Electricity and Magnetism
• Announcements
• Capacitors
– Dielectric
• Experiment EF
Mar 8 2002
web.mit.edu/8.02x/www
Announcements
• Handout
– Notes, question on Exp EF
• Pset 4 due today
• HVPS due today
• Reading suggestions
– Giancoli 24/5-6 (Today)
Mar 8 2002
web.mit.edu/8.02x/www
Announcements
• Program for next week
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Electric currents
Resistance
Ohm’s law
Electric Power
DC circuits
RC circuits
Kirchoff’s Rules
• Giancoli Chapters 25, 26
Mar 8 2002
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Announcements
• HVPS
– due today
– needed for many other experiments
– common errors
•
•
•
•
•
Winding primary in opposite direction to secondary
Poor soldering
missing connections
wrong circuits (LVPS regulator instead of HVPS transistor)
mis-reading circuit diagram
• Lab session today!
Mar 8 2002
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Parallel Plate Capacitor
C=e0 A/d
V
d big
• Change d
– change C
• Q constant
slope = 1/C
V2
d small
V1
d bigger -> C smaller ->
V bigger for fixed Q
Mar 8 2002
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Q0
Q
Energy stored in Capacitor
• Can store more energy, if
– C bigger
– V bigger
Mar 8 2002
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Demo (loud...)
C = 100mF
U = 800 J
thin wire
Vab = 4000 V
Mar 8 2002
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Where is the energy stored?
• Energy is stored in Electric
Field
• E2 gives Energy Density:
• U/Volume = ½ e0 E2
Mar 8 2002
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d
Electric Circuits
C2
5
6
2
3
C1
1
V14 4
Mar 8 2002
• Two capacitors in parallel
• V56 = V23 = V14 (after capacitor
is charged)
• Q1/C1 = Q2/C2 = V14
• Qtot = Q1 +Q2
• Ctot = (Q1 +Q2 )/ V14 = C1+C2
• Capacitors in parallel ->
Capacitances add!
web.mit.edu/8.02x/www
Electric Circuits
Capacitor
C
Wire
V
Voltage source (like LVPS)
Mar 8 2002
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Electric Circuits
2
•
•
•
•
35
C1
Two capacitors in series
V14 = V23 + V56
Q = Q1 = Q2
Vtot = Q1/C1 +Q2/C2 =
6
Q/(C1+C2)
• 1/Ctot = 1/C1+1/C2
C2
• Inverse Capacitances add!
1
Mar 8 2002
V14
4
web.mit.edu/8.02x/www
Dielectrics
Mar 8 2002
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Dielectrics
• Parallel Plate Capacitor:
– C = e0 A/d
– Ex. A = 1m2, d=0.1mm
-> C ~ 0.1mF
Mar 8 2002
web.mit.edu/8.02x/www
Dielectrics
• Parallel Plate Capacitor:
– C = e0 A/d
– Ex. A = 1m2, d=0.1mm
-> C ~ 0.1mF
Mar 8 2002
web.mit.edu/8.02x/www
In your toolbox:
2 cm
C = 1000mF
Dielectrics
• Parallel Plate Capacitor:
– C = e0 A/d
– Ex. A = 1m2, d=0.1mm
-> C ~ 0.1mF
• How do they do that?
• Where to get a factor of 10000?
Mar 8 2002
web.mit.edu/8.02x/www
In your toolbox:
2 cm
C = 1000mF
Dielectric Demo
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Mar 8 2002
• Start w/ charged capacitor
- -Q • d big -> C small -> V large
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web.mit.edu/8.02x/www
Dielectric Demo
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• Start w/ charged capacitor
- -Q • d big -> C small -> V large
• Insert Glass plate
• Now V much smaller
• C bigger
• But A and d unchanged !
Mar 8 2002
web.mit.edu/8.02x/www
Dielectric Demo
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• Start w/ charged capacitor
- -Q • d big -> C small -> V large
• Insert Glass plate
• Now V much smaller
• C bigger
• But A and d unchanged !
• Glass is a Dielectric
Mar 8 2002
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Microscopic view
Mar 8 2002
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Microscopic view
Remember: Dipoles
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Dipole Moment
L
Mar 8 2002
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p=q L
Microscopic view
Remember: Dipoles
+ -
Dipole Moment
L
E=0
Mar 8 2002
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p=q L
Microscopic view
Remember: Dipoles
+ -
Dipole Moment
p=q L
L
+ -
+ + E>0
E=0
Mar 8 2002
web.mit.edu/8.02x/www
Microscopic view
+ -
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E=0
Def: Polarization
P = n <p> = const. E
Density: #dipoles/volume
Mar 8 2002
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Microscopic view
Polarization
P = const. E = e0 c E
Susceptibility
Mar 8 2002
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Microscopic view
Polarization
P = const. E = e0 c E
Glass
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Mar 8 2002
web.mit.edu/8.02x/www
Microscopic view
Polarization
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Mar 8 2002
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P = const. E = e0 c E
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web.mit.edu/8.02x/www
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Microscopic view
Inside: Charges compensate
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Mar 8 2002
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web.mit.edu/8.02x/www
Surface: Unbalanced
Charges!
- -Q
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Microscopic view
Inside: Charges compensate
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Mar 8 2002
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+Surface
- +layer:
+ - charges
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Thickness
L
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+reduce
- +field!
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web.mit.edu/8.02x/www
Surface: Unbalanced
Charges!
- -Q
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Dielectric Constant
Surface charge density
Mar 8 2002
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Dielectric Constant
Surface charge density
Polarization
Mar 8 2002
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Dielectric Constant
Surface charge density
Polarization
Mar 8 2002
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Dielectric Constant
Add contributions to E
Mar 8 2002
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Dielectric Constant
Add contributions to E
E from plates and E from
Dielectric surface charge
K: Dielectric Constant
Field w/o Dielectric
Mar 8 2002
web.mit.edu/8.02x/www
Dielectric Constant
• Dielectric reduces field E0 (K > 1)
– E = 1/K E0
• Dielectric increases Capacitance
– C = Q/V = Q/(E d) = K Q/(E0d)
• This is how to make small capacitors
with large C !
Mar 8 2002
web.mit.edu/8.02x/www
Dielectric Constant
• Examples
Material
Vacuum
Air
Plexiglass
Water
Ethanol
Ceramics
Glass
Mar 8 2002
K
1
1.0006
3.4
80.4
23
~5000
5-10
web.mit.edu/8.02x/www
Dielectric Constant
• Examples
Material
Vacuum
Air
Plexiglass
Water
Ethanol
Ceramics
Glass
Mar 8 2002
K
1
1.0006
3.4
80.4
23
~5000
5-10
Similar to vacuum
Large!
C in HVPS
web.mit.edu/8.02x/www
‘Puzzle’ Demo
Mar 8 2002
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‘Puzzle’ Demo
Copper
Glass
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+
Mar 8 2002
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‘Puzzle’ Demo
• Where does the charge sit for second
spark?
• Discuss with your neighbour!
Mar 8 2002
web.mit.edu/8.02x/www
‘Puzzle’ Demo
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Mar 8 2002
web.mit.edu/8.02x/www
‘Puzzle’ Demo
Mar 8 2002
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web.mit.edu/8.02x/www
‘Puzzle’ Demo
Mar 8 2002
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web.mit.edu/8.02x/www
‘Puzzle’ Demo
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‘Puzzle’ Demo
Surfaces charges remain on Glass !
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‘Puzzle’ Demo
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‘Puzzle’ Demo
Mar 8 2002
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Experiment EF
Mar 8 2002
web.mit.edu/8.02x/www
Experiment EF
• Finally a real experiment, using tools
built earlier!
• Measure e0
Mar 8 2002
web.mit.edu/8.02x/www
Experiment EF
MMM2
HVPS
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V
V
MMM1
+Q
d
-Q
Al Foil
How do we measure e0 with this?
Mar 8 2002
web.mit.edu/8.02x/www
MMM2
HVPS
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V
V
MMM1
+Q
d
Al Foil
Mar 8 2002
web.mit.edu/8.02x/www
-Q
MMM2
HVPS
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V
V
MMM1
+Q
d
Al Foil
Mar 8 2002
web.mit.edu/8.02x/www
-Q
MMM2
HVPS
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V
V
MMM1
+Q
d
Al Foil
Mar 8 2002
web.mit.edu/8.02x/www
-Q
MMM2
HVPS
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V
V
MMM1
+Q
d
Al Foil
Mar 8 2002
web.mit.edu/8.02x/www
-Q
MMM2
HVPS
+
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V
V
MMM1
+Q
d
Al Foil
Q = CV = e0A/d V
Mar 8 2002
web.mit.edu/8.02x/www
-Q
MMM2
HVPS
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V
V
MMM1
+Q
d
Al Foil
Q = CV = e0A/d V
Mar 8 2002
web.mit.edu/8.02x/www
-Q
MMM2
HVPS
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V
V
MMM1
+Q
d
Al Foil
Q = CV = e0A/d V
Mar 8 2002
web.mit.edu/8.02x/www
-Q
How to get force?
Mar 8 2002
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How to get force?
Balance unknown Force with
known Force -> Gravity!
Mar 8 2002
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How to get force?
t: thickness
Balance unknown Force with
known Force -> Gravity!
Mar 8 2002
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