2. A sphere of radius A has a charge Q uniformly spread throughout its volume. Find the difference in the electric potential, in other words, the voltage difference, between the center and a point 2A from the center. There is a conducting spherical shell, inner radius A and outer radius B. A charge Q 1 is put at the center. If you now put charge -2Q 1 on the shell, find the charge density everywhere.

3. Capacitors Consider two large metal plates which are parallel to each other and separated by a distance small compared with their width. Area A The field between plates is L

4. The capacitance is:

5. Cylindrical Capacitor

6. Capacitors in series: Capacitors in parallel:

7. 1) If a 4-  F capacitor and an 8-  F capacitor are connected in parallel, which has the larger potential difference across it? Which has the larger charge? Quiz 2) Two capacitors are connected in series as shown. If they were initially uncharged, what will be the charge inside the dotted box after connecting points A and B to a battery of voltage V? A B

8. 3) If the wire connecting the capacitors is bent so that capacitors look like A B how do you now call the arrangement?

9. a b C1C1 C3C3 C5C5 C4C4 C2C2 C 1 =C 5 =8.4  F and C 2 =C 3 =C 4 =4.2  F The applied potential is V ab =220 V. a)What is the equivalent capacitance of the network between points a and b? b) Calculate the charge on each capacitor and the potential difference across each capacitor.

10. A BC D

11. Electric field near the surface of a conductor

12. Capacitors in series: Capacitors in parallel:

13. Most capacitors have a non-conducting material, or dielectric, between their conducting plates. When we insert an uncharged sheet of dielectric between the plates, experiments show that the potential difference decreases to a smaller value V (we did this experiment last class!). When the space between plates is completely filled by the dielectric, the ratio is called dielectric constant.

15. Moore’s Law (1965): every 2 years the number of transistors on a chip is doubled Smaller, Denser, Cheaper

17. Current, Ohm’s Law, Etc.