Charge Motion in Metals

Written by William Rountree

Mobile Electron Sea

Metals, like all matter, are made of atoms. These atoms consist of a nucleus surrounded by electrons. The majority of metals have few electrons in the outer orbitals, and these valence electrons aren't tightly bound to the nucleus. As a result they are "free" and able to move through the material. The electrons aren't shared or transferred between atoms; they are available to all nuclei in the metal. Often there is only one free electron per atom, but that is all it takes to create a "sea" of electrons surrounding the atoms. Due to every atom lacking a negatively charged electron, the atoms are positively charged and remain bound together by the "sea." There is an even distribution of positive and negative charges, so the net electric field inside of metal is zero.

Charge Motion

Electrons naturally repel each other. When an electric field is applied to a metal, the mobile electrons begin to experience a force and accelerate. The electrons continue to accelerate until they collide with other objects in the mobile electron sea. This process continues to propagate throughout the metal for as long as an external field is applied to the metal.

An electron's average speed as it moves through the metal, v, is described as it's drift speed. This speed can be found by dividing the momentum of the electron, p, by its mass, m:

    v = p/m

Assuming that the momentum is zero when the electrons collide, the momentum of the electron is equivalent to the force on the electron multiplied by the time between collisions, Δt . Remember, the force on a point charge is qE, where q is the charge of the particle (e for an electron) and E is the net electric field. Therefore, the drift speed can rewritten as:

    v = (eEΔt)/m

The drift speed is proportional to the electric field, so to simplify the relationship a new term is introduced. The electron mobility, μ, describes how easily an electron can move through a material, and varies with temperature and material.

    μ = (eΔt)/m

Substituting this term back in to the equation for drift speed clarifies the relationship between the speed of a mobile charge, the electric field, and the material's electrical properties.

    v = μE

History

This model for the motion of electrons in metal is credited to physicist Paul Drude, who first proposed the model in 1900 three years after J.J. Thompson discovered the electron. Dubbed the Drude Model, this theory was expanded by Hendrik Lorentz five years after it was introduced. After the development of quantum theory the model was updated from the previous classical version.

References

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/conins.html#c1 http://physics.bu.edu/~okctsui/PY543/1_notes_Drude_2013.pdf