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Agenda

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. Charge Triangle. +Q. Equilateral Triangle Side Length = L Charges Pinned

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Agenda

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  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? +Q +Q

  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 +Q +Q

  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 +Q +Q

  6. Charges “Far” Away First one r0 = infinity rF = top of triangle Work done? DE = WNC E=KE+PE KE0=KEF=0 PE0=0 W=PEF W=? +Q L L L +Q +Q

  7. Building Up W1 = 0 Now move to bottom left Realize W2 = PEF2 PEF2 =? PEF = kQ1Q2/L PEF = kQ2/L W2 = kQ2/L +Q L L L +Q +Q

  8. Built W1 = 0 W2 = kQ2/L W3 = 2kQ2/L WT = PE = 3kQ2/L Energy Dependence? Usefulness? What does + mean? Order? +Q L L L +Q +Q

  9. Built Try This one 1st top (+Q) 2nd Bot Left (-Q) 3rd Bot right (+Q) W1 = 0 W2 = -kQ2/L W3 = kQ2/L – kQ2/L =0 PE = -kQ2/L Negative? +Q L L L -Q +Q

  10. Built Again 1st Bot Left (-Q) 2nd Top (+Q) 3rd Bot right (+Q) W1 = 0 W2 = -kQ2/L W3 = -kQ2/L + kQ2/L =0 PE = -kQ2/L Order Independent Path Independent! Usefulness +Q L L L -Q +Q

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

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

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

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

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

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

  17. Calculate Field at Center 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 +Q 1 L L y Guess Center x 2 3 L +Q +Q How to find r?

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

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

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

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

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

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

  24. Calculate Field at Center Step 1: Assign Axes & Signs Step 2: Method Step 3: Will Calculate Each Field Now for #2 Magnitude? Same as #1 Direction +Q 1 L L |E2| E2y E2x 60o 2 3 L +Q +Q

  25. Calculate Field at Center Step 1: Assign Axes & Signs Step 2: Method Step 3: Will Calculate Each Field Now for #3 +Q 1 L L |E3| E3y E3x 2 3 L +Q +Q

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

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

  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

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