Because is impossible to calculate the antiderivative of a function of
more than one variable, indefinite multiple integrals do not exist so
they are all definite integrals.

http://en.wikipedia.org/wiki/Multiple_integral


Currents, i.e. moving electric charges, produce magnetic fields. There
are no magnetic charges. Maxwell's equations tell us how to compute
the electric fields and magnetic field produced by charged particles.
The terms electrostatics and magnetostatics refer to steady state
conditions, when all charges are at rest or only steady currents are
flowing. Then the charge densities do not change anywhere. Under
those conditions Maxwell's equations are given below...

http://electron9.phys.utk.edu/phys13.../m7/Ampere.htm


In Section V we derive the electric and magnetic fields
from the Coulomb-gauge potentials
and show that they are the well known expressions,
causal and propagating with speed c, despite
the instantaneous nature of the scalar potential.
This ground has been traveled before in this
journal by Brill and Goodman6 and recently by Rohrlich.7
There is also Problem 6.20 in my
book.2 Our discussion here is different and I think
more transparent because of the form of our
solution for AC. Some aspects of Brill and Goodman come
close. In Section VI we discuss
briefly the quasi-static limit of the vector potential in
the Coulomb gauge and its use to obtain a
Lagrangian for the interaction of charged particles that
is correct to order 1/c2 in the velocities.
Section VII is devoted to a class of gauges we call the
velocity gauge (v-gauge) in which the scalar
potential propagates with an arbitrary speed v.
The Lorenz and Coulomb gauges are limiting
cases, v = c and v = , respectively. The gauge function
and the potentials are determined, as are
the electromagnetic fields (the same as always).

http://arxiv.org/abs/physics/0204034



Sue...

"Sue..." wrote in message
oups.com...
|
|
| Because is impossible to calculate the antiderivative of a function of
| more than one variable, indefinite multiple integrals do not exist so
| they are all definite integrals.
|
| http://en.wikipedia.org/wiki/Multiple_integral
|
|
| Currents, i.e. moving electric charges, produce magnetic fields.

BULL****!
Changing electric fields produce magnetic fields, "current"
is a by-product.
Androcles.

Androcles wrote:
"Sue..." wrote in message
oups.com...
|
|
| Because is impossible to calculate the antiderivative of a function of
| more than one variable, indefinite multiple integrals do not exist so
| they are all definite integrals.
|
| http://en.wikipedia.org/wiki/Multiple_integral
|
|
| Currents, i.e. moving electric charges, produce magnetic fields.

BULL****!
Changing electric fields produce magnetic fields, "current"
is a by-product.
Androcles.

Charges come in 0.511 MeV packages Eh?

I can think of two ways to produce a *change*.
You know of a third way?

Sue...

"Sue..." wrote in message
oups.com...
|
| Androcles wrote:
| "Sue..." wrote in message
| oups.com...
| |
| |
| | Because is impossible to calculate the antiderivative of a
function of
| | more than one variable, indefinite multiple integrals do not exist
so
| | they are all definite integrals.
| |
| | http://en.wikipedia.org/wiki/Multiple_integral
| |
| |
| | Currents, i.e. moving electric charges, produce magnetic fields.
|
| BULL****!
| Changing electric fields produce magnetic fields, "current"
| is a by-product.
| Androcles.
|
| Charges come in 0.511 MeV packages Eh?

Nope. Charges come in 1,000,000 micro eV packages,
by definition of "electron Volt". If you want a charge of 0.511 MeV,
you need 511,000 electrons bunched together. They don't like crowds,
you'll have a distributed charge. Maybe you are confusing charge with
mass.

| I can think of two ways to produce a *change*.

Can you? How nice.
Androcles

Androcles wrote:
"Sue..." wrote in message
oups.com...
|
| Androcles wrote:
| "Sue..." wrote in message
| oups.com...
| |
| |
| | Because is impossible to calculate the antiderivative of a
function of
| | more than one variable, indefinite multiple integrals do not exist
so
| | they are all definite integrals.
| |
| | http://en.wikipedia.org/wiki/Multiple_integral
| |
| |
| | Currents, i.e. moving electric charges, produce magnetic fields.
|
| BULL****!
| Changing electric fields produce magnetic fields, "current"
| is a by-product.
| Androcles.
|
| Charges come in 0.511 MeV packages Eh?

Nope. Charges come in 1,000,000 micro eV packages,
by definition of "electron Volt". If you want a charge of 0.511 MeV,
you need 511,000 electrons bunched together. They don't like crowds,
you'll have a distributed charge. Maybe you are confusing charge with
mass.

| I can think of two ways to produce a *change*.

Can you? How nice.
Yes, snip, annihilation or however you
want to demonstrate it. ;-)
Spatial displacement is a second way.

You didn't mention a third way. :-(

Sue...


Androcles

"Sue..." wrote in message
ups.com...
|
| Androcles wrote:
| "Sue..." wrote in message
| oups.com...
| |
| | Androcles wrote:
| | "Sue..." wrote in message
| | oups.com...
| | |
| | |
| | | Because is impossible to calculate the antiderivative of a
| function of
| | | more than one variable, indefinite multiple integrals do not
exist
| so
| | | they are all definite integrals.
| | |
| | | http://en.wikipedia.org/wiki/Multiple_integral
| | |
| | |
| | | Currents, i.e. moving electric charges, produce magnetic
fields.
| |
| | BULL****!
| | Changing electric fields produce magnetic fields, "current"
| | is a by-product.
| | Androcles.
| |
| | Charges come in 0.511 MeV packages Eh?
|
| Nope. Charges come in 1,000,000 micro eV packages,
| by definition of "electron Volt". If you want a charge of 0.511 MeV,
| you need 511,000 electrons bunched together. They don't like crowds,
| you'll have a distributed charge. Maybe you are confusing charge
with
| mass.
|
| | I can think of two ways to produce a *change*.
|
| Can you? How nice.
| Yes, snip, annihilation or however you
| want to demonstrate it. ;-)
| Spatial displacement is a second way.
|
| You didn't mention a third way. :-(
|
| Sue...
Your thread title is "Making Maxwell radiate".
Please stay on topic.
Androcles.

Androcles wrote:
"Sue..." wrote in message
ups.com...
|
| Androcles wrote:
| "Sue..." wrote in message
| oups.com...
| |
| | Androcles wrote:
| | "Sue..." wrote in message
| | oups.com...
| | |
| | |
| | | Because is impossible to calculate the antiderivative of a
| function of
| | | more than one variable, indefinite multiple integrals do not
exist
| so
| | | they are all definite integrals.
| | |
| | | http://en.wikipedia.org/wiki/Multiple_integral
| | |
| | |
| | | Currents, i.e. moving electric charges, produce magnetic
fields.
| |
| | BULL****!
| | Changing electric fields produce magnetic fields, "current"
| | is a by-product.
| | Androcles.
| |
| | Charges come in 0.511 MeV packages Eh?
|
| Nope. Charges come in 1,000,000 micro eV packages,
| by definition of "electron Volt". If you want a charge of 0.511 MeV,
| you need 511,000 electrons bunched together. They don't like crowds,
| you'll have a distributed charge. Maybe you are confusing charge
with
| mass.
|
| | I can think of two ways to produce a *change*.
|
| Can you? How nice.
| Yes, snip, annihilation or however you
| want to demonstrate it. ;-)
| Spatial displacement is a second way.
|
| You didn't mention a third way. :-(
|
| Sue...
Your thread title is "Making Maxwell radiate".
Please stay on topic.
Well... you are the one that brougt up
the 1/r^3 component.
Did not.
Did.
Did not.
Did too!
I'm telling!
Can't! 'cause I will first! )

Sue...

Androcles.

"Sue..." wrote in message
ups.com...
|
| Androcles wrote:
| "Sue..." wrote in message
| ups.com...
| |
| | Androcles wrote:
| | "Sue..." wrote in message
| | oups.com...
| | |
| | | Androcles wrote:
| | | "Sue..." wrote in message
| | |
oups.com...
| | | |
| | | |
| | | | Because is impossible to calculate the antiderivative of a
| | function of
| | | | more than one variable, indefinite multiple integrals do
not
| exist
| | so
| | | | they are all definite integrals.
| | | |
| | | | http://en.wikipedia.org/wiki/Multiple_integral
| | | |
| | | |
| | | | Currents, i.e. moving electric charges, produce magnetic
| fields.
| | |
| | | BULL****!
| | | Changing electric fields produce magnetic fields, "current"
| | | is a by-product.
| | | Androcles.
| | |
| | | Charges come in 0.511 MeV packages Eh?
| |
| | Nope. Charges come in 1,000,000 micro eV packages,
| | by definition of "electron Volt". If you want a charge of 0.511
MeV,
| | you need 511,000 electrons bunched together. They don't like
crowds,
| | you'll have a distributed charge. Maybe you are confusing charge
| with
| | mass.
| |
| | | I can think of two ways to produce a *change*.
| |
| | Can you? How nice.
| | Yes, snip, annihilation or however you
| | want to demonstrate it. ;-)
| | Spatial displacement is a second way.
| |
| | You didn't mention a third way. :-(
| |
| | Sue...
| Your thread title is "Making Maxwell radiate".
| Please stay on topic.
| Well... you are the one that brougt up
| the 1/r^3 component.
| Did not.
| Did.
| Did not.
| Did too!
| I'm telling!
| Can't! 'cause I will first! )

Tell my granddaughter. She likes pantomime.
My grandson thinks his 5 times table is trivial and
boring, no challenge whatsoever, and he's not bothered
by germs anymore (but still washes his hands).
He's still a little young to explain Einstein and
Maxwell to, but already interested in simple
electrical circuits as I was at that age. I think I'll
buy him a 9V battery of cells for xmas, with a
free solenoid.
You can buy your own. )
Androcles

Androcles wrote:
"Sue..." wrote in message
oups.com...
| Charges come in 0.511 MeV packages Eh?

Nope. Charges come in 1,000,000 micro eV packages,
by definition of "electron Volt".

Just out of curiosity, what do you think the definition of
"electron volt" is?

(It's a unit of energy, not charge)

- Randy

P.S. 0.511 MeV is the amount of energy E=mc^2 where m is
the mass of an electron.