Electric flux lines simulation for educational applets

[Heissenburger]

Electric flux lines simulation for educational applets

A friend of mine is trying to show electric flux lines for some
applets for students on a 3D Java simulation system. We're
looking for some way to generate and show those electric flux
lines as "real" things in space. Are there equations for
those?

I have tried working out the equation for a system with one
positive charge and one negative charge, assuming coordinates
s.t. charges -q1 and +q2 are at (-1,0) and (1,0) respectively.
using Coulomb's Law to analyse the forces and i got the
following set of differential equations (k = some constant)

dx/dt = - k q1 (x+1) / ((x+1)^2+y^2)^(3/2)
- k q2 (x-1) / ((x-1)^2+y^2)^(3/2)

dy/dt = - k q1 y / ((x+1)^2+y^2)^(3/2)
+ k q2 y / ((x-1)^2+y^2)^(3/2)

1. Are my DEs correct?

2. Are there fast and accurate (maybe to order 2) methods
to solve the equations to generate the electrical lines?

3. Are there any alternative / better ways?

--
sesame-seeded top bun
+ pickles + cheese
+ sigma_x . sigma_p >_ hbar / 2
+ bottom bun

[Bill Miller]

"Heissenburger" <heisse...@gmail.con> wrote in message
news:i50un8$5tj$1...@speranza.aioe.org...

You might want to look at Oleg Jefimenko's book, Electricity and Magnetism.
At the beginning of Chapter II he shows a variety of lines of force --
magnetic and electric. He also wrote a nice paper, "Demonstration of the
Electric Fields of Current-Carrying Conductors" AJP 30, 19, 1962.

Also in E & M section 6-6, pp168-173 he develops a "Method Of Curvilinear
Squares" that might be applicable for applet-ing

All the best,

Bill Miller

[glen herrmannsfeldt]

Heissenburger <heisse...@gmail.con> wrote:
> Electric flux lines simulation for educational applets

> A friend of mine is trying to show electric flux lines for some
> applets for students on a 3D Java simulation system. We're
> looking for some way to generate and show those electric flux
> lines as "real" things in space. Are there equations for
> those?

(snip)

> dx/dt = - k q1 (x+1) / ((x+1)^2+y^2)^(3/2)
> - k q2 (x-1) / ((x-1)^2+y^2)^(3/2)

That sounds like the hard way.

It isn't hard to calculate the potential or field for a
distribution of charges. Flux lines go in the direction
of field lines, and their spacing should be proportional
to the field strength.

-- glen

[Salmon Egg]

In article <8diqdn...@mid.individual.net>,
"Bill Miller" <kt...@yahoo.com> wrote:

Although it is not the easiest read, I refer to Smythe's Static and
Dynamic Electricity. There are sections on two and three-dimensional
potential distributions. The potential gradient js going to be tangent
to a flux line. It may also pay to looke ip the mathematics of envelopes.

Bill

--
An old man would be better off never having been born.