Level 1: Twice as Thick, Same Current: How Fast Do Electrons Drift?
Which wire has the stronger field inside?
Two copper wires of the same length, with diameters d and 2d, are joined in series and carry a steady current. The ratio of the electric field inside the thin wire to that inside the thick wire is:
In series the current I is the same in both wires, but the current density J = I/A is not. The field that drives the electrons is E = ρJ, with the same resistivity ρ in both wires.
So the field in the thin wire is four times stronger, and most of the voltage drops across the thin wire. The same current does not mean the same field; the field follows the current density.
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