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

In summary: Originally posted by Student08 Electrons move in circles in a magnetic field, on the other hand, for different reasons. The magnetic force and the gravity are both types of central force. The difference between them is that the magnetic force is always pointing in one direction, whereas the gravity is not always pointing in one direction.
  • #1
Student08
2
0
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.
 
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  • #2
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/physics/ElectromagneticField.html

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

The Gravitational Force:
http://scienceworld.wolfram.com/physics/GravitationalForce.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
 
  • #3
Originally posted by cookiemonster
Magnetic forces are central? That's news to me!

Thanks for your nice explanations 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.
 
  • #4
Originally posted by Student08
Originally posted by cookiemonster
Magnetic forces are central? That's news to me!

Thanks for your nice explanations 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.

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.
 
  • #5
Also, a circle is an ellipse.
 

1. What is the main difference between electrons and planets under a central force?

The main difference between electrons and planets under a central force is their size and mass. Electrons are subatomic particles that are much smaller and lighter than planets, which are astronomical objects that can be significantly larger and more massive.

2. How do electrons and planets behave differently under a central force?

Electrons and planets behave differently under a central force due to their size and mass. Electrons are affected by the force of the central object, but their small size and high speed allow them to exhibit wave-like properties. On the other hand, planets are much more massive and their motion is mainly determined by the gravitational force of the central object.

3. Can electrons and planets both orbit a central object?

Yes, both electrons and planets can orbit a central object. However, the nature of their orbits is very different. Electrons exhibit wave-like behavior and their orbits are not fixed, but described by a probability distribution. Planets, on the other hand, have well-defined elliptical orbits around the central object.

4. What is the role of the central force in the behavior of electrons and planets?

The central force plays a crucial role in the behavior of both electrons and planets. It is responsible for keeping them in orbit around the central object and determining the shape and size of their orbits. The strength of the central force also affects the speed and energy of the particles or objects.

5. Are there any similarities between electrons and planets under a central force?

Yes, there are some similarities between electrons and planets under a central force. Both are affected by the force of the central object, and their motion is determined by the balance between the central force and their own inertia. Additionally, both can exhibit wave-like properties, although in different ways.

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