Magnetism & Inertia: Can Objects Orbit Each Other?

[litewk]

Hi,
Is it possible for two objects of nearly the exact same size, mass, and magnetic field strength to form something analogous to a curved space orbit in a relatively flat space by balancing inertia with magnetism? In other words, can two mutually magnetic objects orbit around a common center of magnetism for any length of time at some given distance scale?
If so, can all four fundamental forces of physics form six relationships via their orbital time period ratios. It seems like macro orbits have no meaning in the quantum world but this thought occurred to me a while back and I am non-degreed so I'm unable to solve this one easily.
Thanks for your time.

 

[chrisbaird]

Any force that is central and attractive, like gravity, will lead to conservation of angular momentum, meaning that stable orbits are possible. The electrostatic force between two opposite charges is central and attractive, and the magnetostatic force between two ideal opposite magnetic poles is central and attractive, so you might think that electric charges or magnets could form stable orbits around each other. The problem is that orbits require motion, which mean we are no longer in statics. When motion is involved, the magnetic and electric field become coupled, and you enter the realm of electrodynamics. The electromagnetic (Lorentz) force is not central and therefore two electromagnetic objects cannot form a stable orbit with each other (classically speaking). This means classically that electrons should not form stable orbits around nuclei. This is the problem that lead to the need for a quantum description of atoms.

 

[DrFurious]

I disagree with chrisbaird. Not all central force orbits are stable. In fact, (Bertrand's theorem) only TWO types of orbits are stable: inverse-square law (gravity, electrostatics) and a radial harmonic oscillator type.

The attraction between two magnets is certainly NOT 1/r^2. I can't even remember what it is off the top of my head, but I remember trying to figure it out at some point and it was complicated... something like 1/r^3, or something similar.

 

[pallidin]

In other words, can two mutually magnetic objects orbit around a common center of magnetism for any length of time at some given distance scale?

If there is a rotational impulse provided, yes(this prevents/slows the collapse). If not, no.

 

[Bill_K]

The pair of objects taken together will have a time-varying dipole moment. Therefore they will radiate electromagnetic waves, lose both energy and angular momentum and ultimately collapse.

 

[chrisbaird]

DrFurious,

Thank you for clarifying. I did not mean to imply that a central force is a sufficient condition, just a necessary condition. Hence the word 'possible'.

Also, the attraction between two idealized point-like magnetic poles is an inverse square law, or similarly the force between two infinitesimal strips of current is an inverse square law. (See Jackson Eq. 5.10 for example.) Of course, idealizations like this are non-physical and when we go to actual macroscopic objects, the fields and forces get more complicated.

- Chris

 

[DrFurious]

Also, the attraction between two idealized point-like magnetic poles is an inverse square law, or similarly the force between two infinitesimal strips of current is an inverse square law. (See Jackson Eq. 5.10 for example.) Of course, idealizations like this are non-physical and when we go to actual macroscopic objects, the fields and forces get more complicated.

Your reference is spot on. And the fields do get pretty complicated :)

Word to the wise though: if you have to do an experiment, don't rely on the magnetic result from (e.g. Jackson). Cause you will go crazy. Other non-dipole forces behave a lot easier.