"Gene Fuller" wrote in message
...
art wrote:


But Jimmie my friend, now you have an understanding of Gaussian law
what is preventing you adding the metric of time or a length of time
to the statics law?


Art,

Adding the "metric of time" is exactly what J.C. Maxwell did, in 1865. The
detailed hard work surrounding Maxwell's Equations, as we know them today,
was probably more attributable to Oliver Heaviside. However, Maxwell gets
the credit for adding the time contribution.

unfortunately art is stuck on one of the 4 equations and is ignoring all the
others. if he really understood maxwell's work he would know:

Gauss' Law is for static electric charges and fields.
Ampere's Law is for static magnetic fields, that is fields set up by
constant (read non-time varying) currents.
Faraday's Law introduced the time varying part of the relation between
magnetic fields and currents.
Then Maxwell tied them together with the displacement current into the 4
equations that we have been using and which have successfully been used to
calculate all kinds of electromagnetic phenomena for many years.

By talking about curl of electric fields art is forgetting that this is one
of the representations of Faraday's law:
curl(E)= -dB/dt (E and B are vectors of course) which automatically adds
the time relationship that he is trying to force into Gauss's law where it
has no place.

personally i recommend ignoring him until he goes back to fields and waves
101 and gets the equations straight.

On Fri, 09 Mar 2007 16:45:31 GMT, Dave
wrote:
Gauss' Law is for static electric charges and fields.

It is usually used for problems in electrostatics, but it is not
confined to such problems. The differential form of it is just one of
the Maxwell equations:

div E(x,t) = 4\pi\rho(x,t)

Integrate it over a fixed surface and you get the integral form, which
is Gauss's law. It is valid with time-dependent charge densities and
time-dependent electric fields.

--John

"John E. Davis" wrote in message
...
On Fri, 09 Mar 2007 16:45:31 GMT, Dave
wrote:
Gauss' Law is for static electric charges and fields.

It is usually used for problems in electrostatics, but it is not
confined to such problems. The differential form of it is just one of
the Maxwell equations:

div E(x,t) = 4\pi\rho(x,t)

Integrate it over a fixed surface and you get the integral form, which
is Gauss's law. It is valid with time-dependent charge densities and
time-dependent electric fields.

no, i'm afraid you can't just put a 't' on each side and have it make sense
in the general case. time varying charge implies a current, a current
implies a magnetic field, then you have to include Ampere's law and add
curl(E)=-dB/dt to the mix. while you may be able to constrain the changes
in rho(t) to some short time or constant current and eliminate the dB/dt
part of the problem, that would only apply in specific conditions, not to
the general case.

On Sat, 10 Mar 2007 13:08:39 GMT, Dave
wrote:
no, i'm afraid you can't just put a 't' on each side and have it make sense
in the general case. time varying charge implies a current, a current
implies a magnetic field, then you have to include Ampere's law and add
curl(E)=-dB/dt to the mix. while you may be able to constrain the changes
in rho(t) to some short time or constant current and eliminate the dB/dt
part of the problem, that would only apply in specific conditions, not to
the general case.

I encourage you to review the Maxwell equations in a book on
electrodynamics. I personally like the book by Jackson, which is
oriented more towards physicists. In any case, the equation that I
wrote is one of the 4 Maxwell equations. It is valid for arbitrary
time-dependent electric fields. All it says is that the divergence of
the electric field at a point is proportional to the charge density at
that point:

div E(x,t) = 4\pi\rho(x,t) (Gaussian Units)

If you integrate this over a closed surface, and then use the
divergence theorem you get

\integral dA.E(x,t) = 4\pi \integral dV \rho(x,t)

The integral on the right-hand side is 4\pi times the total
(time-varying) charge enclosed by the surface. The other equations
are also valid, including the one you wrote.

Coincidently earlier this morning I was reviewing the derivation of
the energy loss of a heavy charged particle as it passes through
matter. The derivation made use of a very long cylinder with the
charged particle traveling along the axis of the cylinder. One point
in the calculation required the integral of the normal component
electric field (dA.E) produced by the charged particle over the
surface of the cylinder. That is, the left hand side of the above
equation. The answer is given by the right hand side of the above
equation. In this case, the charge density \rho(x,t) was created by
the moving charged particle.

--John

"John E. Davis" wrote in message
...
On Sat, 10 Mar 2007 13:08:39 GMT, Dave
wrote:
no, i'm afraid you can't just put a 't' on each side and have it make
sense
in the general case. time varying charge implies a current, a current
implies a magnetic field, then you have to include Ampere's law and add
curl(E)=-dB/dt to the mix. while you may be able to constrain the changes
in rho(t) to some short time or constant current and eliminate the dB/dt
part of the problem, that would only apply in specific conditions, not to
the general case.

I encourage you to review the Maxwell equations in a book on
electrodynamics. I personally like the book by Jackson, which is
oriented more towards physicists. In any case, the equation that I
wrote is one of the 4 Maxwell equations. It is valid for arbitrary
time-dependent electric fields. All it says is that the divergence of
the electric field at a point is proportional to the charge density at
that point:

div E(x,t) = 4\pi\rho(x,t) (Gaussian Units)

If you integrate this over a closed surface, and then use the
divergence theorem you get

\integral dA.E(x,t) = 4\pi \integral dV \rho(x,t)

The integral on the right-hand side is 4\pi times the total
(time-varying) charge enclosed by the surface. The other equations
are also valid, including the one you wrote.

Coincidently earlier this morning I was reviewing the derivation of
the energy loss of a heavy charged particle as it passes through
matter. The derivation made use of a very long cylinder with the
charged particle traveling along the axis of the cylinder. One point
in the calculation required the integral of the normal component
electric field (dA.E) produced by the charged particle over the
surface of the cylinder. That is, the left hand side of the above
equation. The answer is given by the right hand side of the above
equation. In this case, the charge density \rho(x,t) was created by
the moving charged particle.

--John

Gauss's law in Jackson's 'Classical Electrodynamics' 2nd edition, ppg
30-32,33 has NO 't'. nor does it in Ramo-Whinnery-VanDuzer 'Fields and
Waves in Communications Electronics' ppg 70-72(differential form),
75-76(integral form)

your final statement means that you are obviously outside the applicability
of Gauss's law since you have a moving charged particle, which can not be
described by a static field. i would guess that whatever derivation you are
looking at placed some other restrictions on the conditions such that you
could approximate the field by that type of equation. possibly a small
velocity or short distance or very short time period.

On Sat, 10 Mar 2007 18:38:08 GMT, Dave
wrote:
Gauss's law in Jackson's 'Classical Electrodynamics' 2nd edition, ppg
30-32,33 has NO 't'. nor does it in Ramo-Whinnery-VanDuzer 'Fields and
Waves in Communications Electronics' ppg 70-72(differential form),
75-76(integral form)

This is not surprising since that chapter in Jackson deals with
electrostatics. Look at section 1.5 on page 17. The section states:

The Maxwell equations are differential equations applying locally
at each point in space-time (x,t). By means of the divergence
theorem and Stoke's theorem they can be cast in integral form. [...
a few sentences later...] Then the divergence theorem applied to
the first and last [Maxwell] equations yields the integral
statements... The first is just Gauss's law...

--John

"John E. Davis" wrote in message
...
On Sat, 10 Mar 2007 18:38:08 GMT, Dave
wrote:
Gauss's law in Jackson's 'Classical Electrodynamics' 2nd edition, ppg
30-32,33 has NO 't'. nor does it in Ramo-Whinnery-VanDuzer 'Fields and
Waves in Communications Electronics' ppg 70-72(differential form),
75-76(integral form)

This is not surprising since that chapter in Jackson deals with
electrostatics. Look at section 1.5 on page 17. The section states:

The Maxwell equations are differential equations applying locally
at each point in space-time (x,t). By means of the divergence
theorem and Stoke's theorem they can be cast in integral form. [...
a few sentences later...] Then the divergence theorem applied to
the first and last [Maxwell] equations yields the integral
statements... The first is just Gauss's law...

--John

yes, referring to all 4 Maxwell equations you do have a 't' dependency.
however, even equations 1.13 and 1.14 referred to by your quote have NO time
dependency in them. the equations on the next page,1.15 and 1.16 have the
time dependency that the 't' in your quote refers to. remember, those
integrals are NOT integrals over time, they are over the surface or volume.

On 9 Mar, 22:13, (John E. Davis) wrote:
On Fri, 09 Mar 2007 16:45:31 GMT, Dave
wrote:

Gauss' Law is for static electric charges and fields.

It is usually used for problems in electrostatics, but it is not
confined to such problems. The differential form of it is just one of
the Maxwell equations:

div E(x,t) = 4\pi\rho(x,t)

Integrate it over a fixed surface and you get the integral form, which
is Gauss's law. It is valid with time-dependent charge densities and
time-dependent electric fields.

--John

John, you have hit it on the nose. It is the logic that is important
and that logic applies for a resonant array in situ
inside a closed border whether time is variant or otherwise.
The importantant point of the underlying logic that all inside the
arbitary border must be in equilibrium at the cessation of time
because the issue is not the static particles but of the flux. Period
Thus the very reason for a conservative field in that
it is able to project static particles in terms of time if time was
added. For static particles time is not involved therefore
ALL vectors are of ZERO length and direction is an asumption based on
the action if and when time is added.
John, you included time but did not mention time variant, was this for
a reason? I have specifically use time variance since that enclosed
within the border is an array in equilibrium
from which the conservative field is drawn from.
I am so pleased that some one came along that concentrated on the
logic and not the retoric and abuse.
Art

"art" wrote in message
oups.com...
On 9 Mar, 22:13, (John E. Davis) wrote:
On Fri, 09 Mar 2007 16:45:31 GMT, Dave
wrote:

Gauss' Law is for static electric charges and fields.

It is usually used for problems in electrostatics, but it is not
confined to such problems. The differential form of it is just one of
the Maxwell equations:

div E(x,t) = 4\pi\rho(x,t)

Integrate it over a fixed surface and you get the integral form, which
is Gauss's law. It is valid with time-dependent charge densities and
time-dependent electric fields.

--John

John, you have hit it on the nose. It is the logic that is important
and that logic applies for a resonant array in situ
inside a closed border whether time is variant or otherwise.
The importantant point of the underlying logic that all inside the
arbitary border must be in equilibrium at the cessation of time
because the issue is not the static particles but of the flux. Period
Thus the very reason for a conservative field in that
it is able to project static particles in terms of time if time was
added. For static particles time is not involved therefore
ALL vectors are of ZERO length and direction is an asumption based on
the action if and when time is added.
John, you included time but did not mention time variant, was this for
a reason? I have specifically use time variance since that enclosed
within the border is an array in equilibrium
from which the conservative field is drawn from.
I am so pleased that some one came along that concentrated on the
logic and not the retoric and abuse.
Art

he may have hit what you believe correctly.. but unfortunately it is not a
valid generalization. as i stated in my other message:

no, i'm afraid you can't just put a 't' on each side and have it make sense
in the general case. time varying charge implies a current, a current
implies a magnetic field, then you have to include Ampere's law and add
curl(E)=-dB/dt to the mix. while you may be able to constrain the changes
in rho(t) to some short time or constant current and eliminate the dB/dt
part of the problem, that would only apply in specific conditions, not to
the general case.

On 10 Mar, 06:41, "Dave" wrote:
"art" wrote in message

oups.com...



On 9 Mar, 22:13, (John E. Davis) wrote:
On Fri, 09 Mar 2007 16:45:31 GMT, Dave
wrote:

Gauss' Law is for static electric charges and fields.

It is usually used for problems in electrostatics, but it is not
confined to such problems. The differential form of it is just one of
the Maxwell equations:

div E(x,t) = 4\pi\rho(x,t)

Integrate it over a fixed surface and you get the integral form, which
is Gauss's law. It is valid with time-dependent charge densities and
time-dependent electric fields.

--John

John, you have hit it on the nose. It is the logic that is important
and that logic applies for a resonant array in situ
inside a closed border whether time is variant or otherwise.
The importantant point of the underlying logic that all inside the
arbitary border must be in equilibrium at the cessation of time
because the issue is not the static particles but of the flux. Period
Thus the very reason for a conservative field in that
it is able to project static particles in terms of time if time was
added. For static particles time is not involved therefore
ALL vectors are of ZERO length and direction is an asumption based on
the action if and when time is added.
John, you included time but did not mention time variant, was this for
a reason? I have specifically use time variance since that enclosed
within the border is an array in equilibrium
from which the conservative field is drawn from.
I am so pleased that some one came along that concentrated on the
logic and not the retoric and abuse.
Art

he may have hit what you believe correctly.. but unfortunately it is not a
valid generalization. as i stated in my other message:

no, i'm afraid you can't just put a 't' on each side and have it make sense
in the general case. time varying charge implies a current, a current
implies a magnetic field, then you have to include Ampere's law and add
curl(E)=-dB/dt to the mix. while you may be able to constrain the changes
in rho(t) to some short time or constant current and eliminate the dB/dt
part of the problem, that would only apply in specific conditions, not to
the general case.- Hide quoted text -

- Show quoted text -

Thats O.K. David,
The appeal made for this thread was for people outside of America
since eamericans were more interested in other things and I am
assuming the Gentleman is from outside America. This discussion in the
past has been bedeviled with arraogance and abuse to the neglect of
logic, this has been the mode of this group for a very long time. If
there was not such derision you could have looked up Gaussian law on
the web where you would have found the mathematics behind the logic.
If you had done this you would have found that curl is a part of the
mathematical underpinning that in the event of time that part of the
equation is zero. If time was part o0f the logic then you insert the
value of curl in the equation, look up curl for your self and place it
in the original equation which you are not changing i.e. concentrate
on the mathematics and the underlying logic and the result becomes
apparent.( and I have stated as such in past threads)
This has been there for more than a hundred years so don't be
disappointed that you and others did not realise the significance.
It was my mathematical interest in antennas and circumstances that led
me to this discovery but now the door is open we can all have the
enjoyment of the paths that it reveals.
John, what is your call and where are you from? You are to be
congratulated for delving into logic without being sidetracked by
others. I was just at the point of giving up and to wait for my patent
application to be printed some time.
Regards
Art XG