1. Capacitance, Dielectrics, Electric Energy Storage
Chapter 22
Capacitance, Dielectrics, Electric Energy Storage

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

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

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

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

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

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

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

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

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

11. 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?
d = 1mm
S =10cm2
Solution: (a)
(b) Energy stored:
Maximum U ? 11

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

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

14. Insulating material in capacitors → dielectric
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
Also noted as : relative permittivity 14

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

16. 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? C V
battery disconnected? 16

17. Half filled dielectric
Question: How does the capacitance change 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. Molecular description (2)
Polar
Nonpolar Q -Q
Polarization - +
Induced field Eind
Bound charge 19

20. Thinking & question
Thinking: Why charged objects can attract small paper scraps or water flow? C V
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. These chapters should be studied by yourself
Some useful concepts and equations:
Ohm’s law: V = I R
Current & resistance
Current density:
Microscopic statement of Ohm’s law:
(ch23, pr.24)
conductivity & resistivity 22