1. 23. Electrostatic Energy & Capacitors 1.Electrostatic Energy 2.Capacitors 3.Using Capacitors 4.Energy in the Electric Field

2. The lifesaving jolt of a defibrillator requires a large amount of energy delivered in a short time. Where does that energy come from? Capacitor

3. 23.1. Electrostatic Energy Electrostatic Energy = work done to assemble the charge configuration of a system. Reference ( 0 energy): when all component charges are widely separated. Bringing q 1 in place takes no work. Bringing in q 2 takes Bringing in q 3 takes Total electrostatic energy

4. 23.2. Capacitors Capacitor: pair of conductors carrying equal but opposite charges. Usage: store electrical energy Parallel-Plate Capacitor: 2 conducting plates of area A separated by a small distance d. Plates are initially neutral. They’re charged by connecting to a battery. Charge transfer  plates are equal but oppositely charged. Large A, small d  E  0 outside. Far from the edges

5. Capacitance Parallel-plate capacitor:  C = Q / V = capacitance Parallel-plate capacitor See Probs 41 & 42 Practical capacitor ~  F ( 10  6 F) or pF ( 10  12 F ) Charging / Discharging

6. Energy Stored in Capacitors When potential difference between capacitor plates is V, work required to move charge dQ from  to + plate is Work required to charge the capacitor from 0 to V is = U = energy stored in capacitor Note: In a “charged” capacitor, Q is the charge on the + plate. The total charge of the capacitor is always zero. E  dr < 0

7. Example 23.1. Parallel-Plate Capacitor A capacitor consists of two circular metal plates of radius R = 12 cm, separated by d = 5.0 mm. Find (a) Its capacitance, (b) the charge on the plates, and (c) the stored energy when the capacitor is connected to a 12-V battery. (a) (b) (c)

8. 23.3. Using Capacitors Computer memories: billions of 25 fF capacitors. Rectifiers: mF Fuel-cells: 10 2 F 220-mF electrolytic capacitor 1 F 43 pF to 2.2 mF

9. Practical Capacitors Inexpensive capacitors: Thin plastic sandwiched between aluminum foils & rolled into cylinder. Electrolytic capacitors (large capacitance): Insulating layer developed by electrolysis. Capacitors in IC circuits (small capacitance): Alternating conductive & insulating layers.

10. Dielectrics Dielectrics: insulators containing molecular dipoles but no free charges. Dielectric layer lowers V between capacitor plates by factor 1/  (  > 1).  = dielectric constant Molecular dipoles aligned by E 0. Dipole fields oppose E 0. Net field reduced to E = E 0 / . Hence V = V 0 / . Q is unchanged, so C =  C 0.

11.  : 2 ~ 10 mostly Working voltage V = Max safe potential < E bkd d

12. Example 23.2. Which Capacitor? A 100-  F capacitor has a working voltage of 20 V, while a 1.0-  F capacitor is rated at 300 V. Which can store more charge? More energy?

13. GOT IT? 23.1. You need to replace a capacitor with one that can store more energy. Which will give you greater energy increase: (a) a capacitor with twice the capacitance and same working voltage as the old one, or (b) a capacitor with the same capacitance and twice the working voltage?

14. Connecting Capacitors Two ways to connect 2 electronic components: parallel & series Parallel: Same V for both components  Series: Same I (Q) for both components 

15. GOT IT? 23.2. You have 2 identical capacitors with capacitance C. How would you connect them to get equivalent capacitances (a) 2 C, and (b) ½ C ? Which combination would have the higher working voltage? parallel series

16. Example 23.2. Connecting Capacitors Find the equivalent capacitance of the combinations shown in the Figure. If the maximum voltage to be applied between points A and B is 100 V, what should be the working voltage of C 1 ? ( min. working voltage )

17. Bursts of Power San Francisco’s BART train: KE of deceleration stored as EE in ultracapacitor. Stored EE is used to accelerate train. Capacitors deliver higher energy much more quickly than batteries. Flash light: Battery charges capacitor, which then discharges to give flash. Other examples: Defibrillator, controlled nuclear fusion, amusement park rides, hybrid cars, …

18. 23.4. Energy in the Electric Field Charging a capacitor rearranges charges  energy stored in E Energy density = energy per unit volume Parallel-plate capacitor: Energy density : is universal

19. Example 23.4. A Thunderstorm Typical electric fields in thunderstorms average around 10 5 V/m. Consider a cylindrical thundercloud with height 10 km and diameter 20 km, and assume a uniform electric field of 1  10 5 V/m. Find the electric energy contained in this storm. ~ 1400 gallons of gasoline.

20. Example 23.5. A Shrinking Sphere A sphere of radius R 1 carries charge Q distributed uniformly over its surface. How much work does it take to compress the sphere to a smaller radius R 2 ? Work need be done to shrink sphere Extra energy stored here

21. You’re at point P a distance a from a point charge +q. You then place a point charge  q a distance a on the opposite side of P as shown. What happens to (a) the electric field strength and (b) the electric energy density at P ? (c) Does the total electric energy U = ∫ u E dV of the entire field increase, decrease, or remain the same? GOT IT? 23.3. doubles quadruples decrease Negative work done to bring in –q.