1. Physics for Scientists and Engineers II, Summer Semester 2009 Lecture 5: May 29 th 2009 Physics for Scientists and Engineers II

2. Physics for Scientists and Engineers II, Summer Semester 2009 Electric Field Calculation from Electric Potential

3. Physics for Scientists and Engineers II, Summer Semester 2009 Example: Electric Dipole (similar to Ex. 25.4) x y q-q aa P

4. Physics for Scientists and Engineers II, Summer Semester 2009 Example: Electric Dipole (similar to Ex. 25.4) x y q-q aa P

5. Physics for Scientists and Engineers II, Summer Semester 2009 Example: Electric Dipole (similar to Ex. 25.4) x y q-q x+a x-a P

6. Physics for Scientists and Engineers II, Summer Semester 2009 Example: Electric Dipole (similar to Ex. 25.4)

7. Physics for Scientists and Engineers II, Summer Semester 2009 Example: Electric Dipole (similar to Ex. 25.4) y

8. Physics for Scientists and Engineers II, Summer Semester 2009 Electric Potential Due to Continuous Charge Distributions P r dq

9. Physics for Scientists and Engineers II, Summer Semester 2009 Example P(x=a,y=b) y x O x L dx b a dq= dx r

10. Physics for Scientists and Engineers II, Summer Semester 2009 Example

11. Physics for Scientists and Engineers II, Summer Semester 2009 Example

12. Physics for Scientists and Engineers II, Summer Semester 2009 Example: Chapter 25, Problem 38 R O 2R Find the electric potential at O. Linear charge density =  Three contributions to V: left straight piece, curved piece, and right straight piece.

13. Physics for Scientists and Engineers II, Summer Semester 2009 Example: …and another one R O R Find the electric potential at O. Charge +Q is evenly distributed. R +Q -Q

14. Physics for Scientists and Engineers II, Summer Semester 2009 Electric Potential Due to a Charged Conductor Charged conductor in electrostatic equilibrium (no net charge movement) A B C The electric potential is constant throughout a charged conductor in electrostatic equilibrium.

15. Physics for Scientists and Engineers II, Summer Semester 2009 Electric Potential and Field of a Charged Spherical Conductor + + + + + + + + + + + + V E

16. Physics for Scientists and Engineers II, Summer Semester 2009 Two Connected Charged Spheres (far apart, so electric field of one sphere does not significantly the affect charge distribution on the other sphere) r1r1 r2r2 metal wire q1q1 q2q2

17. Physics for Scientists and Engineers II, Summer Semester 2009 Two Connected Charged Spheres (far apart)

18. Physics for Scientists and Engineers II, Summer Semester 2009 Electric Field in the Cavity within a Conductor Charged conductor in electrostatic equilibrium (no net charge movement) A B

19. Physics for Scientists and Engineers II, Summer Semester 2009 Chapter 26: Capacitance and Dielectrics +Q-Q Assume you have two charged conductors having equal but opposite amounts of charge on them:

20. Physics for Scientists and Engineers II, Summer Semester 2009 Definition of “Capacitance”

21. Physics for Scientists and Engineers II, Summer Semester 2009 The Plate Capacitor + - +Q -Q d Area = A A battery has a potential difference  V (“voltage”) between it’s two terminals. Assume: Before the wires are connected, Q=0 on the plates.  1) There will be an electric field within the wire going from the left plate to the negative terminal and 2) There will be an electric field within the wire going from the positive terminal to the right plate.  Electrons will move opposite to the field lines (from the negative terminal to the left plate and from the right plate to the positive terminal)  The left plate gets charged negatively and the right plate gets charged positively as electrons leave it. The increasing charges on the plates create an increasing additional electric field in the wires, opposite to that produced by the battery terminals. Once enough charge is on the plates, the electric field in the wires is zero.  The capacitor is now “fully charged”.  The higher the voltage of the battery, the more charge can accumulate on the capacitor.