What's different between electrons and planet under a central force?

Student08

Why electrons do a circumferential motion under the magnetic force and planets do a elliptical motion under the gravity? I don't understand this because the magnetic force and the gravity are all central force. Can anyone tell me what's the difference between them, in words, mathematics or in physics principle. I'm a high school student who want to know about this. Thanks.[*(]

cookiemonster

Magnetic forces are central? That's news to me!

Orbits are elliptical (or hyperbolic, depending on energy) because gravity is an inverse square law. conic sections are the solutions to the orbit equation for an inverse square law. Why is gravity an inverse square law? Good question!

Electrons move in circles in a magnetic field, on the other hand, for different reasons.

I'd elaborate a bit more, but it's 5 in the morning and I'd kinda like to sleep before the sun comes up. So instead I'll kindly refer you to scienceworld, which has all sorts of nice equations with little explanation. Depending on what level of high school student you are, it may or may not be very enlightening.

Electromagnetic Field:
http://scienceworld.wolfram.com/phys...eticField.html

The Lorentz Force (Electromagnetic force, basically):
http://scienceworld.wolfram.com/phys...entzForce.html

The Gravitational Force:
http://scienceworld.wolfram.com/phys...onalForce.html

The electromagnetic field page has a nice little derivation of the motion of a charge in a constant electromagnetic field.

And welcome to the forums.

cookiemonster

Student08

[quote]Originally posted by cookiemonster
[b]Magnetic forces are central? That's news to me!

Thanks for your nice explainations and references. Central here I mean in the centre of the orbit. I'm in grade 11, but I still can't follow you well. I will study more. Then, If the magnetic force is inverse to the radius? I know I may ask a stupid question. But they really puzzle me.

selfAdjoint

[quote]Originally posted by Student08
[b]In classical physics the electric force follows the same inverse square law as Newton's gravity. That would hold the elecrically charged electrons in classical orbits, just like a little solar system, and about 1900 that was the theory.

But even at that time there was a problem with the little solar system model of the atom. All electromagnetism is governed, so they understood at that time, by Maxwell's equations. And Maxwell's equations say that an accelerated charge must radiate electromagnetic waves and lose energy that way. And turning aside from a straight line path, as in orbiting, is acceleration. So why don't the electrons in the atom radiate and lose energy?

Well to collapse a lot of history, quantum physics was discovered, and it was seen that the electrons really don't have a well defined position or path, those things are only defined probabilistically. So electromagnetism is saved, but quantum weirdness comes in.

russ_watters

Also, a circle is an ellipse.