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

• If the current density is not uniform:

• The direction of j is usually in the direction of the E-Field

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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:

• Note: the (-) sign indicates the direction of (positive - conventional) current, which is opposite to the direction of the velocity of the electrons

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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:

• Note: the rms velocity of thermal electrons in an ideal gas is a factor of 109 faster!

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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

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