Coulomb’s Law

1. Coulomb’s Law Point Charge :

2. Line Charge :

3. Surface Charge :

4. Volume Charge

5. Prob. 2.6: Electric Field at a height z above the centre of a circular plate of uniform charge density.

7. (Infinite Sheet) Limiting Case :

8. Prob. 2.41. Electric Field at a height z above the centre of a square plate of uniform charge density.

10. Any kind of charge distribution can be treated as a volume distribution 1. Point charges :

11. 2. Line Charge

12. 3. Surface Charge

13. Divergence of the Electric Field

14. Examples : 1. Point Charge

15. Infinite Charge Sheet

16. Gauss’ Law

17. Applications of Gauss’ Law Although Gauss’ Law is valid for any kind of charge distribution and any Gaussian Surface, its applicability to determine the electric field is restricted only to symmetrical charge distribution

18. 1. Electric field of a point charge Gaussian Surface

19. Gaussian Surface

20. Prob. 2.16 Long co-axial cable : i) Inner solid cylinder of radius a carrying uniform volume charge density ρ ii) outer cylindrical surface of radius b carrying equal and opposite charge of uniform density σ. Find field in regions i) s<a ii) a<s<b iii) s>b

21. s < a

22. a < s < b

23. s > a

25. Prob. 2.17 Infinite plane slab of thickness 2d (-d<y<d) of uniform volume charge density ρ. Find E in regions i) y<-d ii) –d<y<d iii) y>d

26. -d < y < d

28. Curl of the Electric Field

29. Where, V can be constructed as :

30. The scalar field is called the electric potential and the point is the zero of the potential

31. Changing the zero of the potential Let be the potentials with the zero (reference points) at respectively

32. Prob. 2.20 One of the following is an impossible electrostatic field. Which one? For the possible one, find the potential and show that it gives the correct field

33. Conventionally, the zero of the potential is taken at infinity : Potential of a point charge (zero at infinity) :

34. Charge located at :

35. Potentials of Extended Charge Distributions : Line Charge : Surface Charge :

36. Volume Charge : Prob. 2.26 The conical surface has uniform charge density σ. Find p.d between points a & b

38. Prob. 2.9 Suppose the electric field in some region is found to be : a) Find the charge distribution that could produce this field b) Find the total charge contained in a sphere of radius R centered on the origin. Do it in two different ways.

39. Work done in moving a charge in an electric field If the charge is brought from infinity to the point :

40. If V is the potential of a point charge Q located at then,

41. Electrostatic Energy of a Charge Distribution It is the work done to assemble the charge configuration, starting from some initial configuration Given Config. Initial Config.

42. The standard initial configuration is taken to be one in which all small (infinitesimal) pieces of charge are infinitely separated from one another.

43. 1. Point Charges

45. Electrostatic Energy of Continuous Charge Distribution :

46. The electrostatic energy of a charge distribution can be expressed as an integral over the electric field of the distribution :

47. Proof :

49. Including more and more volume in the integral,

50. A sphere of radius R carries a charge density . Find the energy of the configuration in two different ways. b) Find the potential everywhere and do the integral : Prob. 2.45 a) Find the energy by integrating over the field