The Electrical Properties of Solids — Question 3

Question 3

Electron drift is opposite to conventional current density

A solid contains mobile electrons at $n=5.00\times10^{28}\,\mathrm{m^{-3}}$. A current $I=2.00\,\mathrm A$ flows in positive x through $A=1.00\,\mathrm{mm^2}$. Use $e=1.602\times10^{-19}\,\mathrm C$.

1. Find the current density and electron drift velocity.

2. Estimate the drift time over 1.00 cm and distinguish it from signal propagation time.

Question 3 - Solution

Electron drift is opposite to conventional current density

(a) Method and calculation

$$\boxed{J_x=I/A=2.00\times10^6\,\mathrm{A/m^2}}.$$$$J_x=-nev_{d,x}\Rightarrow\boxed{v_{d,x}=-2.497\times10^{-4}\,\mathrm{m/s}}.$$

(b) Interpretation and further calculation

$$t_d=L/|v_d|=.0100/(2.497\times10^{-4}).$$$$\boxed{t_d=40.05\,\mathrm s};\quad t_d\ne\text{electromagnetic signal transit time}.$$

Physical check

Drift is the small average motion superposed on microscopic electron velocities. Establishing a circuit field does not require one electron to traverse the entire wire.