The electromagnetic signal moves at the speed of light, but the electrons move much more slowly.
We define the drift speed as the speed that the electrons move through the wire.
This diagram depicts electrons moving through a wire of cross-section A, from a time span from t to t + Δt.
The electrons undergo collisions and have some random motion, but move as a group at drift speed vd.
We define the electron current as the number of electrons per time passing a cross-section.
We can also write the electron current in terms of the number density (electrons per volume) and the drift speed.
Recall our model of a conductor as a lattice of atoms, nuclei with electron shells.
These atoms are ions, since the valence electrons are free to move within the lattice.
The potential difference from a battery or charged capacitor sets up a nonuniform charge distribution.
When the circuit is completed, the electrons have a pathway to flow, and move through the lattice.
While moving through the lattice, electrons undergo collisions with the ions in the metal.
Valence electrons are free to move within the lattice.
We can model a collision using this PHeT simulation.
The electric field provides the force on the electrons to speed them up between collisions.
Recall that the electric force can be defined as F = qE. Here we define the charge of an electron as e, to write F = eE.
We can use kinematics to write the equation of motion for electrons under the acceleration provided by the electric field.
The average velocity is equal to the drift speed. The time between collisions is defined as τ.
We can use substitution to write the electron current in terms of the drift speed and τ.
We can relate our electron current to the current I. The total charge of Ne electrons is just the charge
of an electron times the number of electrons.
The electron current ie is the rate of electrons flowing through the wire.
The current I is the rate of charge flowing through the wire.
The direction of the current is (incorrectly) defined to be the direction of flow of positive charges.
The direction was defined by Benjamin Franklin,
who assumed that the flow was caused by an excess (+) of one kind of charge toward a deficit (-) of charge.
This idea was basically correct, but when electrons were later discovered and assigned to have negative charge,
the sign convention was determined to be wrong, but kept for historical reasons.
Consider this simple circuit, with a charged capacitor and two light bulbs.
When the switch is closed, electrons will flow through the wire.
Which light bulb is brighter?
A. bulb A
B. bulb B
C. they will be equally bright
Conservation in electric current
Electrons flowing through a wire obey conservation laws. Electrons cannot be created or destroyed as they flow through a wire
or a component of an electrical circuit like a light bulb or resistor.
Each electron carries its fundamental charge, so the amount of charge flowing is also conserved.
Energy carried by the electrons is used up as they pass through the filament of a light bulb.
Some of the energy given to the electrons by the battery or other power source is converted to thermal energy.
The current is not used up. The rate of flow of electrons into the filament of a light bulb is the same as the rate of flow
of electrons out of the bulb. Current is constant everywhere in a circuit, as long as there are no junctions involved.