Conductor current in a wire

Some people must resort to relativity to explain conductor current. Not so. It is simple!
By utilizing a token Drift Current, current in a medium is explained. Defeatists argue that true drift current is subject to Skin Effect, Temperature, latice structure, manufacturing techniques, and such. Mere technicalities do not matter: the CONCEPT survives as a most wonderful tool.

Depiction of moving charge in a long wire:
Depicted in the center of the wire are current carriers with a certain drift velocity.
Depicted, for the wire as a whole, are equal numbers of carriers, producing a net zero electrostatic charge.
For every moving charge there exists a co-charge of opposite polarity. Neutral atoms are in brown.
In an actual wire (for DC current) the electrons, holes, and neutral atoms are all randomized with equal distribution. There are lasting effects of watching too many cartoons as a kid. In my case, the residual effects seem to be permanent.

Current in a stationary copper wire (negative carriers).
To demonstrate one aspect of the produced magnetic field, I place a moving electron outside the wire. A free electron travels alongside the copper wire at a speed that is the same as the "drift-velocity" of the inside drift electrons. This speed is incredibly slow - much less than any relativistic speeds! Without getting overly dramatic, I would like to emphasize:
" MUCH LESS than any relativistic speeds!

The free electron, traveling parallel to the wire, experiences a vector force directly toward the wire, simply from the magnetic field of the wire.

 Magnetic field B near long wire.
The magnetic field:
For example;
If one amp is flowing in the wire, the magnetic field one meter away is:
2E-7 Tesla.

Lorentz force

The force on the electron:
First we must calculate the drift velocity...
v = free electron velocity; arbitrarily chosen as the drift-velocity.

Let A be the cross-section area of the wire:
A = PI r^2.
v*t is the horizontal length traveled by q in one second.
Volume of wire is A*vt

Density of Cu:
Atomic mass of Cu is 64; 64gm/6.0E23 atoms.
Density of Cu is 9gm/cm3, 9000gm/m3
Number of atoms (carriers/atom=1) per meter3 = 6.0E23 atoms/64g * 9E3g
De: Carrier density = 8.4E25 free-valence electrons/m3

I is one amp:
Ie: electron current = q/t = q/1.6E-19 electrons /t

I arbitrarily choose a wire radius of .01m
Wire radius= .01m, A=pi r^2 = A = 7.85E-5 m2
v = (Ie current)/(De density) /(A cross-section)
v = (1/1.6E-19)/(8.4E25)/(7.85E-5)
v = 9.5E-4 m/s
v is a non-relativistic speed.

The force on the free electron is:
3E-29 Newton.

An observer travels alongside the wire in the direction of the electrons. The drift-electrons appear to not be moving, and the free electron appears not to be moving. The wire itself appears to be moving to the left.

Clearly, there is no difference in the magnetic field from the first example. The magnetic field is moving relative to the ("static") free electron; Same result!
And rightly so; According to maxwell, it does not matter which is moving.
Collectively - because of the (long) wire - a magnetic field is produced from the wire, and is "locked" to it in vector space. The force on the free electron is 3E-29 Newton, the same as before.
Macroscopically; it works.

However, the fine details inside the wire are not working. Drift electrons, and free electrons, traveling parallel to each other produce No magnetic field - that is anchored or referenced to a system other than the moving electrons themselves. Neither electron moves relative to the others field.
Macroscopically, my wire model works, but Microscopically it fails. Totally fails! I think I will go out and weed the roses.

By taking a compromise of the two perspectives, a totally new perspective arrives.
It was out by the roses...
Have equal charges produced; no mater the perspective.
Like this...

Two types of intrinsic carriers: electrons and holes. In the case of metal, the holes will be the absence of conduction electrons of an atom.

 electrostatic requirement
The charge distribution must be zero.
(To keep little pieces of paper from sticking to the wire...)

 magnetic requirement
To keep the magnetic force correct...
Current carrying wire in a magnetic field.
I could be wrong, but I think holes would be always associated with an atom which is at "rest": or always intimately associated with the "wire". Holes have a physical position the same as the wire, and are part of the wire, and travel with it. This notion would explain how a wire produces a magnetic field regardless of its reference plane.

Perhaps the concept is easier to visualize if the observer speed is half the drift speed to the right. Now the negative charge carriers are moving with half the drift speed to the right;
And the holes are moving at half drift speed to the left.

Unlike free charges of a beam, wire-current is produced from electron and hole pairs. Unlike a beam, a wire has a magnetic field that is "stationary".

The two q are equal: holes = electrons
The velocities must be unequal, and the speeds may be unequal.
Including the condition that either speed may be zero.

 speed of transmission
This model dramatizes the transference of the electrical signal at near the speed of light down the wire. Only "dramatizes"; Drift speed is not the same.

Hall effect:
This really brings home the point!

A magnetic field is shown going UP.
 Hall effect
Positive carriers approach the magnetic field. The charged carriers have a magnetic field of their own as indicated. You can see if you place a magnet vector (pointing up) along side a carrier magnetic vector (pointing down), The field lines attract, and the charge will move to its right. The field lines repel on the charges other side. You will find working with field lines is much safer and easier than working palms and fingers.

The positive charges are pulled orthogonally to their direction of motion, to their right, with a force qvB. (I have ignored diagraming the force.) However, I have diagramed the current in a flat hole-based bar which experiences the same forces. The positive carriers favor their right side (your left, marked with a + sign). For this force to remain true, the bar must exhibit positive carriers.

If, on the other hand, the current remains in the same conventional direction but composed of electrons aproaching from the opposite direction, then the voltage will be reversed. The terminal closest to the observer will be negative in this case. If the carriers are holes approaching from the indicated direction, they will favor the same terminal as negative carriers approaching from the opposite direction, and thus reverse the sign.

But how did the opposite sign get there? My point is that a conductor has both holes and free electrons too, and if one side is positive then the other side must be negative. Simiconductors will restrict holes or electrons preferentially. But the quantity of holes and electrons used in actual current must be equal. The difference in these two charge velocities must be equal to the Drift Velocity.
Hall effect:

My model predicts equal numbers of charge carriers, not only from the above discussion of current in a wire, but also from the basic concept of obtaining a voltage measurement: it takes two points to measure a voltage, or a voltage difference.

What I have shown is that the drift velocities DO predict current and the a magnetic field IF you include BOTH the carriers. A subject that all physics books so subtilely avoid turns out to produce no paradoxes at all.

Here is the best example of all!
Shown is a section of a blood vessel or artery.
Here is a blood flow monitor. A doctor uses this to measure the speed of flow of blood. The blood has no net charge: It has electrolytes of equal number. There are two metal contacts placed against the blood vessel. Blood is a good conductor and the walls are also a fairly good conductor. A positive voltage is measured on the closest - near side - electrode, depicted in green. The unavoidable supposition is that the flow of blood is not a current of just solely positive current or of solely negative current. The undebatable feature is that there is a drift velocity. With this instrument - it does not matter - if the ions are predominantly positive, they go to the left in the magnetic field, producing a voltage positive on the left - or, if the ions are predominantly negative, they go the right, resulting in a negative voltage on the right. Ether case, same result.

Here it is from yet a different angle...
If the blood vessel were a copper wire and there was current as depicted, the wire would move to your left and toward the observer. If the current were electrons, but flowing from the opposite direction, the wire would still move to the left. If the current were electrons moving in the depicted direction, the wire would move to the right. In all cases the wire would move. In this case of drift velocity, the wire does not move. This is because drift velocity of negative and positive is not only the same, but also the quantity of positive and negative is equal.

Drift velocity, in a copper wire, can not exist out of context of equal charge carriers. Equal charge carriers constitute a medium.

Stay away from those that taut relativity, and isolate reference frames from mediums. Those same people think that fish exist out of water. Our "material things" come from this medium of "empty" space. The Either, a concept of hundreds of years ago, really does exist. But it is not an antagonistic either, and not one of "seperate". The Either (empty space) is a calm and quite sea of electrical waves. And we are composed of those same waves. We are just bigger, and in contrast, are a collection of standing waves that have identities. But that is a whole nuther story. The point of this page: the copper wire is a "medium" for current.