agenda today & monday– problems ch. 21-23 tuesday – lab 5 & quiz today –charged...
DESCRIPTION
Think E conservation Want to find total energy Kinetic Energy? Calculate PE of each charge –No double counting! Total Energy = Energy needed to Build itTRANSCRIPT
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 +Q
+QEquilateral TriangleSide Length = LCharges PinnedHow much E in system?PE at infinity = 0How to solve this?
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
Charge Triangle
+Q +Q
+QBuild it one Charge at a timeFirst set all Charges PE = 0
Charges “Far” Away
+Q+Q
+Q
Build it one Charge at a timeFirst set all Charges PE = 0Now move them into positionOne at a timeCalculate work each time
Charges “Far” Away
+Q+Q
+QFirst oner0 = infinityrF = top of triangleWork done?E = WNC E=KE+PEKE0=KEF=0PE0=0W=PEF W=?
L
L
L
Building Up
+Q
+Q
+QW1 = 0Now move to bottom leftRealize W2 = PEF2
PEF2 =?PEF = kQ1Q2/LPEF = kQ2/L W2 = kQ2/L
L
L
L
Built
+Q +Q
+QW1 = 0W2 = kQ2/L W3 = 2kQ2/LWT = PE = 3kQ2/L Energy Dependence?Usefulness?What does + mean?Order?
L
L
L
Built
-Q +Q
+Q
Try This one1st top (+Q)2nd Bot Left (-Q)3rd Bot right (+Q)W1 = 0W2 = -kQ2/LW3 = kQ2/L – kQ2/L =0PE = -kQ2/LNegative?
L
L
L
Built
-Q +Q
+Q
Again1st Bot Left (-Q)2nd Top (+Q)3rd Bot right (+Q)W1 = 0W2 = -kQ2/LW3 = -kQ2/L + kQ2/L =0PE = -kQ2/LOrder IndependentPath Independent!Usefulness
L
L
L
Examine Stability
+Q +Q
+Q
Where could I place a charge so that it would not move?Where is Electric Field zero?
L
L
L
Examine Stability
+Q +Q
+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
Calculate Field at Center
+Q +Q
+Q
Step 1: Assign Axes & Signs
L
L
L
Guess Center
Calculate Field at Center
+Q +Q
+Q
Step 1: Assign Axes & SignsStep 2: MethodSuperposition
L
L
L
Guess Center
x
y
Calculate Field at Center
+Q +Q
+Q
Step 1: Assign Axes & SignsStep 2: MethodStep 3: Will Calculate Each Field
L
L
L
Guess Center
x
y
Calculate Field at Center
2 3
1
+Q +Q
+Q
Step 1: Assign Axes & SignsStep 2: MethodStep 3: Will Calculate Each FieldField From Charge 1
L
L
L
Guess Center
x
y
Calculate Field at Center
2 3
1
+Q +Q
+Q
Step 1: Assign Axes & SignsStep 2: MethodStep 3: Will Calculate Each FieldField From Charge 1Examine Directions & MagDirection?Direction = -yMagnitude
L
L
L
Guess Center
x
y
2
11 QE kr
How to find r?
Calculate Field at Center
2 3
1
+Q +Q
+Q
Step 1: Assign Axes & SignsStep 2: MethodStep 3: Will Calculate Each FieldDirection E1 = -yNeed r to get Magnitude
L
L
L
Guess Center
x
y
2
QE kr
Calculate Field at Center
2 3
1
+Q +Q
+Q
Step 1: Assign Axes & SignsStep 2: MethodStep 3: Will Calculate Each FieldDirection E1 = -yNeed r to get Magnitude
L
L
L
x
y
2
QE kr
Vertical Line Makes Right Triangler is H/2
r
H
60o
Now what?
Calculate Field at Center
2
QE kr
2 3
1
+Q +Q
+Q
Step 1: Assign Axes & SignsStep 2: MethodStep 3: Will Calculate Each FieldDirection E1 = -yNeed r to get Magnitude
L
L
L
x
y
r
H
60o
sin 60
3234
oH L
H L
r L
Calculate Field at Center
2
QE kr
2
2
2 2
34
111
311 4
16 1613 3
r L
QE kr
QE k L
Q QE k kL L
2 3
1
+Q +Q
+Q
Step 1: Assign Axes & SignsStep 2: MethodStep 3: Will Calculate Each FieldDirection E1 = -yWrite E1 in Vector Form
L
L
L
x
y
r
H
60o
2
2
1
161 03
161 03
NE x y CQ NE x k y CL
Q NE x y k CL
Calculate Field at Center
2
2
3,4
161 03
QE k r Lr
Q NE x y k CL
2 3
1
+Q +Q
+Q
Step 1: Assign Axes & SignsStep 2: MethodStep 3: Will Calculate Each FieldNow for #2Magnitude?Same as #1
L
L
L
r
60o
Calculate Field at Center
2 2
2
16 3,3 4
161 03
Q QE k k r Lr L
Q NE x y k CL
2 3
1
+Q +Q
+Q
Step 1: Assign Axes & SignsStep 2: MethodStep 3: Will Calculate Each FieldNow for #2Magnitude?Same as #1Direction
L
L
L
r
60o
Calculate Field at Center
2 2
16 3,3 4
1 0 0 1
3 122 2
Q QE k k r Lr L
E x E y x y E
E x y E
2 3
1
+Q +Q
+Q
Step 1: Assign Axes & SignsStep 2: MethodStep 3: Will Calculate Each FieldNow for #2Magnitude?Same as #1Direction
L
L
L
60oE2y
E2x
|E2|
Calculate Field at Center
2 2
16 3,3 4
1 0 0 1
3 122 2
Q QE k k r Lr L
E x E y x y E
E x y E
2 3
1
+Q +Q
+Q
Step 1: Assign Axes & SignsStep 2: MethodStep 3: Will Calculate Each FieldNow for #3
L
L
L
E3y
E3x
|E3|
Calculate Field at Center
2 2
16 3,3 4
1 0 0 1
3 122 2
3 132 2
Q QE k k r Lr L
E x E y x y E
E x y E
E x y E
2 3
1
+Q +Q
+Q
Step 1: Assign Axes & SignsStep 2: MethodStep 3: Will Calculate Each FieldStep 4: Add them Up
L
L
L
Calculate Field at Center
2 2
16 3,3 4
1 0 0 1
3 122 2
3 132 2
1 2 3
Q QE k k r Lr L
E x E y x y E
E x y E
E x y E
ET E E E
2 3
1
+Q +Q
+Q
Step 1: Assign Axes & SignsStep 2: MethodStep 3: Will Calculate Each FieldStep 4: Add them Up
L
L
L
ETX = 0, ETY=0, ET=0Can place any charge there & let goStable?
Agenda
• HMWK Due Next Thursday• Tuesday – lab 5 & Quiz• Today
– Charged Building Blocks• Distributions• Atomic Stability
– Continuous Charge Distribution (Monday)• Gravity Equivalent• Complex Layers