Some questions regarding electric properties of materials [closed]

Question

I was reading Chapter 29 on Halliday-Resnick-Krane regarding this but couldn't understand these things.

1. Suppose you have a conductor in an electric field. In normal conditions the field inside the conductor is zero, and charges deposit on the surface of the conductor. But then why does the electrons move in a wire (say in my house's electrical wiring) ? It's written "suppose there were a mechanism to remove electrons from the top of the slab, carry them around an external path, and re-inject them at bottom of the slab" - yes, it's clear if you do that there would be electron flow, but how does the mechanism to remove electrons and inject them back work ?

2. Why does electrical effects seems to occur immediately while the drift speed is very slow ? (There's the garden hose analogy, but I don't understand it clearly)

3. Although current flow is not dependent on the surface through which you're measuring it (i.e it's same irrespective of you take the surface to be slanted w.r.t to the direction the electrons are flowing or directly perpendicular to the direction the electrons are flowing), does't current density changes on which surface you're measuring it ? (i.e high when measured w.r.t a surface perpendicular to the flow of electrons but low w.r.t a surface slanted to the flow of electrons ?) Then how is the current density in a hollow sphere or conical frustum or objects like that defined ?

4. (Related with the above question) How do you define resistance for a object which is not like a rod (say antipodal points in a hollow sphere or two ends of a conical frustum) ? The formula $R = \frac{V}{I}$ (or $R = \frac{\rho L}{A}$) don't work for the things I mentioned, because although $V$ is constant, $I$ is not constant through various slices of the objects right ?

5. When electrons flow through a conductor (like an electric wire), what's the electric field inside the wire ?

Answer 1

Your questions are entirely in the classical domain, there can be no confusion about this.

1) This is essentially what a car battery does. In it a chemical potential separates charges. A chemical reaction occurs if the terminals are connected to to a resistor.

2) The speed is determined by the speed of electromagnetic excitations inside the material. In a metal the plasma oscillation transfers electromagnetic energy. In a dielectric optical phonons are involved.

3) Indeed the current density per surface unit depends on the orientation of the surface , in a trivial manner.

4) You can always define the resistance between two points contacting a conductor of any shape as R=V/I.

5) The electric field is $\vec E = \vec J / \sigma$ where $J$ is the current density and $\sigma$ is the material conductivity.

Answer 2

You are confusing two frameworks, the classical electromagnetic one, when talking of conductors and fields, and the quantum one when talking of electrons.

The classical electric field emerges from the quantum mechanical level. Going to the level of electrons and nuclei and lattices in conductors sees the details which have to build up to zero macroscopic electric field in the conductor, in macroscopic units, because the transition from classical to quantum mechanical is mathematically smooth. In a conductor you can add bodily electrons and subtract electrons from the surface only, that's all. The lattice inside remains tied up with the quantum mechanical forces keeping electrons around nuclei and atoms in their places.

For 1 and 2. At the quantum level electromagnetic forces move with the velocity of light, the atoms transfer the electrical impulse to each other , which goes with the velocity of light. The electrons participating in this impulse have to move step wise, electrons absorbed at the source of the potential difference will leave a positive hole which will attract an electron from the atom behind, and the transfer will take place with velocities according to the medium and the forces, much less than the velocity of light. They jump from atom to atom, and that gives the drift velocity. The impulse itself, because it goes with the velocity of light is practically instantaneous.(think of a stadium wave, the signal itself can travel much faster than the people who are waving their hands would be able to run)

I have answered already 6, it is zero, because atoms and molecules are neutral and stay neutral. (within an atom it is another story).

Maybe somebody else will answer 3 4 and 5.