1. Agenda Today & Monday– Problems Ch. 21-23 Tuesday – lab 5 & Quiz Today –Charged Building Blocks Distributions Atomic Stability –Continuous Charge Distribution (if Time) Gravity Equivalent Complex Layers

2. Charge Triangle +Q Equilateral Triangle Side Length = L Charges Pinned How much E in system? PE at infinity = 0 How to solve this?

3. Think E conservation Want to find total energy Kinetic Energy? Calculate PE of each charge –No double counting! Total Energy = Energy needed to Build it

4. Charge Triangle +Q Build it one Charge at a time First set all Charges PE = 0

5. Charges “Far” Away +Q Build it one Charge at a time First set all Charges PE = 0 Now move them into position One at a time Calculate work each time

6. Charges “Far” Away +Q First one r 0 = infinity r F = top of triangle Work done?  E = W NC E=KE+PE KE 0 =KE F =0 PE 0 =0 W=PE F W=? L L L

7. Building Up +Q W1 = 0 Now move to bottom left Realize W 2 = PE F2 PE F2 =? PE F = kQ1Q2/L PE F = kQ 2 /L W 2 = kQ 2 /L L L L

8. Built +Q W1 = 0 W2 = kQ 2 /L W3 = 2kQ 2 /L WT = PE = 3kQ 2 /L Energy Dependence? Usefulness? What does + mean? Order? L L L

9. Built -Q+Q Try This one 1 st top (+Q) 2 nd Bot Left (-Q) 3 rd Bot right (+Q) W1 = 0 W2 = -kQ 2 /L W3 = kQ 2 /L – kQ 2 /L =0 PE = -kQ 2 /L Negative? L L L

10. Built -Q+Q Again 1 st Bot Left (-Q) 2 nd Top (+Q) 3 rd Bot right (+Q) W1 = 0 W2 = -kQ 2 /L W3 = -kQ 2 /L + kQ 2 /L =0 PE = -kQ 2 /L Order Independent Path Independent! Usefulness L L L

11. Examine Stability +Q Where could I place a charge so that it would not move? Where is Electric Field zero? L L L

12. Examine Stability +Q Where could I place a charge so that it would not move? Where is Electric Field zero? L L L Guess Center Yes – Infinity is also correct, as always

13. Calculate Field at Center +Q Step 1: Assign Axes & Signs L L L Guess Center

14. Calculate Field at Center +Q Step 1: Assign Axes & Signs Step 2: Method Superposition L L L Guess Center x y

15. Calculate Field at Center +Q Step 1: Assign Axes & Signs Step 2: Method Step 3: Will Calculate Each Field L L L Guess Center x y

16. Calculate Field at Center 23 1 +Q Step 1: Assign Axes & Signs Step 2: Method Step 3: Will Calculate Each Field Field From Charge 1 L L L Guess Center x y

17. Calculate Field at Center 23 1 +Q Step 1: Assign Axes & Signs Step 2: Method Step 3: Will Calculate Each Field Field From Charge 1 Examine Directions & Mag Direction? Direction = -y Magnitude L L L Guess Center x y How to find r?

18. Calculate Field at Center 23 1 +Q Step 1: Assign Axes & Signs Step 2: Method Step 3: Will Calculate Each Field Direction E1 = -y Need r to get Magnitude L L L Guess Center x y

19. Calculate Field at Center 23 1 +Q Step 1: Assign Axes & Signs Step 2: Method Step 3: Will Calculate Each Field Direction E1 = -y Need r to get Magnitude L L L x y Vertical Line Makes Right Triangle r is H/2 r H 60 o Now what?

20. Calculate Field at Center 23 1 +Q Step 1: Assign Axes & Signs Step 2: Method Step 3: Will Calculate Each Field Direction E1 = -y Need r to get Magnitude L L L x y r H 60 o

21. Calculate Field at Center 23 1 +Q Step 1: Assign Axes & Signs Step 2: Method Step 3: Will Calculate Each Field Direction E1 = -y Write E1 in Vector Form L L L x y r H 60 o

22. Calculate Field at Center 23 1 +Q Step 1: Assign Axes & Signs Step 2: Method Step 3: Will Calculate Each Field Now for #2 Magnitude? Same as #1 L L L r 60 o

23. Calculate Field at Center 23 1 +Q Step 1: Assign Axes & Signs Step 2: Method Step 3: Will Calculate Each Field Now for #2 Magnitude? Same as #1 Direction L L L r 60 o

24. Calculate Field at Center 23 1 +Q Step 1: Assign Axes & Signs Step 2: Method Step 3: Will Calculate Each Field Now for #2 Magnitude? Same as #1 Direction L L L 60 o E2 y E2 x |E2|

25. Calculate Field at Center 23 1 +Q Step 1: Assign Axes & Signs Step 2: Method Step 3: Will Calculate Each Field Now for #3 L L L E3 y E3 x |E3|

26. Calculate Field at Center 23 1 +Q Step 1: Assign Axes & Signs Step 2: Method Step 3: Will Calculate Each Field Step 4: Add them Up L L L

27. Calculate Field at Center 23 1 +Q Step 1: Assign Axes & Signs Step 2: Method Step 3: Will Calculate Each Field Step 4: Add them Up L L L ET X = 0, ET Y =0, ET=0 Can place any charge there & let go Stable?

28. Agenda HMWK Due Next Thursday Tuesday – lab 5 & Quiz Today –Charged Building Blocks Distributions Atomic Stability –Continuous Charge Distribution (Monday) Gravity Equivalent Complex Layers