1. 22 Electric Field II Covering sections 1-5 (omit section 6)

2. 2

3. 3

4. Symmetry 4

5. 5 Gauss’s Law Electric Flux Charge Distribution Relationship between field lines and charge

6. 6 Electric Flux E varies with density of lines Flux is #lines crossing a specific area Flux and “Flow” Symbol  Units: N·m 2 /C Product of Field and Area Can be + or -

7. 7 Electric Flux (cont.) Flux + when leaving a closed surface Flux - when entering a closed surface

8. 8 Electric Flux (cont.) Notice that there is no charge inside and, Net Flux is zero

9. 9 Case where E is spatially uniform:  = E·A (E factored out of integral)  = +EA (E parallel to A)  = -EA (E anti-parallel to A)

10. 10 Flux through both surfaces is identical

11. Charge enclosed determined by (out flux) – (in flux)

12. 12 Net Flux not dependent on shape of enclosing surface or any charges outside the enclosure Net Flux does depend on amount of charge inside enclosure

13. 13 Flux due to a point Q

14. 14 Cylindrical can enclosing part of an “infinite” plane of Q.

15. 15 Net flux = EA + EA + 0 = 2EA == 4  kq E = 4  kq/2A = 2  k(q/A) = 2  k . Plane of Charge cont.

16. 16 Gauss’s Law Permittivity of a vacuum, Gauss’s Law Gauss’s Law in terms of Permittivity

17. 17 Spherical Shell cosine = 1 (symmetry)  = EA = Q/  o E = Q/  o A A = 4  r 2.

18. 18 any closed surface inside shell has Qenc = 0  EA ~ Q = 0  E = 0 Spherical Shell cont.

19. 19 “Field”: Concept or Reality?

20. 20 Long Line

21. 21 Uniform Spherical Volume non-zero values inside same as pt Q outside

22. 22

23. 23 E on Conductor at surface E =  /  o E normal (perpendicular) to surface E is zero inside (with static charges)

24. 24 +Point Q inside Shell shell = neutral conductor -/+ induced on shell

25. 25 Charge Distribution  Field Shape

26. 26 Summary E obtained by sum of effect of all charges charges can be point (ch21) or ‘continuous’ (ch22) E can also be obtained by use of Gauss’s Law for E, where concept of E flux is used.

27. 27

28. 28

29. 29

30. 30