Science and Technology news... :: View topic - Test charge in a change magnetic field...

delt0r · Guest

Here is my question. Perhaps followup on that page is a better idea.
But here is fine.

http://mathbin.net/2491

To sum up. I have a stationary test charge in a changing magnetic
field. What happen?

In my solution the answer is not unique even in the same coordinate
system. I suspect I need to use vector potential, but without forcing
some gauge on that I still have the same problem.

Perhaps you cannot consider a magnetic field independent from its
cause. But that causes other issues... ie a magnetic field has real
energy density.

I realize that these groups get a bit flooded with noise. But I assure
you this is not.

Thanks in advance.

delt0r....

ps crackpots don>t bother replying... please.... The current maxwell>s
equitations are solid.

Benj · Guest

On Nov 18, 5:21 pm, delt0r <greg.ew...@gmail.com> wrote:
[quote]Here is my question. Perhaps followup on that page is a better idea.
But here is fine.

http://mathbin.net/2491

To sum up. I have a stationary test charge in a changing magnetic
field. What happen?

In my solution the answer is not unique even in the same coordinate
system. I suspect I need to use vector potential, but without forcing
some gauge on that I still have the same problem.

Perhaps you cannot consider a magnetic field independent from its
cause. But that causes other issues... ie a magnetic field has real
energy density.

I realize that these groups get a bit flooded with noise. But I assure
you this is not.

Thanks in advance.

delt0r....

ps crackpots don>t bother replying... please.... The current maxwell>s
equitations are solid.
[/quote]
Oh shit! That excludes me, doesn>t it. Too bad, this is USENET free
speech and you can>t stop me from answering! Sorry bunky but
Maxwell>s equations are NOT "solid"! You>ve been taking too much from
your professors on "faith". And the faith-based physics I>m talking
about is the bogus "one E field" dogma. An electrostatic E field, a
qVxB E field and a induction E field all have quit different
properties! Hence they can>t be the "same".

So what happens if you have a solenoid and place a "free charge" in
the end and increase the current? We know that an electron with an
initial velocity will move in a circular orbit. (curl of E) But fact
is that an initial velocity is required! Unlike other E fields which
accelerate a charge in a certain direction, this one will do so in any
direction given by the initial velocity. In other words the E field
doesn>t have a defined direction at the charge! Hence there is no
unique solution to the motion.

I now turn you over to the educated crew who will explain where your
calculations are wrong and how you are stupid, while I go back to
mopping Burger King...

blackhead · Guest

On 18 Nov, 22:21, delt0r <greg.ew...@gmail.com> wrote:
[quote]Here is my question. Perhaps followup on that page is a better idea.
But here is fine.

http://mathbin.net/2491

To sum up. I have a stationary test charge in a changing magnetic
field. What happen?

In my solution the answer is not unique even in the same coordinate
system. I suspect I need to use vector potential, but without forcing
some gauge on that I still have the same problem.

Perhaps you cannot consider a magnetic field independent from its
cause. But that causes other issues... ie a magnetic field has real
energy density.

I realize that these groups get a bit flooded with noise. But I assure
you this is not.

Thanks in advance.

delt0r....

ps crackpots don>t bother replying... please.... The current maxwell>s
equitations are solid.
[/quote]
This point has been raised many times in this newsgroup. For a start,
the stationary charge won>t experience a force, whereas a moving
charge at the same point will; in such a direction as to oppose its
motion if the magnetic field is changing - Lenz>s Law.

Timo Nieminen · Guest

On Tue, 18 Nov 2008, delt0r wrote:

[quote]Here is my question. Perhaps followup on that page is a better idea.
But here is fine.

http://mathbin.net/2491

To sum up. I have a stationary test charge in a changing magnetic
field. What happen?

In my solution the answer is not unique even in the same coordinate
system. I suspect I need to use vector potential, but without forcing
some gauge on that I still have the same problem.

Perhaps you cannot consider a magnetic field independent from its
cause. But that causes other issues... ie a magnetic field has real
energy density.
[/quote]
Can you have a changing magnetic field Bz = at everywhere? No. Can we have
it over a finite volume? First, just consider a single point.

So, curl(E) = -dB/dt, so dEx/dy - dEy/dx = -a.

So, you have a solution Ex = by, Ey = cx, b - c = -a. As you note, there
appears to be no mistake. You can also add an arbitrary electrostatic
field (i.e., constant wrt time E, produced by a stationary charge
distribution), which would have curl = 0.

OK, note that the magnetic field energy is changing at the point. The
magnetic field energy will be u = mu0 B^2/2, so, ignoring the electric
field energy we can write

du/dt = mu0 a^2 t = - div(S) = -div(ExH) = -div(mu0 ExB)
= mu0 a(c-b)t^2 = mu0 a^2 t as required.

So, we see that your solution gives the required energy flow to account
for the change in magnetic energy. This will be the case even if E at the
point in question is zero.

However, note that S = mu0 at ( cx i - by j ); i,j are unit vectors. This
is in the xy plane, but in a direction which depends on the choice of c
and b.

What might this mean physically?

How do we move electromagnetic energy around? With electromagnetic waves.
What kind of electromagnetic wave will give us a Poynting vector in the xy
plane and a changing magnetic field in the z direction? Answer: a plane
wave with plane of polarisation (i.e., its E field) and direction of
propagation both in the xy plane. Your solution describes an arbitrary sum
of such waves. (Note that the linear time dependence means that they>re
not time-harmonic, i.e., sinusoidal, waves.

Which direction the wave(s) will come from in a particular case will
depend on the source - in this sense, you can>t consider the field
independently from the source of the field.

Or, as a mathematician might say, it isn>t enough to have a solution to
your differential equation - your solution must also satisfy the boundary
conditions.

--
Timo Nieminen - Home page: http://www.physics.uq.edu.au/people/nieminen/
E-prints: http://espace.uq.edu.au/list/author_id/1189/
Shrine to Spirits: http://www.users.bigpond.com/timo_nieminen/spirits.html

delt0r · Guest

On Nov 21, 6:23 am, Timo Nieminen <t...@physics.uq.edu.au> wrote:
[quote]
Can you have a changing magnetic field Bz = at everywhere? No.
[/quote]
Yes, I was thinking that this will end up being relevant...

[snip]
[quote]Which direction the wave(s) will come from in a particular case will
depend on the source - in this sense, you can>t consider the field
independently from the source of the field.

Or, as a mathematician might say, it isn>t enough to have a solution to
your differential equation - your solution must also satisfy the boundary
conditions.
[/quote]
I was thinking that this was the problem. But I don>t get to discuss
this
much anymore now i work in biology.

So the way I see it I should use the vector potental as defined from
current
density and go from there.

Thank you so much for putting in the time...

Greg.

Benj · Guest

On Nov 21, 8:44 pm, Salmon Egg <Salmon...@sbcglobal.net> wrote:

[quote]If I have my signs correct this means that power is being sent into the
core from the winding as it gets energized. Remember the Poynting>s
theorem requires integration over a closed surface. How the energy goes
to the gap or around the core still eludes me.
[/quote]
Use of a core is misleading since cores don>t actually work the way
most people "intuitively" think. They do not "concentrate" a field
within them. They actually generate a secondary field which is in such
a form as to cancel the original field from the driving coil outside
the core and increase the field inside the core (and gap). A better
idea would be a toroid with a small gap. But even then there is the
problem that various parts of the toroid are differing distances from
the gap. This means that the "retarded" B field will usually need be
taken into account to deal with what is happening. Nobody ever wants
to do this because it>s too much like work. That usually leads to
erroneous conclusions such as the field always being zero outside a
long solenoid or toroid etc. Just saying...

Salmon Egg · Guest

In article <Pine.LNX.4.50.0811201640160.24407-100000@localhost>,
Timo Nieminen <timo@physics.uq.edu.au> wrote [in part]:

[quote]
So, we see that your solution gives the required energy flow to account
for the change in magnetic energy. This will be the case even if E at the
point in question is zero.

However, note that S = mu0 at ( cx i - by j ); i,j are unit vectors. This
is in the xy plane, but in a direction which depends on the choice of c
and b.

What might this mean physically?

How do we move electromagnetic energy around? With electromagnetic waves.
What kind of electromagnetic wave will give us a Poynting vector in the xy
plane and a changing magnetic field in the z direction? Answer: a plane
wave with plane of polarisation (i.e., its E field) and direction of
propagation both in the xy plane. Your solution describes an arbitrary sum
of such waves. (Note that the linear time dependence means that they>re
not time-harmonic, i.e., sinusoidal, waves.

Which direction the wave(s) will come from in a particular case will
depend on the source - in this sense, you can>t consider the field
independently from the source of the field.

Or, as a mathematician might say, it isn>t enough to have a solution to
your differential equation - your solution must also satisfy the boundary
conditions.
[/quote]
The more I look at this post, the more interesting it gets.
Unfortunately, I do not have the time to invest in getting to the
bottom. Maybe I will be able to do so later.

Assume that you have a magnetic field produced between two pole pieces
attached to the open end of a C-core. A zero resistance winding is
placed on the core. A potential difference is applied to the coil for a
finite time and than brought to zero. From the electrical source, the
winding is an inductor that stores energy. This is the same energy as
stored in the gap between the pole pieces. Assume that the core itself
has no magnetic reluctance. How does energy get transfered from the
electrical source to the magnetic field? I will give a partial answer
because I do not understand the details.

During the applied pulse, current builds up linearly. When the pulse is
over, current continues to circulate in the winding. During the buildup,
there is an inductive emf induced in the wire. This produces the E
vector for the Poynting vector. The H vector for the Poynting vector
comes from the current in the winding. This, as we have seen, builds up
linearly with time. H is along the length of the core. Thus, the
magnitude of the Ponting vector increases linearly with time. After the
pulse is over, there is no E field so that there is no Poynting vector.
The H field is entirely along the length of the core so that there never
is a Poynting vector component pointing along the core length.

If I have my signs correct this means that power is being sent into the
core from the winding as it gets energized. Remember the Poynting>s
theorem requires integration over a closed surface. How the energy goes
to the gap or around the core still eludes me.

Bill

--
Private Profit; Public Poop! Avoid collateral windfall!


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