1. Agenda Today –Problems in Last Few Chapters Tomorrow –Quiz on 21-23, Lab Wed –Shand begins 25

2. Charge Distribution: Conducting Donut Point Charge Outside on Left Which is correct? Why?

3. How to Solve this Problem Practice Ch. 22 What is Electric Field Produced by This? Sphere Hole in Sphere Constant charge density R1 R2 Hole Located at x=-R 1 /2 R 2 = R 1 /8 Charge Density = 

4. How to Create a hole? Simpler way to look at this? R1 R2 Hole Located at x=-R 1 /2 R 2 = R 1 /8 Charge Density = 

5. How to Create a hole? Simpler way to look at this? R1 R2 Hole Located at x=-R 1 /2 R 2 = R 1 /8 Charge Density = 

6. How to Create a hole? Make two spheres One +  & one –  Superposition [Add together] R1 Hole Located at x=-R 1 /2 R 2 = R 1 /8 Charge Density =  R2   Try This?

7. Electric Field & Potential R1 R2 R3 Two Metal Spheres Concentric Outer Hollow Iner: Charged +Q Outer: Charged -Q

8. Electric Field & Potential Everywhere? R1 R2 R3 Two Metal Spheres Concentric Outer Hollow Iner: Charged +Q Outer: Charged -Q Specific Regions 0 <r <R1 R1 < r < R2 R2 < r < R3 R3 < r < Infinity

9. Electric Field & Potential R1 R2 R3 Two Metal Spheres Concentric Outer Hollow Iner: Charged +Q Outer: Charged -Q Specific Regions 0 <r <R1 R1 < r < R2 R2 < r < R3 R3 < r < Infinity

10. Electric Field & Potential R1 R2 R3 Specific Regions 0 <r <R1 R1 < r < R2 R2 < r < R3 R3 < r < Infinity -Q +Q Where is charge located?

11. Metals: E = 0 Inside Metal R1 R2 R3 Specific Regions 0 <r <R1 R1 < r < R2 R2 < r < R3 R3 < r < Infinity -Q +Q Where is charge located? - - - - - -- - - +- - - - - -- - - - - - - + ++ + + +

12. Metals: E = 0 Inside Metal R1 R2 R3 Specific Regions 0 <r <R1 R1 < r < R2 R2 < r < R3 R3 < r < Infinity -Q +Q Gauss’s Law Field =0 if Q ENCL =0 Charges on Outer Surface - - - - - -- - - +- - - - - -- - - - - - - + ++ + + +

13. Electric Field? R1 R2 R3 Specific Regions 0 <r <R1: E = ? R1 < r < R2: E=? R2 < r < R3: E = ? R3 < r < Infinity: E = ? -Q +Q - - - - - -- - - +- - - - - -- - - - - - - + ++ + + +

14. Electric Field? R1 R2 R3 Specific Regions 0 <r <R1: E = 0 R1 < r < R2: E=? R2 < r < R3: E = 0 R3 < r < Infinity: E = 0 -Q +Q - - - - - -- - - +- - - - - -- - - - - - - + ++ + + +

15. Electric Field? R1 R2 R3 Specific Regions 0 <r <R1: E = 0 R1 < r < R2: E = kQ/r 2 R2 < r < R3: E = 0 R3 < r < Infinity: E = 0 -Q +Q - - - - - -- - - +- - - - - -- - - - - - - + ++ + + +

16. Potential First: Reference Point R1 R2 R3 Specific Regions 0 <r <R1 R1 < r < R2 R2 < r < R3 R3 < r < Infinity -Q +Q Gauss’s Law Field =0 if Q ENCL =0 Charges on Outer Surface - - - - - -- - - +- - - - - -- - - - - - - + ++ + + +

17. Potential: Reference Point R1 R2 R3 Specific Regions 0 <r <R1 R1 < r < R2 R2 < r < R3 R3 < r < Infinity -Q +Q V at infinity = 0 (3D ref) E in metal = 0 E outside: kQ ENCL /r 2 - - - - - -- - - +- - - - - -- - - - - - - + ++ + + +

18. Potential: Reference Point Start at r=infinity, work way in R1 R2 R3 Specific Regions 0 <r <R1 R1 < r < R2 R2 < r < R3 R3 < r < Infinity -Q +Q V at infinity = 0 (3D ref) E in metal = 0 E outside: kQ ENCL /r 2 - - - - - -- - - +- - - - - -- - - - - - - + ++ + + +

19. Where is V =0? Where is V= Constant? Try this? Capacitance? (C=Q/V) R1 R2 R3 Specific Regions 0 <r <R1 R1 < r < R2 R2 < r < R3 R3 < r < Infinity -Q +Q V at infinity = 0 (3D ref) E in metal = 0 E outside: kQ ENCL /r 2 - - - - - -- - - +- - - - - -- - - - - - - + ++ + + +

20. Agenda Today –Problems in Last Few Chapters Tomorrow –Quiz on 21-23, Lab Wed –Shand begins 25