1. Lecture 9: Capacitance and Capacitors The interior of a Sony Walkman

2. Physics for Scientists and Engineers Chapter 24: Electrostatic Energy and Capacitance Copyright © 2004 by W. H. Freeman & Company Paul A. Tipler Gene Mosca Fifth Edition

3. Learning Objectives To introduce the concept of capacitance, C To provide a definition for the C of a conductor To calculate C of ideal capacitors

4. The Importance of Capacitors: (a) They store potential energy in the E-field (b) Many applications Examples include: (i) use in electronics (ii) flash units of cameras (iii) pulsed lasers (iv) computer keyboard

5. Capacitance for Charge Q placed on a conductor changes the conductor’s potential by V Define the capacitance C of the conductor by the equation Unit of C - coulomb volt -1 - farad (F)  Q

6. Example: an isolated conducting sphere of radius a and carrying a charge Q So A sphere of radius 9  10 9 m (more than 10 3  that of the Earth) would have a capacitance of about 1 farad. Common capacitors in use: pF-  F

7. Earthing a Radius b Consider two conducting spheres Charge q

8. The two spheres acquire the same potential qaqa qbqb Earthing

9. Same potential means Total charge is constant Thus

10. Important Conclusion Earthed isolated charged bodies share their charge with the Earth - effectively lose that charge. The bodies and the Earth acquire a common potential - called zero of potential.

11. The potential of the earth does not change Because a is very Large Similar to the use of sea level as a reference for height

12. Capacitors It is a system of high capacitance, designed for the storage of separated positive and negative charges A capacitor is achieved by moving charge from one conductor to another

13. It is a measure of the ability of a capacitor to store energy Capacitance of a Capacitor Defined by:

15. 5 Given that : What is

16. Calculation of Capacitance 3 geometries - planar, cylindrical, and spherical Procedure Calculate the change of V Apply C = Q/V

17. (a) The Parallel Plate Capacitor We will ignore any fringing effects

18. d  Gauss’s Law: Potential difference between the two plates: Ed

20. The symbol of a capacitor in electric circuits

21. If the voltage across a parallel plate capacitor is doubled, its capacitance: (a)Doubles (b)Drops by Half (c)Remains the same

22. If the charge on an isolated spherical conductor is doubled, its capacitance: (a)Doubles (b)Drops by Half (c)Remains the same

23. (b) A Long Cylindrical Capacitor (co-axial cable)

24. What is the capacitance per unit length? This is important in determining the transmission characteristics of the cable.

25. Choose a cylindrical Gaussian surface rbrb rara

26. (c) A Spherical Capacitor

27. r a r b Appropriate Gaussian surface is a sphere concentric with, and between, the conducting spheres +Q+Q -Q-Q

28. Hence or Therefore

29. The symbol for spherical capacitor

30. Review and Summary Procedure for calculating the capacitance of a capacitor Calculate the E-field (e.g. use Gauss’s Law) Use Followed by

31. Parallel plates capacitor Cylindrical capacitor Spherical capacitor An isolated sphere

32. Some Capacitances Capacitor TypeCapacitance Parallel Plate Cylindrical Spherical Isolated Sphere

33. Capacitors