Lorentz force and work done: where is the glitch?

[Dale]

The question is what integration method is actually implemented by Wolfram for those functions.

Their documentation is pretty extensive and the software itself is well tested.

I don't think that any of your concerns are problems here. This is a pretty tame equation and the output follows all of the known behaviors. Looking at the input and the output the numerical solution seems good, both quantitatively and qualitatively.

This is a huge topic on its own. It's relevant here...

It is indeed relevant, but not a problem here. I always check the results of numerical techniques against all of the constraints of the problem that I can think of.

Sadly, integration by itself is not sufficient, arguments like these should be settled with or along some actual experiment and measurement data.

Maxwell's equations are quite well validated by experiments and measurements.

Are you suggesting that we should never attempt to make or use any physical theory but should only collect experiment and measurement data for every possible combination of every possible scenario and not make any statements about situations for which we cannot simply look up the measured result?

 

[milesyoung]

I couldn't care less about work done.

Alright, I read your post as you saying the fact that the speed of the electron is constant is perhaps just an error from the numerical method used to simulate its trajectory.

For a brief time I felt my forehead vein starting to pulsate again.

 

[Jabbu]

Their documentation is pretty extensive and the software itself is well tested.

I don't think that any of your concerns are problems here. This is a pretty tame equation and the output follows all of the known behaviors. Looking at the input and the output the numerical solution seems good, both quantitatively and qualitatively.

I'm not using Mathematica, I don't know from the names of those functions whether they imply some specific or default integration method. I'm not concerned, just want to know what method is being used. Usually I'd expect the most simple Euler method would be default as it is the fastest and applicable in many situations, but supposedly not this one. Because it's the fastest method its preferred choice, but I'm not sure about its shortcomings. I would like to know if your integration was done through some variant of the Euler method because it would mean it can be implemented to be conservative after all.

Are you suggesting that we should never attempt to make or use any physical theory but should only collect experiment and measurement data for every possible combination of every possible scenario and not make any statements about situations for which we cannot simply look up the measured result?

I'm working towards exactly that goal. But I can't just use some other software, I have to write it from scratch. To make sure I know what I'm doing I need to closely examine how different integration methods work, and more importantly why and when they do not work.

 

[Nugatory]

I'm working towards exactly that goal. But I can't just use some other software, I have to write it from scratch. To make sure I know what I'm doing I need to closely examine how different integration methods work, and more importantly why and when they do not work.

Start a new thread...
You're asking a very different question than what this thread started with, and the only reason anyone is even working with numerical integration in this thread is that a previous poster refused to accept the proposition that if $f(x)=0$ everywhere then any integration of $f(x)$ over any range whatsoever has to come out zero as well.

 

[johana]

The length of the path is:

$$\int_0^1 |v(t)| dt = 4$$

So the path is indeed 4 m traveled at a constant speed of 4 m/s.

Here is an image of the path.

What magnitude is the force? Is it because the path is circular that no work is done? What if the magnetic field is not uniform and instead of circles the electron ends up wiggling around differently? What about two stationary permanent magnets that snap together after we let them go, is any work done then?

 

[Dale]

I'm working towards exactly that goal.

Frankly, I would actively oppose that goal, I see nothing of value in it. The whole purpose of science is the production of generalizable models of nature, aka theory. If you get rid of theory then you are no longer doing science, any more than if you get rid of experiment.

 

[Nugatory]

What magnitude is the force? Is it because the path is circular that no work is done? What if the magnetic field is not uniform and instead of circles the electron ends up wiggling around differently?

No. The key point is that the magnetic force is always perpendicular to the velocity of the charged particle (by $\vec{F}=\vec{B}\times{q}\vec{v}$) so $\vec{F}\bullet\vec{v}$ is always zero.

What about two stationary permanent magnets that snap together after we let them go, is any work done then?

That's a different problem than the one we're discussing in this thread, which is about a charged particle moving in a magnetic field.

 

[Jabbu]

That's a different problem than the one we're discussing in this thread, which is about a charged particle moving in a magnetic field.

Very interesting thing about it is that it can be simplified to two electrons going around in circles within two parallel planes one above the other. Now beside the centripetal magnetic force that makes them go around in circles there is one more magnetic force, orthogonal to their orbital planes, and actually moves them closer or further apart, if it was not for their electric fields which would dominate and move them apart in any case. But the faster the electrons go the greater their magnetic field is, so I suppose at some point the magnetic attraction could even overcome their electric repulsion.

 

[Dale]

What magnitude is the force?

The magnitude of the force oscillates between about 8.30E-28 N and 8.42E-28 N as shown in the attached image.

What if the magnetic field is not uniform and instead of circles the electron ends up wiggling around differently?

The magnetic field in this problem is not uniform and as a result the electron is not wiggling around in a circle. The magnetic field is slightly stronger near the dipole than away from it, so the force is slightly higher there. As a result, the electron's path turns slightly sharper near the dipole and slightly less sharp away from the dipole. That is the reason why it does not complete a circle, but "drifts" slightly with each pass.

What about two stationary permanent magnets that snap together after we let them go, is any work done then?

Yes, but the work is E.J, as always.

 

[AlephZero]

Frankly, I would actively oppose that goal, I see nothing of value in it. The whole purpose of science is the production of generalizable models of nature, aka theory. If you get rid of theory then you are no longer doing science, any more than if you get rid of experiment.

Jabbu is developing computer ganes, not doing science. Don't let terminology like "physics engine" mislead you.

 

[johana]

The magnitude of the force oscillates between about 8.30E-28 N and 8.42E-28 N as shown in the attached image.

The magnetic field in this problem is not uniform and as a result the electron is not wiggling around in a circle. The magnetic field is slightly stronger near the dipole than away from it, so the force is slightly higher there. As a result, the electron's path turns slightly sharper near the dipole and slightly less sharp away from the dipole. That is the reason why it does not complete a circle, but "drifts" slightly with each pass.

Yes, but the work is E.J, as always.

Does that mean no work done at all? How do you know from E.J is it electric or magnetic force doing the work?

 

[Dale]

Does that mean no work done at all? How do you know from E.J is it electric or magnetic force doing the work?

In this problem there is no E so yes, E.J implies that there is no work done at all. Other problems may have work done, but if you look carefully there is always an E.J involved.