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Unformatted text preview: The Drude Model eEt Average `drift' speed: v = me
For constant temperature v ~ E t - average time between collisions v = uE , u= e t me u mobility of an electron Electron current: i = nAv i = nAuE E and Drift Speed In steady state current is the same everywhere in a series circuit. Ethin Ethick i i What is the drift speed? i = nAv nAthin vthin = nAthick vthick vthin Athick = vthick Athin Note: density of electrons n cannot change What is E?
v = uE uEthin Athick = uEthick Athin Ethin Athick = Ethick Athin Question 1.5.n1 = n2 2.u1 = u2 1018 1 mm 2 mm Every second 1018 electrons enter the thick wire. How many electrons exit from the thin wire every second? A) 1018 B) 1.5 x 1018 C) 2 x 1018 D) 4 x 1018 E) 12 x 1018 Direction of Electric Field in a Wire E must be parallel to the wire E is the same along the wire Does current fill the wire? Is E uniform across the wire? VABCDA C D A = - E1 dl - E3 dl - E2 dl - E3 dl = 0 A B D C VAB 0 VCD 0 E1 = E2
B Electric Field in a Wire E What charges make the electric field in the wires? Bulb filament and wires are metals there cannot be excess charges Are excess charges on the battery? E E i = nAuE A Mechanical Battery Van de Graaff generator Electron Current Field due to the Battery E Ebends In the steady state there must be some other charges somewhere that contribute to the net electric field in such a way that the electric field points upstream everywhere. Field due to the Battery i = nAuE Surface charge arranges itself in such a way as to produce a pattern of electric field that follows the direction of the wire and has such a magnitude that current is the same along the wire. Field due to Battery E Smooth transition from + surface charge to to provide constant E. The amount of surface charge is proportional to the voltage. Amount of Surface Charge
The average magnitude of E in a closed circuit can vary from ~.01 V/m in copper wire to more than 100 V/m in Nichrome wire - due to a much different electron mobility. Surface charge at the end of a battery is ~106 electrons. See 18.X.11,12. Compare to tape: ~1010 electrons What is easy: to draw E and i What is complex: to draw surface charge distribution Connecting a Circuit When making the final connection in a circuit, feedback forces a rapid rearrangement of the surface charges leading to the steady state. This period of adjustment before establishing the steady state is called the initial transient. The initial transient Connecting a Circuit The initial transient Enet The net field in the wire must be zero, because the system is in static equilibrium Connecting a Circuit The initial transient Speed of light: 30 cm/ns In just a few nanoseconds the rearrangement of the surface charges will extend all the way around the circuit. Connecting a Circuit
1. Static equilibrium: nothing moving (no current) 2. Initial transient: short-time process leading to the steady state 3. Steady state: constant current (nonzero) Why Light Comes on Right Away? How fast electrons move? v ~ 50 micron/s It may take hours before electrons from the battery reach light bulb! AC current: E changes direction back and forth `shaking' electrons Surface Charge and Resistors E ithick Just after connection: E may be the same everywhere ithin i = nAv = nAuE ithin = nAthinuE ithick = nAthick uE
After steady state is reached: ithin ithin = ithick ithin = nAthin
uEthin Ethin Athick = Ethick Athin Athin = ithick Athick ithick = nAthick uEthick Surface Charge Distribution in a Circuit 1. Current must be constant: based on i = nAv = nAuE draw distribution of E 2. Based on E draw approximate distribution of surface charges ...
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This note was uploaded on 04/02/2008 for the course PHYS 272 taught by Professor K during the Winter '07 term at Purdue.
- Winter '07