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Notes Thursday 4/30/15
Current
Connect a wire between two plates with opposite charges. Charges flow through the wire until the two
plates are uncharged. By convention, the current is taken in the direction of the flow of the positive
charges (= opposite direction of the flow of the negative charges as is often the case when only
electrons are moving).
To get a steady flow of charges, connect a battery instead to two charged plates.
In the wire, electrons are flowing with a "constant"velocity called the drift velocity = vd. The drift
velocity is fairly small. It is of the order of 0.1 mm/s. It depends on the material of the wire and the
intensity of the current in the wire. Electrons are subjected to the electric force due to the electric field
established by the battery and the resistive force due to the collisions with the atoms of the wire. On
average the net force on the electron is zero and the electron moves with a constant velocity.
If the wire has cross section A and there are n conduction electrons per unit volume in the wire, the
number of electrons going through the cross section A per unit time is the electron current i.
The current I is the amount of charge going through the cross section per unit time: I = i e
Again by convention the direction of the current is the opposite of the direction of motion of the
electrons.
The current density is defined as J = I/A. It is related to the electric field by the conductivity σ.
J=σE
The reciprocal of σ is the resistivity ρ = 1/ σ
The units of ρ are Ω.m. The range of ρ is enormous. Values typically vary between 10-8 and 1024 Ω.m.