Chapter 25 Capacitance In this chapter we will cover the following topics:

1. Chapter 25 Capacitance In this chapter we will cover the following topics: -Capacitance C of a system of two isolated conductors. -Calculation of the capacitance for some simple geometries. -Methods of connecting capacitors (in series, in parallel). -Equivalent capacitance. -Energy stored in a capacitor. -Behavior of an insulator (a.k.a. dielectric) when placed in the electric field created in the space between the plates of a capacitor. -Gauss’ law in the presence of dielectrics. (25-1)

2. q = CV q V- V+ V O ) (25-2)

3. Checkpoint 1: • Does the capacitance C of a capacitor increase, decrease, or remain the same • When the charge q on it is doubled and • When the potential difference V across it is tripled? The capacitance of the capacitor depends only on the geometry of the plates and not on their charge or potential difference.

4. V -_ + (25-3)

5. -q +q -q +q (25-4)

6. V- V+ (25-5)

7. P S N (25-6)

8. S (25-7)

9. S (25-8)

11. Checkpoint 2: • For capacitors charged by the same battery, does the charge stored by the capacitor increase, decrease, or remain the same in each of the following situations? • The plate separation of a parallel-plate capacitor is increased. • The radius of the inner cylinder of a cylindrical capacitor is increased • The radius of the outer spherical shell of a spherical capacitor is increased

12. (25-9)

13. (25-10)

14. (25-11)

15. (25-12)

16. Checkpoint 3: • A battery of potential V stores charge q on a combination of two identical capacitors. What are the potential difference across and the charge on either capacitor if the capacitors are • In parallel • In series ?

20. -q' q' - + dq' - + - + - + - + V' Charge A q q' Voltage B O V V' (25-13)

21. -q q - + - + - + A A - + - + d (25-14)

23. q V -q q' V -q' V q -q V' q -q (25-15)

24. q V -q q' V -q' V q -q V' q -q (25-16)

25. conductor dielectric q (25-17)

29. Example 1:

30. Example 2:

32. Example 3:

33. Example 4:

34. Example 5:

35. Example 6:

36. Example 7:

37. Example 8:

38. Example 9: