Short Version : 23. Electrostatic Energy & Capacitors

1. Short Version : 23. Electrostatic Energy & Capacitors

2. 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 q1 in place takes no work. Bringing in q2 takes Bringing in q3 takes Total electrostatic energy

3. 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

4. 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

5. Energy Stored in Capacitors When potential difference between capacitor plates is V, work required to move charge dQ from  to + plate is E  dr < 0 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.

6. 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 • Its capacitance, • the charge on the plates, and • the stored energy when the capacitor is connected to a 12-V battery. (a) (b) (c)

7. 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.

8. Dielectrics Dielectrics: insulators containing molecular dipoles but no free charges. Molecular dipoles aligned by E0 . Dielectric layer lowers V between capacitor plates by factor 1/ ( > 1).  = dielectric constant Dipole fields oppose E0. Net field reduced to E = E0 / . Hence V = V0 / . Q is unchanged, so C =C0.

9. : 2 ~ 10 mostly Working voltage V = Max safe potential < Ebkd d

10. 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?

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

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

13. 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

14. Example 23.4. A Thunderstorm Typical electric fields in thunderstorms average around 105 V/m. Consider a cylindrical thundercloud with height 10 km and diameter 20 km, and assume a uniform electric field of 1105 V/m. Find the electric energy contained in this storm. ~ 1400 gallons of gasoline.

15. Example 23.5. A Shrinking Sphere A sphere of radius R1 carries charge Q distributed uniformly over its surface. How much work does it take to compress the sphere to a smaller radius R2 ? Work need be done to shrink sphere Extra energy stored here