1. Agenda Today Continuous Charge Distribution Tuesday – lab 5 & Quiz Wed&Fri – Chapter 24 Today –Continuous Charge Distribution Gravity Equivalent Complex Layers HMWK CH. 22 Up Today HMWK Due Thurs.

2. Fields & Potential In a Solid Gravity First Earth M=M E R=R E V=(4/3)  R E 3 SA=4  R E 2  =M/V=3M E /(4  r E 3 ) Even Distribution? Solid Objects Density Volume Surface Area Mass Electrical Objects Charge & Charge Density

3. Find the Zeroes Use reference 0 at infinity (Usual) Earth M=M E R=R E V=(4/3)  R E 3 SA=4  R E 2  =M/V=3M E /(4  r E 3 ) Even Distribution Where is F G =0? Where is PE G = 0?

4. Gauss’s Law Field then Force? Earth M=M E R=R E V=(4/3)  R E 3 SA=4  R E 2  =M/V=3M E /(4  r E 3 ) Even Distribution Flux = Field x Area  = EA

5. Gauss’s Law Field at a point r? Earth M=M E R=R E V=(4/3)  R E 3 SA=4  R E 2  =M/V=3M E /(4  r E 3 ) Even Distribution Choose Surface so E Perp to it. Also, E constant across surface For point charge/sphere  Sphere

6. Gauss’s Law Field at a point r? Earth M=M E R=R E V=(4/3)  R E 3 SA=4  R E 2  =M/V=3M E /(4  r E 3 ) Even Distribution What if “Surface” inside Earth? What is m in equation?

7. Gauss’s Law Field at a point r? Earth M=M E R=R E V=(4/3)  R E 3 SA=4  R E 2  =M/V=3M E /(4  r E 3 ) Even Distribution What if “Surface” inside Earth? What is m in equation?

8. Gauss’s Law Field at a point r? Earth M=M E R=R E V=(4/3)  R E 3 SA=4  R E 2  =M/V=3M E /(4  r E 3 ) Even Distribution V encl =(4/3)  r 3

9. Gauss’s Law Field at a point r? Earth M=M E R=R E V=(4/3)  R E 3 SA=4  R E 2  =M/V=3M E /(4  r E 3 ) Even Distribution

10. Where (r) is field zero? Earth M=M E R=R E V=(4/3)  R E 3 SA=4  R E 2  =M/V=3M E /(4  r E 3 ) Even Distribution

11. Where (r) is field zero? Inside: E=Gr(M E /r E 3 ) Outside: E=GM E /r 2 Two Situations Where is “Special Point” Where r = r E Both must have same value Works: Both E=GM E /r E 2 Inside zero: at center of earth Gravitational pull cancels out Outside only zero at infinity Case similar for small - q & big + q What can be different for Elect? Material Dependence!

12. Interesting Graph 3D Charge Distribution E r r r=r E Linear Inside 1/r 2 outside Discontinuity Value Same

13. What if charged conductor? Metal Charge = +Q Where is field zero? Everywhere inside metal Outside, E=kQ/r 2 Outside is just air + + + + + + + + + + + + + + + + + + + + + + + + +

14. Interesting Graph 3D Metal E r r r=r E Zero Inside 1/r 2 outside Discontinuity Value Not Same?

15. Real Graph 3D Metal E r r r=r E Zero Inside 1/r 2 outside Discontinuity Value Same Exponential Decay Near Surface NanoScale

16. Potential of Charged Conductor? Metal Charge = +Q R=r E, etc.. What is potential in a metal? Constant Where can we find a value? At edge, r=r E V=kQ/r outside V=kQ/r E at edge V=kQ/r E throughout Outside is just air + + + + + + + + + + + + + + + + + + + + + + + + +

17. Interesting Graph 3D Metal V r r r=r E Constant Inside 1/r outside Discontinuity Value Same

18. What if charged Insulator? Insulator Charge = +Q  =1 R=R E, etc… Where is field zero? At center & Infinity Outside, E=kQ/r 2 Inside, E=(k/  )(Qr/r E 3 ) See  can make life interesting For now,  = 1. E=(k)(Qr/r E 3 ) Outside is just air [  = 1] + + + + + + + + + + + + + + + + + + + + + + + + +

19. Interesting Graph 3D Insulating Charge E r r r=r E Linear Inside 1/r 2 outside Discontinuity Value Same What if  >1?

20. Interesting Graph 3D Insulating Charge E r r r=r E Linear Inside 1/r 2 outside Discontinuity Value Not Same? What if  >1? Field becomes smaller inside

21. Interesting Graph 3D Insulating Charge E r r r=r E Linear Inside 1/r 2 outside Discontinuity Value Always Same! What if  >1? Field becomes smaller inside In transition region from inside to outside, k changes value. Exponential Bridge

22. What if charged Insulator? Potential,  = 1 Insulator Charge = +Q  =1 R=R E, etc… Outside is just air [  = 1] + + + + + + + + + + + + + + + + + + + + + + + + +

23. Potential Graph 3D Insulating Charge V r r r=r E Quadratic 1/r outside Discontinuity Value Always Same! What if  >1?

24. What now? Metal Shell Insulator Charge = +Q  =1 R=R E, etc… Outside is just air [  = 1] + + + + + + + + + + + + + + + + + + + + + + + + +

25. What now? Metal Shell Insulator Charge = +Q  =1 R=R E, etc… Outside is just air [  = 1] + + + + + + + + + + + + + + + + + + + + + + + + + What does charge On shell look like?

26. What now? Metal Shell Insulator Charge = +Q  =1 R=R E, etc… Outside is just air [  = 1] + + + + + + + + + + + + + + + + + + + + + + + + + What does charge On shell look like? - - - - - - - - - - + + + + + + + +

27. Metal Shell Insulator Charge = +Q  =1 R=R E, etc… + + + + + + + + + + + + + + + + + + + + + + + + + How much –q on shell? |+q|=|-q|=Q - - - - - - - - - - + + + + + + + + E = 0 in shell E=Q encl /A E=0  Q encl =0

28. Agenda Today Continuous Charge Distribution Tuesday – lab 5 & Quiz Wed&Fri – Chapter 24 Today –Continuous Charge Distribution (if Time) Gravity Equivalent Complex Layers HMWK CH. 22 Up Today HMWK Due Thurs.