Randy Poe wrote:

Timothy Golden BandTechnology.com wrote:

Randy Poe wrote:

Timothy Golden BandTechnology.com wrote:

Randy Poe wrote:

I really don't get why you object to this idea of describing
the same experiment from two different viewpoints, or think
that somehow there is a "physical level" which combines
elements of the physics as described in either point of
view.

This is no different from describing a collision of two
cars, from the point of view of either one.

Right, and this is an experiment that can factualy be carried out.

So your view is that an experiment involving a test charge and
a wire can't be carried out?

The
facts of the car collision are what we care about. Likewise in this
magnetism problem we can factually do it. We may not have a true test
charge but we can use a voltmeter.

We can have a charged object. People have been charging
objects for centuries.

A voltmeter is a different experiment. A voltmeter won't
look like a current to a moving observer, and it won't
therefore be described as experiencing a magnetic
force.

So we take a 6 volt battery and hook it up to a loop of wire.

This is to create a current in the wire?

Now we
take the voltmeter and look for voltage about the wire with the ground
end of the voltmeter tied anywhere in the system. No voltage will be
found.

Are you sure? Have you ever heard of "corona discharge"?
High-voltage wires spontaneously discharge particles into
the surrounding air. Why do you think that happens?

Well the voltage around this loop is going to be zero.

Two problems with this:

1. This is an idealization which is not true in any actual
experiment. There is a voltage drop across wires. It
would be dangerous to grab a high-voltage wire with
two hands, even if you weren't standing on the ground.

2. It is not voltage drop across the wire which creates
an E-field that affects the test charge. The question you
should be pondering is whether there is a voltage
gradient and E-field PERPENDICULAR to the wire. That
is the one that moves the test charge.

Think about a pair of charged capacitor plates. The
voltage between any two points on those plates is zero.
Does that lead you to conclude there is no E-field
between the plates?

Batteries have
something called internal resistance and so long as the wire is thick
and relatively short the voltage drop over it will be negligible. From
the voltmeter's perspective any point from either terminal of the
battery would suffice as a reference ground.

If you want to know the voltage difference between a point
on the wire and the ground, you don't connect your
voltmeter between the wire and the wire. It is not true
that "any point on the loop would serve as a ground"
in answering the question as to whether there is an
E-field here.

So I guess you really are claiming that there is no
electric field resulting from current flowing through a
neutral wire. Again, I'll ask you where you think
corona discharge comes from, and why it's dangerous
to touch high-voltage wires. Your claim is that every place
on a high-voltage wire is at the same voltage as ground,
right?

If you touch a high-voltage wire, do you think that is a
safe thing to do? If there were no voltage difference between

The worst thing that could happen is that the battery explodes due to
internal heating and off-gasing of hydrogen.

Is it safe to touch a high-voltage wire?

To really do this
experiment you'd probably want to only run the battery for short
intervals. This would also preserve the battery life. So say you could
turn the battery on for a tenth of a second and then turn it off for
ten seconds, taking a voltage measurement toward the end of the tenth
of a second so that the system settles.

A voltage measurement between points on the loop tells
you nothing about the E-field described here. That test
charge is not in the wire. It is not moving along the wire.

This would effectively be
1/100th duty cycle which I would think should be safe. You'd want to
verify that things did indeed settle out. A short enough duration pulse
will eventually break this system turning the problem into a transient
analysis rather than a DC analysis.

the wire and ground, it would be.

- Randy

I have been corresponding with the author of the page and in doing so I
have found an error in my understanding. The test charge is explicitly
stated in the diagram as travelling at v, the same velocity as the
charges in the wire. Why these velocities are equal and what happens
when the test charge velocity is zero may still be open questions but
my assumption that the test charge is at zero velocity (lab frame) in
the setup is not valid.

Don't you think there should be a v1 and a v2 here? Certainly whatever
solution is arrived at won't be general with the two locked together.

That's right, it's not a general experiment. It's a special case,
designed so that there is a static E-field from one point of
view and a static B-field from another.

In the general case, both fields will always be present.

I'm of the understanding that this method is going to replace classical
magnetism with an electrostatic force.

Schroeder really dismisses the stationary case right up front:

"The wire has to be electrically neutral in the lab frame, so there
must be a bunch of negative charges, at rest, separated by the same
average distance. Therefore there's no electrostatic force on a test
charge Q outside the wire."

I'm just not comfortable with this problem so I think I'll resign from
it.