1. Unit 3, Day 4: Microscopic View of Electric Current Current Density Drift Velocity Speed of an Electron in as Wire Electric Field inside a Current Carrying Conductor

2. Current Density When a potential difference is applied across a conducting wire, an electric field is generated parallel to the walls of the wire Inside the conductor, the E-field is no longer zero, because charges are free to move within the conductor Current Density is defined as the current through the wire per unit of Cross-Sectional Area If the current density is not uniform: The direction of j is usually in the direction of the E-Field

3. Drift Velocity When the E-Field is first applied, the electrons initially accelerate but soon reach a more or less steady state average velocity. This average velocity is in the direction opposite of the E-Field and is known drift velocity Drift velocity is due to electrons colliding with metal atoms in the conductor

4. Drift Velocity Calculation n - Free electrons (of charge e) travel a displacement l, in a time Δt, through a cross-sectional area A, at a current density j, The drift velocity is: Note: the (-) sign indicates the direction of (positive - conventional) current, which is opposite to the direction of the velocity of the electrons

5. Speed of an Electron in a Wire Given: Cu wire, Φ=3.2 mm (r = 1.6 x 10 -3 m) I=5.0A, T = 20°C (293 K), assuming 1 free electron per atom: Note: the rms velocity of thermal electrons in an ideal gas is a factor of 10 9 faster!

6. Electric Field inside a Current Carrying Conductor Current carrying conductor of length l and cross- sectional area A, having resistance R, with a potential difference across it of ΔV