Physics 212 Lecture 4, Slide 1

1. Physics 212 Lecture 4, Slide 1

2. Main Point 1 First, Gauss� law can be used to actually calculate the spatial dependence of the electric field produced by sufficiently symmetric charge distributions. In particular, since we live in a three spatially dimensioned world, there are three kinds of symmetric charge distributions (spherical, cylindrical, and planar) that produced fields that can be calculated directly from Gauss� law. Physics 212 Lecture 4, Slide 2

3. Main Point 2 Second, we used Gauss� law to demonstrate that any excess charge on a conductor must reside on its surface. We applied the same ideas to determine that a point charge placed at the center of a spherical shell conductor induces a charge on both the inner and outer surfaces in order to produce a zero electric field in the shell. Physics 212 Lecture 4, Slide 3

4. Main Point 3 We start with the observation that the field lines produced by spherically symmetric charge distributions expand fully into three dimensions; their density decreases as 1/surface area of a sphere or 1/r2. If we squeeze the spherically symmetric charge distribution into a cylindrically symmetric distribution, the field lines become perpendicular to the axis and can expand only into two dimensions; their density decreases as 1/surface area of a cylinder or 1/r. If we further squeeze the cylindrically symmetric charge distribution into a plane, the field lines become perpendicular to the plane but have no space to expand into. Consequently, their density remains constant leading to a field that is constant over all space. Physics 212 Lecture 4, Slide 4

5. Physics 212 Lecture 4, Slide 5 Careful here� inside means part of conductor, does NOT include cavity of a conductor!Careful here� inside means part of conductor, does NOT include cavity of a conductor!

6. Physics 212 Lecture 4, Slide 6 Gauss� Law

7. Physics 212 Lecture 4, Slide 7

8. Physics 212 Lecture 4, Slide 8 Charge in Cavity of Conductor

9. Physics 212 Lecture 4, Slide 9 Infinite Cylinders Last answers allow for mistake of doing inner radius instead of outer.Last answers allow for mistake of doing inner radius instead of outer.

10. Physics 212 Lecture 4, Slide 10 Gauss� Law Symmetries

11. Physics 212 Lecture 4, Slide 11

12. Physics 212 Lecture 4, Slide 12 Checkpoint 1

13. Physics 212 Lecture 4, Slide 13 Checkpoint 2

14. Physics 212 Lecture 4, Slide 14 Checkpoint 3 Draw gaussian surfaces and fieldDraw gaussian surfaces and field

15. Physics 212 Lecture 4, Slide 15 Checkpoint 4

16. Physics 212 Lecture 4, Slide 16

17. Physics 212 Lecture 4, Slide 17

18. Physics 212 Lecture 4, Slide 18