Lecture 8: June 8 th 2009

1. Lecture 8: June 8th 2009 Physics for Scientists and Engineers II Physics for Scientists and Engineers II , Summer Semester 2009

2. Electric Current Electric current: A net flow of charges. + + + + + + Surface of area A, perpendicular to flow of charges Average current through A: SI units of current: Instantaneous current through A: Physics for Scientists and Engineers II , Summer Semester 2009

3. Electric Current Direction Definition: The direction of the current is in the same direction as the flow of positive charge.  The direction of current is opposite to the direction in which negative charge flows. + + + + + + - - - - - - Physics for Scientists and Engineers II , Summer Semester 2009

4. Charge Carriers Metals: Electrons are the charge carriers (negative charge flows). Electrolytes: Typically both positively and negatively charged ions contribute to the flow of charge. - - - - - - Physics for Scientists and Engineers II , Summer Semester 2009

5. Electric Field in Conducting Wires Closed loop: • DV=constant in wire • E=0 inside the wire • Electrons do not move on average. Battery in the loop: • DV exists from one end of the • wire to the other end. • E inside the wire • Electrons move within the wire opposite to the electric field in the wire. • Electric current flows through the wire in the direction of electric field. (charge carriers are NOT in an electrostatic equilibrium). + - V=lower V=higher Physics for Scientists and Engineers II , Summer Semester 2009

6. Microscopic Model of Current in a Metal Assumption: Charge carriers move with a drift speed vd. A q Only charge carriers that are in the gray cylinder will pass through cross sectional area A in a time interval Dt. The amount of charge in the gray cylinder is: Physics for Scientists and Engineers II , Summer Semester 2009

7. Microscopic Model of Current in a Metal Average current in the conductor: Physics for Scientists and Engineers II , Summer Semester 2009

8. Example: Drift Speed in a Copper Wire Assume: 12-gauge copper wire (A=3.31x10-6m2) Iavg=1.0 A (for running a typical light bulb) q = 1.60x10-19C (magnitude of the charge of an electron) Need: n (volume density of free electrons in copper) Physics for Scientists and Engineers II , Summer Semester 2009

9. Example: Drift Speed in a Copper Wire 12-gauge copper wire (A=3.31x10-6m2) Iavg=1.0 A (for running a typical light bulb) q = 1.60x10-19C (magnitude of the charge of an electron) n=8.46x1028 1/m3 Assuming the current is always in the same direction, how long would it take an electron to drift through 5 m of wire? Physics for Scientists and Engineers II , Summer Semester 2009

10. Current Density (current per unit area) “conductivity of the material” Physics for Scientists and Engineers II , Summer Semester 2009

11. Ohm’s Law Rewritten Physics for Scientists and Engineers II , Summer Semester 2009

12. A Model for Electrical Conduction (Paul Drude’s model in 1900) Drift speed approx. 10-4 m/s - Average speed between collisions: approx. 106m/s Physics for Scientists and Engineers II , Summer Semester 2009

13. A Model for Electrical Conduction (Paul Drude’s model in 1900) Conductivity and resistivity in terms of microscopic quantities. Physics for Scientists and Engineers II , Summer Semester 2009

14. Superconductivity R=0 for some materials below a critical temperature. (Useful in superconducting magnets  no permanent power supply necessary, but needs constant cooling) Physics for Scientists and Engineers II , Summer Semester 2009

15. Electrical Power New circuit element: The resistor Potential Energy Change of Charge +q: c d Pot. energy increases for the charge, but chemical pot. energy in battery decreases. a b + - Pot. energy decreases for the charge. The potential energy is lost in collisions to the atoms in the resistor (the resistor heats up). Physics for Scientists and Engineers II , Summer Semester 2009

16. Electrical Power As charge passes through resistor: Physics for Scientists and Engineers II , Summer Semester 2009