works again the deflection and antialignes (emitting photons) and the magnetic dipole moment follows the spin. From LX question it is not clear, what makes the deflection, a magnetic field or a mechanical device. Commented Jun 14, 2015 at 16:39

At the level of magnetic & electric forces, there's really no change. At the moment that is depicted above, the negative charge will feel a magnetic field pointing into the page; and so it will feel an additional attractive force towards the positive charge. If the charges are held at a fixed distance by a rigid rod, this would cause a slight change in the tension required of the rod, but nothing more.

However, that's not the interesting answer. The interesting answer is that this is an accelerating dipole, and so it will emit energy in the form of electromagnetic waves. Thus, the rotation will slow down and eventually stop. This is not easy to see on the level of magnetic and electric forces acting on the charges; to actually see it, you have to take into account the amount of time necessary for electromagnetic "news" to travel around the system at the speed of light. Nevertheless, once you do this, you'll find that the charges will slow down. I believe that in this case, you'll end up with $\omega \propto 1/\sqrt{t}$ for long amounts of time, but I'd have to go through the math more carefully to check.

• How take in account the time ? you mean I need to give the radius of the circle and the speed of charges ? I added informations in the question. mass is 2.5e-21 kg like that the centrifugal force is cancel by the electrostatic force. The charge is 1.6e-19C.
– L X
Commented Jun 14, 2015 at 16:33