Applying Newton's 2nd law to single charged particle

In summary: Chrged particle radiates EM energy-should we not take these facts into account? Rather I think to make some applications of Lorentz force, these idealizations are adopted...They are not reality. There is a difference between "idealization" and "simplification". When you ignore air resistance in simple free-fall measurement, that is a simplification. When you require more precise results and realize the simplification isn't sufficient, you ADD more relevant factors that influences the dynamics. You keep doing this until your model matches the results as accurately as you require.
  • #1
How much are we justified in applying Newton's 2nd law in predicting trajectories of a single charged particle?What will be the answer for a number of charges?Of course, we have cyclotron motion at hand, but still...as we know, sub atomic level physics needs quantum mechanical consideration and linear superposition is liable to question here...So my question...
 
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  • #2
Classical electromagnetism and Newton's laws don't go well hand in hand, since electromagnetism requires a relativistic description of massive point charges. Accelerator physics is in the realm of quantum physics, of course.

Daniel.
 
  • #3
I wasn't aware that combining Maxwell's equations with the Lorentz force law led to any glaring contradictions in the non-relativistic energy regime. Could you elaborate a bit, dexter? I'm curious as to what we see.
 
  • #4
dextercioby said:
Classical electromagnetism and Newton's laws don't go well hand in hand, since electromagnetism requires a relativistic description of massive point charges. Accelerator physics is in the realm of quantum physics, of course.

Daniel.

Actually, accelerator physics is predominantly classical. Particle trajectory software such as PARMELA use purely classical mechanics and E&M.

... unless you are confusing "accelerator physics" with "high energy physics".

Zz.
 
  • #5
They don't. It's just that the theory is not unitary, so it can't offer a complete description of electromagnetic phenomena at classical level.

Daniel.
 
  • #6
ZapperZ said:
Actually, accelerator physics is predominantly classical. Particle trajectory software such as PARMELA use purely classical mechanics and E&M.

... unless you are confusing "accelerator physics" with "high energy physics".

Zz.

Perhaps. :blushing: So is accelerator physics not about HEP ?

Daniel.
 
  • #7
dextercioby said:
Perhaps. :blushing: So is accelerator physics not about HEP ?

Daniel.

Correct.

Accelerators are used in a number of different applications. The accelerated particle can be funnel into a synchrotron storage ring, for example. Or it can be used in a medical device to generate x-ray either for diagnostic or treatment. Having it as part of a particle collider facility is simply one example of its use. The physicists who work in accelerator physics very often do not know much about high energy/particle physics.

The APS publishes a FREE journal dedicated to accelerator/beam physics called Physical Review Special Topic - Accelerator and Beams (PRSTAB).

http://prst-ab.aps.org/

This is in addition to the section in PRL on Plasma and Beam.

You'll find the type of subject matter that is covered in there that are part of this area of study. You won't see any high energy physics papers.

Zz.
 
  • #8
...The discussion seems to go beyond my point in this thread.What I asked was that when we calculate circular/cycloidal trajectories of a charged particle using Newton's 2nd law, does it mean a physical reality or just mathematical analysis?
 
  • #9
Kolahal Bhattacharya said:
...The discussion seems to go beyond my point in this thread.What I asked was that when we calculate circular/cycloidal trajectories of a charged particle using Newton's 2nd law, does it mean a physical reality or just mathematical analysis?

In physics aren't mathematical calculations and physical reality presumed to be the same thing if the theory being used is correct?
 
  • #10
Yes, but to a certain extent and with a level of understanding.You may refer to the beginning Jackson's 2nd chapter where he writes,"...such idealizations as point charges or electric fields at a point must be viewed as mathematical constructs that permit a description of the phenomena at the macroscopic level, but that may fail to have meaning microscopically".
When Griffiths makes a calulation of the helical or cycloidal trajectory, it raises question whether we are justified in equating ma with the Lorentz force, being applied on a single isolated particle...Chrged particle radiates EM energy-should we not take these facts into account? Rather I think to make some applications of Lorentz force, these idealizations are adopted...They are not reality.
 
  • #11
Kolahal Bhattacharya said:
Yes, but to a certain extent and with a level of understanding.You may refer to the beginning Jackson's 2nd chapter where he writes,"...such idealizations as point charges or electric fields at a point must be viewed as mathematical constructs that permit a description of the phenomena at the macroscopic level, but that may fail to have meaning microscopically".
When Griffiths makes a calulation of the helical or cycloidal trajectory, it raises question whether we are justified in equating ma with the Lorentz force, being applied on a single isolated particle...Chrged particle radiates EM energy-should we not take these facts into account? Rather I think to make some applications of Lorentz force, these idealizations are adopted...They are not reality.

There is a difference between "idealization" and "simplification".

When you ignore air resistance in simple free-fall measurement, that is a simplification. When you require more precise results and realize the simplification isn't sufficient, you ADD more relevant factors that influences the dynamics. You keep doing this until your model matches the results as accurately as you require.

The same thing here. So far, we haven't seen any 'size effect' of the electron that has been manifested in various experiments. Thus, the simplification to a point charge works! Until there's something relevant, either experimentally or theoretically, that requires a more indepth consideration of an electron size, then the point-charge model works perfectly fine for our use.

The same principle applies to the helical path of charge particles.

Zz.
 
  • #12
So, what about the radiation of the chargged particle in cyclotron motion?Classically,it needs to have radiated...
 
  • #13
Kolahal Bhattacharya said:
So, what about the radiation of the chargged particle in cyclotron motion?Classically,it needs to have radiated...

What makes you think it doesn't? Cyclotrons and synchrotrons USE the radiation generated by such motion.

Zz.
 
  • #14
If I remeber correctly, I believe that even electrons in a cathode ray tube travel so fast that the Newtonian approximation is no longer accurate, and you need to include relativistic dilation terms.
 
  • #15
ObsessiveMathsFreak said:
If I remeber correctly, I believe that even electrons in a cathode ray tube travel so fast that the Newtonian approximation is no longer accurate, and you need to include relativistic dilation terms.

I don't think this has anything to do with classical vs. relativistic. It has more to do with classical vs. quantum mechanical. In particular, it is the commonly asked question on why "classical" motion of charged particles will radiate if they move in a circular/accelerating path, while it does radiate when it is in "orbit" in an atom.

We have already addressed this issue in the FAQ thread in the General Physics forum, because we get this type of question very often.

Zz.
 
  • #16
Kolahal Bhattacharya said:
Chrged particle radiates EM energy-should we not take these facts into account?

Yes, in principle we need to account for this radiation. In practice, however, the effects are negligible in many situations, including most simple textbook exercises.
 

What is Newton's Second Law?

Newton's Second Law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.

How does Newton's Second Law apply to single charged particles?

In the case of a single charged particle, the net force acting on the particle is equal to the product of its charge and the electric field it is in. This results in an acceleration of the particle in the direction of the electric field.

What is the equation for Newton's Second Law in terms of single charged particles?

The equation is F=ma, where F is the net force on the particle, m is its mass, and a is its acceleration.

Can Newton's Second Law be used to calculate the motion of a charged particle in an electric field?

Yes, by using the equation F=ma and the known values for the force and mass of the particle, the resulting acceleration can be calculated. This can then be used to determine the particle's motion in the electric field.

Are there any limitations to applying Newton's Second Law to single charged particles?

Yes, this law only applies to particles that are in an electric field. Additionally, it does not take into account any other forces that may be acting on the particle, such as magnetic forces.

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