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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 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 I j or I j A A • If the current density is not uniform: I jdA • The direction of j is usually in the direction of the E-Field 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 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: j I vD or ne neA • Note: the (-) sign indicates the direction of (positive conventional) current, which is opposite to the direction of the velocity of the electrons Speed of an Electron in a Wire • Given: Cu wire, Φ=3.2 mm (r = 1.6 x 10-3m) I=5.0A, T = 20°C (293 K), assuming 1 free electron per atom: N # e ( in 1 mole) 28 e n 8.4 10 m 3 m (1 mole) V e I I 5 m vD 4 . 6 10 s 2 neA ne r • Note: the rms velocity of thermal electrons in an ideal gas is a factor of 109 faster! 1.2 105 ms Electric Field inside a Current Carrying Conductor • Current carrying conductor of length l and crosssectional area A, having resistance R, with a potential difference across it of ΔV l Re member R , I j A, & V E l A If V I R l Then E l j A jl A or E j Writing it another way j E E