hour 1: working in groups expt. 1: visualizations hour 2 ... › courses › physics ›...
TRANSCRIPT
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1P04 -
Class 04: Outline
Hour 1:Working In GroupsExpt. 1: Visualizations
Hour 2:Electric Potential
Pick up Group Assignment at Back of Room
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2P04 -
Groups
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P04 -
Advantages of Groups
• Three heads are better than one• Don’t know? Ask your teammates• Do know? Teaching reinforces knowledge
Leave no teammate behind!• Practice for real life – science and
engineering require teamwork; learn to work with others
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P04 -
What Groups Aren’t
• A Free Ride
We do much group based work (labs & Friday problem solving). Each individual must contribute and sign name to work
If you don’t contribute (e.g. aren’t in class) you don’t get credit
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P04 -
Group Isn’t Working Well?
1. Diagnose problem and solve it yourself -- Most prevalent MIT problem: free rider.
2. Talk to Grad TA3. Talk to the teamwork consultant
Don’t wait: Like most problems,teamwork problems get worse the longer you ignore them
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P04 -
Introduce Yourselves
Please discuss:• What is your experience in E&M?• How do you see group working?• What do you expect/want from class?• What if someone doesn’t participate?• What if someone doesn’t come to class?
Try to articulate solutions to foreseeable problems now (write them down)
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7P04 -
Experiment 1: Visualizations
Need experiment write-up from course packet.
Turn in tear sheet at end of classEach GROUP hands in ONE tear sheet
signed by each member of group
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8P04 -
Last Time:Gravitational & Electric Fields
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9P04 -
Gravity - Electricity
Mass M Charge q (±)
2ˆMG
r= −g r 2
ˆeqkr
=E rCREATE:
g m=F g E q=F E
This is easiest way to picture field
FEEL:
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10P04 -
Potential Energyand Potential
Start with Gravity
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11P04 -
Gravity: Force and Work
Gravitational Force on m due to M:
2ˆg
MmGr
= −F r
Work done by gravity moving m from A to B:
g
B
g AW d= ⋅∫ F s PATH
INTEGRAL
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12P04 -
Work Done by Earth’s GravityWork done by gravity moving m from A to B:
ggW d= ⋅∫F s
( )2ˆ ˆˆ
B
A
GMm
rdr rdθ−⎛ ⎞= ⋅ +⎜ ⎟
⎝ ⎠∫ r r θ
1 1
B A
GMmr r
⎛ ⎞= −⎜ ⎟
⎝ ⎠
2
B
A
r
r
GMm drr
= −∫B
A
r
r
GMm
r= ⎡ ⎤⎢ ⎥⎣ ⎦
What is the sign moving from rA to rB?
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13P04 -
Work Near Earth’s Surface
2 ˆ ˆE
GM gr
≈ − = −g y yG roughly constant:
Work done by gravity moving m from A to B:
( )ˆB
Amg d= − ⋅∫ y sg gW d= ⋅∫F s
By
yAmgdy= −∫ ( )B Amg y y= − −
Wg depends only on endpoints– not on path taken –Conservative Force
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14P04 -
Potential Energy (Joules)B
g B A g g extAU U U d W W∆ = − = − ⋅ = − = +∫ F s
02ˆ(1) g g
GMm GMmU Ur r
= − → = − +F r
• U0: constant depending on reference point• Only potential difference ∆U has
physical significance
0ˆ(2) g gmg U mgy U= − → = +F y
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15P04 -
Gravitational Potential(Joules/kilogram)
Define gravitational potential difference:
g( / )B Bg
g A A
UV m d d
m∆
∆ = = − ⋅ = − ⋅∫ ∫F s g s
gFieldForce Energy Potential
Just as , g gU V→ ∆ → ∆F g
That is, two particle interaction single particle effect
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16P04 -
PRS Question:Masses in Potentials
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17P04 -
Move to Electrostatics
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18P04 -
Gravity - Electrostatics
2ˆMG
r= −g r
Mass M Charge q (±)
2ˆe
qkr
=E r
g m=F g E q=F EBoth forces are conservative, so…
B
g gAU d∆ = − ⋅∫ F s
B
EAU d∆ = − ⋅∫ F s
B
AV d∆ = − ⋅∫ E s
B
g AV d∆ = − ⋅∫ g s
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19P04 -
Potential & Energy
B
A
V d∆ ≡ − ⋅∫E sUnits:
Joules/Coulomb = Volts
Work done to move q from A to B:
ext B AW U U U= ∆ = −
q V= ∆ Joules
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20P04 -
Potential: Summary Thus Far
Charges CREATE Potential Landscapes
0 0"0"
( )V V V V d= + ∆ ≡ − ⋅∫r
r E s
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21P04 -
Potential Landscape
Positive Charge
Negative Charge
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22P04 -
Potential: Summary Thus Far
Charges CREATE Potential Landscapes
0 0"0"
( )V V V V d= + ∆ ≡ − ⋅∫r
r E s
Charges FEEL Potential Landscapes
( ) ( )U qV=r r
We work with ∆U (∆V) because only changes matter
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23P04 -
Potential Landscape
Positive Charge
Negative Charge
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24P04 -
3 PRS Questions:Potential & Potential Energy
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25P04 -
Creating Potentials:Two Examples
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26P04 -
Potential Created by Pt Charge
θrsd ˆˆ θdrdr +=
B
B A AV V V d∆ = − = − ⋅∫ E s
2
ˆr
kQ rE =
2 2
ˆB B
A A
drkQ d kQr r
= − ⋅ = −∫ ∫r s
1 1
B A
kQr r
⎛ ⎞= −⎜ ⎟
⎝ ⎠
Take V = 0 at r = ∞:
rkQrV =)(ChargePoint
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27P04 -
2 PRS Questions:Point Charge Potential
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28P04 -
Potential Landscape
Positive Charge
Negative Charge
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29P04 -
Deriving E from V
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30P04 -
Deriving E from V
ˆx∆ = ∆s i
A = (x,y,z), B=(x+∆x,y,z)
B
A
V d∆ = − ⋅∫E s
( , , )
( , , )
x x y z
x y z
V d+∆
∆ = − ⋅∫ E s ≅ − ⋅∆E s ˆ( ) xx E x= − ⋅ ∆ = − ∆E i
xV VEx x
∆ ∂≅ − → −
∆ ∂Ex = Rate of change in V
with y and z held constant
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31P04 -
Deriving E from VIf we do all coordinates:
V= −∇E
ˆ ˆ ˆV V Vx y z
⎛ ⎞∂ ∂ ∂= − +⎜ ⎟∂ ∂ ∂⎝ ⎠
E i + j k
ˆ ˆ ˆ Vx y z
⎛ ⎞∂ ∂ ∂= − +⎜ ⎟∂ ∂ ∂⎝ ⎠
i + j k
Gradient (del) operator:
ˆ ˆ ˆx y z∂ ∂ ∂
∇ ≡ +∂ ∂ ∂i j+ k
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32P04 -
In Class ProblemFrom this plot of potential vs. position, create a plot of electric field vs. position
Bonus: Is there charge somewhere? Where?
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33P04 -
Configuration Energy
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34P04 -
Configuration EnergyHow much energy to put two charges as pictured?
1) First charge is free2) Second charge sees first:
1 2
1212 2 2 1
14 o
q qU W q V
rπε= = =
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35P04 -
Configuration EnergyHow much energy to put three charges as pictured?
1) Know how to do first two2) Bring in third:
( )3 3 1 2W q V V= + 3 1 2
0 13 234q q q
r rπε⎛ ⎞
= +⎜ ⎟⎝ ⎠
Total configuration energy:
1 3 2 31 22 3 12 13 23
0 12 13 23
14
q q q qq qU W W U U Ur r rπε
⎛ ⎞= + = + + = + +⎜ ⎟
⎝ ⎠
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36P04 -
In Class Problem
How much energy in joules is required to put the three charges in the configuration pictured if they start out at infinity?
What is the electric potential in volts at point P?
Suppose you move a fourth change +3Q from infinity in to point P. How much energy does that require (joules)?