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### (way)(OT): Lorentz Force worked numerical example.

by BrowserUk (Pope)
 on Aug 01, 2008 at 12:18 UTC Need Help??
BrowserUk has asked for the wisdom of the Perl Monks concerning the following question:

The description pretty much says it all. I'm looking for a worked numerical example of a Lorentz Force calculation. Showing how the force acting on the conductor varies with voltage/current flowing through the conductor. I've looked and looked, but not found anything.

1. It's going to be used in a OpenGL simulation written in Perl.
2. There always seems to be a person, or several persons here, that not just know any given subject, but understand the subject, whatever it may be, well enough that they can put things in terms I can unerstand. Eg. simple!
3. My eyes just glaze over when I just attempt to parse stuff like this.

Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.
"Science is about questioning the status quo. Questioning authority".
In the absence of evidence, opinion is indistinguishable from prejudice.

Replies are listed 'Best First'.
Re: (way)(OT): Lorentz Force worked numerical example.
by apl (Monsignor) on Aug 01, 2008 at 13:23 UTC
I'm not certain this will help (my last Physics class was 31 years ago), but you should take a look at Physics::Lorentz (which points to the underlying Transformation and Vector classes).

Revised: Please ignore, and my apologies. If anyone would think to check CPAN, it would be you...

The package you suggest is for working with the Lorentz Transformation, which is used in special relativity. The OP here is concerned with electromagnetic interaction, which is quite different indeed.

But, it was worth a shot! And a good shot, seeing as I was born when you took your last physics course ;)

Many thanks for the gentle correction. After I posted, I realized that the OP was BrowserUk, who I know would have checked CPAN. So I immediately knew I was wrong...

So... what is the dominant paradigm of the day? (I was taught that a new theory was seldom adopted before the death of the acceptors of the prior theory. In spite of the talk of Quantum Computing, I'd expect Quantum to be as dead as Heisenberg...)

Re: (way)(OT): Lorentz Force worked numerical example.
by pc88mxer (Vicar) on Aug 01, 2008 at 13:51 UTC
Re: (way)(OT): Lorentz Force worked numerical example.
by amarquis (Curate) on Aug 01, 2008 at 14:44 UTC

I couldn't find an online example worked out, surprisingly.

Most of the stuff in the wiki article isn't needed for your case. What you need is the expression for the force on a current carrying wire: F = I (L X B). F is the force, I is the current. L is a vector with magnitude equal to the length of the wire, and its direction is the direction of the current flow. B is the magnetic field vector. All of this assumes a constant field along the wire and a straight wire.

That's likely not the case, so you have to go to infinitesimal wire segements and integrate: dF = I (dL x B).

I don't know if this has made it any clearer for you, I'm assuming from your post history that you have done stuff with vectors/numerical integration before and just needed the bullpucky separated from the stuff you need in the wiki article. If it hasn't helped, I wouldn't mind doing an example in Perl tonight/tomorrow evening if nobody else has.

Edit: How is your model of the situation stored? I assume you've got a function that, given x,y,z, gives you the magnetic field vector at that point, but what of the wire?

Re: (way)(OT): Lorentz Force worked numerical example.
by zentara (Archbishop) on Aug 01, 2008 at 16:24 UTC
From my old Physics, the first thing I thought of was Maxwell's Equations. I googled for "Maxwell Lorentz straight wire" and got alot of hits, like

Free Maxwell book with real solved problems See Chapter4 Problems for straight wire.

Maxwell Answers Search for Oersted on that page.

The big problem as I see it, is what are the assumptions made to simplify calculations. For instance, do you assume a uniform temperature always( affects resistance)? Another simplification would be assuming the wire has 0 radius, otherwise you need to account for different current flow at the skin versus the center. You might want to ask in the newsgroup sci.physics.

If you wanted some real world examples, I would also look at Electrical Engineering sites for examples of power line computations. I'm sure somewhere, some EE has a rule of thumb calculation for the Force on his power lines, especially at substations where short connections are made at high power. Maybe there is a Schaum's Outline Guide for Electrical Engineering, which contains simplified calculations and solutions for common problems?

I'm not really a human, but I play one on earth Remember How Lucky You Are
...to account for different current flow at the skin versus the center.

Ampere's Law tells us that current through a wire is confined to the "skin".

Ok, then you need to decide whether you will do your computations from the skin surface, or assume the current is at the center of the conductor. A skin calculation will be quite abit more difficult. To be honest, the whole idea of trying to accurately compute these things from formulas, for the real world is mind-boggling, if not futile.

I'll bet they use some sort of supercomputer simulation, to get formulas with fudge factor constants for different conditions and materials.

I'm not really a human, but I play one on earth Remember How Lucky You Are
Re: (way)(OT): Lorentz Force worked numerical example.
by pc88mxer (Vicar) on Aug 01, 2008 at 14:53 UTC
It's going to be used in a OpenGL simulation written in Perl.
BrowserUK, is your goal to create a cool video like this one: Magnetic Movie?
Re: (way)(OT): Lorentz Force worked numerical example.
by BrowserUk (Pope) on Aug 02, 2008 at 04:18 UTC

Rather than reply to every post individually, this is a collective thanks to everyone who replied. I have more than enough reading to keep me going for a while, along with a bunch of equations I understand, and some worked examples to give me a feel for the values involved. I couldn't have asked for more. My faith in the collective wisdom of this place is reconfirmed.

Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.
"Science is about questioning the status quo. Questioning authority".
In the absence of evidence, opinion is indistinguishable from prejudice.
Re: (way)(OT): Lorentz Force worked numerical example.
by dHarry (Abbot) on Aug 01, 2008 at 15:15 UTC

Maybe this is something? em_uniform1d.cpp Be sure to check the documentation link on the page as well.

Hope this helps.

Update:
I have decompiled a Java applet (guess that makes me a sinner?!) but the code s*ck*d.

Re: (way)(OT): Lorentz Force worked numerical example.
by LesleyB (Friar) on Aug 01, 2008 at 22:20 UTC

It depends how accurate you want your simulation to be, how confident you are with vector calculus and numerical integration.

The force on a wire carrying an electrical current can be approximated by F=BIL where, B is the magnetic flux density the conductor is exposed to, I is the current running through the wire and L is the length of the conductor.

This is a highly simplified equation which can be taken as an upper bound on the numbers you should achieve partly because it relies on an infinitely long conductor.

The numerical simulation of time varying electrodynamic problems is not trivial. For example, time stepping requires good guesses of skin depth to be able to achieve any accuracy.

This may be of interest just to get the numbers out.

same simulation will incorporate gravity

Each answer generates a thousand new questions. If you will incorporate gravity, what will be the mass of your conductor? Which brings up what is the conductor made of? Copper, Alumunum, Gold? Then if you need to assume an infinitely long conductor, your weight will be infinite. :-( Or how is the finite conductor terminated at the ends, which brings up all sorts of tensile strenth and flexibility coefficients, because the force will be working against the conductor's ability to flex.

I was thinking last night, that you could probably just make an OpenGl video of a line segment wiggling like an inch worm, and claim that a current pulse of X magnitude, Y duration, and Z shape caused it. Then let the skeptics write the equations for you as they try to prove you wrong. :-) That would be real hubris.

I'm not really a human, but I play one on earth Remember How Lucky You Are
Re: (way)(OT): Lorentz Force worked numerical example.
by hangon (Deacon) on Aug 02, 2008 at 01:48 UTC

This rail gun intro might be helpful to you. At least the math is comprehensible.

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