Chapter 22 Capacitance, Dielectrics, Electric Energy Storage

1. Chapter 22 Capacitance, Dielectrics, Electric Energy Storage

2. +Q -Q Q R Capacitors & capacitance Capacitor / condenser: device that stores charge For a given capacitor: Q∝ V C: Capacitance of capacitor Unit: farad (F), μF & pF Symbol in diagram: 2

3. Capacitors Capacitance depends on Size, shape, relative position, insulating material 3

4. d S +Q -Q Determine capacitance For a parallel-plate capacitor: (ignoring edge effect) 4

5. R1 R2 L Cylindrical capacitor Example1: A capacitor consists of two coaxial cylindrical shells (R1, R2), both with length L>>R2. Calculate the capacitance. 5

6. R2 R1 Q1 Q2 Spherical capacitor Question: A capacitor consists of a sphere surrounded by a concentric spherical shell (R1, R2). Calculate the capacitance. -Q1 Q1+Q2 6

7. Capacitors in series and parallel 1) In series 2) In parallel 7

8. d Capacitor combination Example2:Are the capacitors in series or parallel? 1) 2) parallel parallel Example3:How does C, Q, V change if d→2d ? 8

9. dq +q -q Electric energy storage Charged capacitor stores electric energy Work required to store charges: Energy stored: 9

10. S d Energy in the field How does the electric energy distribute? Energy per unit volume / energy density: Electric energy is stored in the electric field! 10

11. S =10cm2 d = 1mm Energy in capacitor Example4:A parallel-plate capacitor is charged at 220V. (a) What is the capacitance; (b) how much electric energy can be stored? Solution: (a) (b) Energy stored: Maximum U ? 11

12. R2 R1 Q -Q Different methods Example5:Determine the electric energy stored in a spherical capacitor. Solution: 2 methods to solve it. a) By using the capacitance: Energy stored: 12

13. R2 R1 Q -Q Q b) By using the energy density: Total energy: Discussion: Isolated conductor sphere? 13

14. Also noted as : relative permittivity Dielectrics Insulating material in capacitors → dielectric ① Harder to break down → V ↗ ② Distance between plates ↘ ③ Increases the capacitance: where K is the dielectric constant 14

15. : the permittivity of material All in electric expressions → Permittivity of material If a dielectric is completely filled the space: In a specific region filled with dielectric: 15

16. V C Electrostatics in dielectric In a specific region filled with dielectric: field is reduced but not zero The energy density in a dielectric: Example6:How does C, Q, U change? battery disconnected? 16

17. Half filled dielectric Question:How does the capacitancechange if the capacitor is half filled with dielectric? (S, d, K) 1) 2) 17

18. - + Molecular description (1) There are two different types of dielectrics: 1) Polar dielectrics, such as H2O and CO Have permanent electric dipole moments. 2) Nonpolar dielectrics, such as O2 and N2 No permanent electric dipole moments. 18

19. - + - + - + - + Q -Q Molecular description (2) Polar Nonpolar Polarization Induced field Eind Bound charge 19

20. V C Thinking & question Thinking:Why charged objects can attract small paper scraps or water flow? Question:Move a dielectric plate out of a charged capacitor, the electric energy increases, where does the extra energy come from? 20

21. Brief review of Chapter 19-22 Coulomb’s law: Gauss’s law: Electric potential: Capacitance; Electric energy: Dielectrics: 21

22. Chapter 23 & 24 These chapters should be studied by yourself Some useful concepts and equations: Current & resistance Ohm’s law: V = IR Current density: Microscopic statement of Ohm’s law: (ch23, pr.24) conductivity & resistivity 22