Does r=mv/Bq hold true considering Maxwell's E.M wave theory?

• randomgamernerd
In summary, the discussion tries to answer whether equations (1) hold true for an electron with uniform velocity moving in a magnetic field. It is found that they do, but that the electron loses energy in the form of synchrotron radiation.
randomgamernerd

Homework Statement

: [/B]This is a general conceptual doubt, not a numerical based doubt. We were taught that when an electron(or any charged particle) moving with uniform velocity enters a magnetic field(perpendicular to its direction of motion), then a force acts on the electron which makes it move along a circular track.
The radius is given by r=mv/Bq...(1)
Now, suddenly while studying limitations of Bohr’s theory, it stroke me that if his model was rejected based on the fact that an accelerated charged particle continuously emits energy in form of E.M waves, and so the radius of the atom should decrease and the atom will collapse which does not happen, then my question is does equation (1) hold true because here we also have an electron having acceleration...
[Note: I’m aware the cause of the centripetal acceleration is different in both cases, but I don't feel that should make a difference]

: r=mv/Bq[/B]

The Attempt at a Solution

: [/B]As i mentioned above...
Please help.
Well, our currciulum does not cover modern physics in much depth, so may be I’m missing some point here...
Please help
And pardon my horrible english.

Hi,

Good thinking...

(1) holds true, but yes, the electron loses energy in the form of synchrotron radiation

BvU said:
Hi,

Good thinking...

(1) holds true, but yes, the electron loses energy in the form of synchrotron radiation
oh...never heard of that..so does it mean the radius remains constant but the electron still loses energy?

The electron loses energy and slows down, so…

vela said:
The electron loses energy and slows down, so…
so it does form a spiral, that means everywhere in the universe they will form a spiral unless its the case of an atom, right?where we have this fixed orbitals and stuffs, right?

On an atomic scale you are moving into the realm of quantum mechanics, where you do not have 'fixed orbits' in the sense of 'resembling planetary orbits'.

Instead, you have a wave equation to solve and the outcome are wave functions from which features like a most probable distance to the nucleus etc. can be derived.

For large-scale phenomena google betatron, cyclotron, synchrotron, etc.

okay, thanks

1. What is the significance of the equation r=mv/Bq in Maxwell's E.M wave theory?

The equation r=mv/Bq is known as the Lorentz force law, and it describes the force experienced by a charged particle (q) moving at a velocity (v) in an electromagnetic field with strength (B). This equation is important in understanding the behavior of charged particles in electromagnetic fields and is a fundamental component of Maxwell's E.M wave theory.

2. How does the equation r=mv/Bq relate to Maxwell's equations?

The Lorentz force law, r=mv/Bq, is derived from Maxwell's equations, which describe the behavior of electromagnetic fields. Specifically, it is derived from the combination of Maxwell's equations for electric and magnetic fields, known as the Lorentz force equation.

3. Does r=mv/Bq hold true for all types of particles?

Yes, the equation r=mv/Bq holds true for all types of particles that have a charge (q) and are moving at a velocity (v) in an electromagnetic field with strength (B). This includes particles such as electrons, protons, and other charged particles.

4. How does the equation r=mv/Bq help us understand electromagnetic waves?

The Lorentz force law, r=mv/Bq, is a fundamental equation in understanding the behavior of particles in electromagnetic fields. Electromagnetic waves are made up of oscillating electric and magnetic fields, and the Lorentz force law describes how these fields interact with charged particles. This helps us understand how electromagnetic waves propagate and interact with matter.

5. Are there any limitations to the equation r=mv/Bq in Maxwell's E.M wave theory?

While the equation r=mv/Bq is a fundamental part of Maxwell's E.M wave theory, it does have some limitations. For example, it does not take into account quantum effects and is only applicable to classical systems. Additionally, it does not consider relativistic effects for particles moving at very high speeds. Therefore, while it is a useful equation, it may not fully explain all aspects of electromagnetic wave behavior.

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