EXAM 1, September 22, Thursday Ch.21-23, Lectures 1-6.

1. EXAM 1, September 22, ThursdayCh.21-23, Lectures 1-6. 1. Finding E(x,y,z) or E(r) using a) E of a point charge and superposition principle, b) or Gauss’s law c) or 2. Finding a force a) b) or

2. 3. Finding potential using a) b) or potential of a point charge and superposition principle 4) Finding the work and potential energy

3. Preparation for Exam 1. Look in advance at the formula sheet on the website of the course 2. Problems worked out in Lecture notes 3. Previous midterm exams on my website 4. WebCT and assigned homework

4. At the Exam • You’ll get 3 problems+ formula sheet • Ask me the questions if you do not understand the formulation of the problem • Start with the figure • Get a general (algebraic) solution • Indicate the units • Get numerical results if required (bring your calculator)

5. Lectures 7 (Ch. 24)Capacitance and capacitors 1. Definitions and functions 2. Types of capacitors 3. Effective capacitance (capacitors in series and parallel) 4. Dielectrics 5. Energy stored in capacitor

6. Capacitoris a device to store the charge and energy. It consists oftwo conductors (+Q,-Q), separated by a dielectric. • Store Q and V in order • To use it on demand (camera flash, energy back up,…) • To block surges of Q and V protecting sensitive devices • Part of tuner of a radio, selecting specific frequency of radio waves • Binary code of a memory Capacitance: does not depend neither on Q no on V. It is defined by the geometrical sizes and by a dielctric inside

7. Types of capacitors1. II plate capacitor

8. Spherical capacitor a b

9. Cylindrical capacitor a b

10. SI unit of C [C]=[Q]/[V]=1C/1V=1F(farad) Symbol: Typically C~1pF-1 F A=? Michael Faradey (1791-1867) ! Supercapacitors: C~1F-1kF d EL • 1. Using porous conductors (carbon) to increase an effective A EL EL 2. Electrolyte (EL) as 1 of 2 conductors oxide layer with an effective d~1nm

11. Commercial capacitors

12. Capacitors in parallel: C=C1+C2

13. Capacitors in series:

14. Example 1. Capacitors networks Example 2. You have 3 capacitors with capacitances 5 nF, 2nF and 2nF. Your circuit needs 6 nF. What do you do?

15. Example 1. Capacitors networks Example 2. You have 3 capacitors with capacitances 5 nF, 2nF and 2nF. Your circuit needs 6 nF. What do you do? 2nF 5 nF 2nF

16. Dielectricsdifferent from vacuum or air are typically used in capacitors • to increase the capacitance: C=KC0, K>1 • to improve a mechanical stability (avoid touching between conducting plates) • to increase the dielectric strength compared to air (for air: Ecr=3MV/m) Polarization of dielectric in E

17. Then a battery was removed and a dielectric was inserted. Polarization of dielectric led to induced charge on the plates,σi, reducing E between plates: Suppose capacitor was charged, σ is the surface charge density, K≥1 is a dielectric constant, ε=Kε0 is a dielectric permittivity

18. Suppose capacitor is connected to a battery with voltage, V. Then a dielectric is inserted. v

19. !

20. Coulomb’s Law For charges interacting in a dielectric medium Gauss’s Law Q q

21. Potentical energy stored in the capacitor V dq E -q q Density of Energy U can be viewed as energy stored in E inside capacitor

22. Insert dielectric, C=KC0 Does U ↑or↓? 1. Charged Capacitor. Battery is removed. Then a dielectric is inserted. Q -Q - + dl F F - +

23. 2. Capacitor is connected to battery with V=const. Then a dielectric is inserted V Energy is supplied by the battery, increasing the charge on the plates and keeping V=const

24. Find 1)Charge and energy of the 1st capacitor before the switch was closed. 2) Charge of each capacitor, voltage and total energy after closing the switch .

25. Example 24.15 Data: C1= C2 = C3 = C4 =C=4ϻF; Vab =28V Find: Q1,Q2 , Q3,Q4,V1,V2 , V3,V4