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

2. 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: Instantaneous current through A: SI units of current:

3. 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. - - - - - -

4. 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. - - - - - -

5. Physics for Scientists and Engineers II, Summer Semester 2009 5 Electric Field in Conducting Wires Closed loop:  V=constant in wire  E=0 inside the wire  Electrons do not move on average. + - V=higher V=lower  V 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). Battery in the loop:

6. 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 v d. A q Only charge carriers that are in the gray cylinder will pass through cross sectional area A in a time interval  t. The amount of charge in the gray cylinder is:

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

8. 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 -6 m 2 ) I avg =1.0 A (for running a typical light bulb) q = 1.60x10 -19 C (magnitude of the charge of an electron) Need: n (volume density of free electrons in copper)

9. Physics for Scientists and Engineers II, Summer Semester 2009 9 Example: Drift Speed in a Copper Wire 12-gauge copper wire (A=3.31x10 -6 m 2 ) I avg =1.0 A (for running a typical light bulb) q = 1.60x10 -19 C (magnitude of the charge of an electron) n=8.46x10 28 1/m 3 Assuming the current is always in the same direction, how long would it take an electron to drift through 5 m of wire?

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

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

12. Physics for Scientists and Engineers II, Summer Semester 2009 12 A Model for Electrical Conduction (Paul Drude’s model in 1900) - Average speed between collisions: approx. 10 6 m/s Drift speed approx. 10 -4 m/s

13. 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.

14. 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)

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

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