How do point charges in a conductor move and stop?

[sophiecentaur]

Only in a fluid.

 

[feynman1]

Only in a fluid.

can't get what you mean

 

[sophiecentaur]

can't get what you mean

In a solid, the ions are locked in place; in a fluid they can move.

 

[feynman1]

In a solid, the ions are locked in place; in a fluid they can move.

Very well! In a physics textbook with point charges (+ and -), should we always regard + to be ions and - to be electrons? Then if the context is a solid, + point charges can't move, but there's no such restriction on physics textbooks, why?

 

[sophiecentaur]

Very well! In a physics textbook with point charges (+ and -), should we always regard + to be ions and - to be electrons? Then if the context is a solid, + point charges can't move, but there's no such restriction on physics textbooks, why?

The Physics books that I have read all tell us that charge is carried in metals (and other solids) by negative charges (electrons). Can you find anywhere that the "restriction" is relaxed? By definition, if the positive ion cores in solids could move then why wouldn't the 'solid' flow and be a liquid? Or are you just trying to wind me up?

PS If you consider the +holes in a semiconductor to be charge carriers, they only exist because of the motion of electrons from atom and the + ions do not actually move; holes are just a way of thinking about it.

 

[feynman1]

The Physics books that I have read all tell us that charge is carried in metals (and other solids) by negative charges (electrons). Can you find anywhere that the "restriction" is relaxed? By definition, if the positive ion cores in solids could move then why wouldn't the 'solid' flow and be a liquid? Or are you just trying to wind me up?

A pair of + and + charges could be initially in the interior of a metal. Afterwards both charges will be repelled and move in the metal. If this appears in a textbook, that'll look quite normal and none doubts about whether + charges are supposed to move?

 

[sophiecentaur]

If this appears in a textbook,

I challenge you to find this idea in a textbook. Ions (+ and -) are held in place in a solid and that is what defines the solid phase. If they could move around then would the solid be solid? In a solution (e.g. water) the theory describes the simple situation of a Salt (NaCl) Solution as mobile Na⁺ and Cl^- having been separated from each other (in their solid state).

Taking this one stage further, it does happen that impurity ions can slowly make their way below the surface of a 'pure' solid material but, unless the substance is near its melting point, the time scale is many years. Alloys can form on the surface of metals when a melted solder (+ metal ions) can penetrate the faces of two copper wires and form a bond. But I would say that none of this is regarded as a flow of electric current.

 

[feynman1]

I challenge you to find this idea in a textbook.

Do you mean this pic in a textbook can only be correct if it implies that this happens in a fluid or free space?

 

[Lord Jestocost]

This illustration depicts the magnetic force when considering the "convential current" in a conductor.
http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magfor.html

 

[vanhees71]

I read the picture as describing the magnetic part of the Lorentz force on a positively charged point particle. That holds in free space as well as in the medium. In the latter case, of course, there are other forces by interaction with the medium, which can be described macroscopically by friction. The relevant transport coefficient is electric conductivity.

In a usual metallic conductor, what's moving are the conduction electrons which are quasifreely moving quasiparticles.

In semiconductors the charge carriers can be either negatively or positively charged quasiparticles, depending on the doping of the material. The positively charged quasiparticles are microscopically "holes", i.e., unoccupied electron states.

Which electric charge the relevant quasiparticles make up a current within a solid can be measured by making use of the Hall effect, which is based on the above pictured force of a charged particle in a magnetic field.

 

[sophiecentaur]

Learning by telling never works as well as learning by reading and listening.

 

[feynman1]

Does electrostatic equilibrium in a metal mean that electrons don't move at all or they do move but their electric effects like electric field remain constant in some sense?

 

[feynman1]

From non Newtonian mechanics, what will happen to electrons when they hit a conductor wall?

 

[Vanadium 50]

what will happen to electrons when they hit a conductor wall

You are (still) describing a classical path. Electrons behave quantum-mechanically, not classically.

 

[feynman1]

You are (still) describing a classical path. Electrons behave quantum-mechanically, not classically.

What's the correct way of describing this without using 'hit'?

 

[f95toli]

What's the correct way of describing this without using 'hit'?

Did you look at the link to the wiki about Friedel oscillations?
A defect and a surface is not exactly the same thing, but both will break the periodicity of the lattice. The Friedel oscillation model should give you some idea of how this works.

 

[feynman1]

Did you look at the link to the wiki about Friedel oscillations?
A defect and a surface is not exactly the same thing, but both will break the periodicity of the lattice. The Friedel oscillation model should give you some idea of how this works.

Thanks for the suggestion. I did, but don't get what it implies. Could you give any qualitative result?

 

[f95toli]

Thanks for the suggestion. I did, but don't get what it implies. Could you give any qualitative result?

I am not sure that would help since I would just be repeating what is on the wiki page. Do you understand the bit about describing the electrons using a plane wave-like wavefunction with a specific Fermi wave vector?

If not, you need to start by reading more about solid state physics. There is now way you can understand what happens at a surface unless you have some idea of what happens inside a solid.

 

[feynman1]

I am not sure that would help since I would just be repeating what is on the wiki page. Do you understand the bit about describing the electrons using a plane wave-like wavefunction with a specific Fermi wave vector?

If not, you need to start by reading more about solid state physics. There is now way you can understand what happens at a surface unless you have some idea of what happens inside a solid.

Thank you. Not knowing much about solid state, so looking for a layman's/Newtonian description.

 

[f95toli]

Thank you. Not knowing much about solid state, so looking for a layman's/Newtonian description.

Newtonian mechanics is not of much use in solid state systems.
Since the electrons in the case of Friedel oscillations (and in many other cases) are described as plane waves you will find that wave mechanics (interference/diffraction) is more relevant if you insist on using some parts of classical physics. However, that still won't help you e.g. explain scattering between different k-states.

 

[feynman1]

Newtonian mechanics is not of much use in solid state systems.
Since the electrons in the case of Friedel oscillations (and in many other cases) are described as plane waves you will find that wave mechanics (interference/diffraction) is more relevant if you insist on using some parts of classical physics. However, that still won't help you e.g. explain scattering between different k-states.

What happens to the wave probability function of an electron when getting close to the boundary?

 

[berkeman]

What happens to the wave probability function of an electron when getting close to the boundary?

https://en.wikipedia.org/wiki/Potential_well

 

[sophiecentaur]

What happens to the wave probability function of an electron when getting close to the boundary?

Is it likely or unlikely to appear outside the surface? There's a clue about the probability function at points near the 'boundary'. That's really a tautology because that is what defines a boundary.

 

[feynman1]

https://en.wikipedia.org/wiki/Potential_well

Take 1D. An electron is put in a 1D conductor with a potential V=0 -1<x<1 and very high elsewhere. Schrodinger's solution suggests the prob distribution on the well boundaries -1 and 1 is the least (and 0 for an infinite well). Why does this result contradict charges staying on the boundary of a conductor?

 

[sophiecentaur]

Why does this result contradict charges staying on the boundary of a conductor?

The probability distribution has to go to zero at some stage, past a notional boundary. Any model must include this, surely?

 

[feynman1]

The probability distribution has to go to zero at some stage, past a notional boundary. Any model must include this, surely?

If electrons must stay on the boundary under electrostatic equilibrium, shouldn't the prob function collapse to 1 on the boundary?

 

[sophiecentaur]

My point was that beyond what might be called the boundary, the probability has to approach zero. It can’t be less than zero.

 

[Lord Jestocost]

Thanks for the suggestion. I did, but don't get what it implies. Could you give any qualitative result?

Friedel oscillations

Have a look at Figure 2a in http://venables.asu.edu/qmms/PROJ/metal1a.html.
The figure depicts the electron density at a metal surface in the Jellium model.

 

[nasu]

Take 1D. An electron is put in a 1D conductor with a potential V=0 -1<x<1 and very high elsewhere. Schrodinger's solution suggests the prob distribution on the well boundaries -1 and 1 is the least (and 0 for an infinite well). Why does this result contradict charges staying on the boundary of a conductor?

A single electron does not model the situation in a metal which is not neutral. You need to take into account the interaction between electrons. This is what makes the extra charge to go on the surface. Maybe if you put two electrons in a potential well you get some of the features you are looking at.

 

[Mister T]

Let's speak in the classical context (non quantum). We assume that point charges move in a conductor following Newtonian mechanics. How do point charges move along the boundary of the conductor and how do they stop (equilibrium) in the end?

I think you will get the answer you're seeking if, instead of looking at single electrons, you look at collections of electrons. Imagine a differential element of charge ##dq##. It is a collection of electrons that is macroscopically small enough to be treated as a differential element, but it is microscopically large enough to contain a large number of electrons.

Loosely speaking, the differential elements ##dq## repel each other until they get as far apart from each other as they possibly can. Then the net force on each element is zero.

 

[feynman1]

I think you will get the answer you're seeking if, instead of looking at single electrons, you look at collections of electrons. Imagine a differential element of charge ##dq##. It is a collection of electrons that is macroscopically small enough to be treated as a differential element, but it is microscopically large enough to contain a large number of electrons.

Loosely speaking, the differential elements ##dq## repel each other until they get as far apart from each other as they possibly can. Then the net force on each element is zero.

Thanks but can the differential element treatment show if electrons will stay on or bounce off the boundary before equilibrium?

 

[feynman1]

A single electron does not model the situation in a metal which is not neutral. You need to take into account the interaction between electrons. This is what makes the extra charge to go on the surface. Maybe if you put two electrons in a potential well you get some of the features you are looking at.

Suppose there are infinitely many electrons in the 1D conductor so that the conductor is already equipotential V=0. Then put another electron in subject to a potential V=0 -1<=x<=1 and very high elsewhere. Would the result differ? The prob function on the boundary would still be small.

 

[nasu]

The potential in a metal is periodic, and is due to the interaction of electrons with the ion cores. The wave function of the electrons are combinations of Bloch functions. But these are obtained by using periodic boundary conditions. The surface effects are not teated in "simple" models that describe the bulk properties of the solid. I don't think you can get the macroscopic properties of conductors with the simple models that you propose. Maybe someone with experience in surface physics could help.

 

[Mister T]

Thanks but can the differential element treatment show if electrons will stay on or bounce off the boundary before equilibrium?

Yes.

 

[feynman1]

Yes.

how?