1 P07 - Class 07: Outline Hour 1: Conductors & Insulators Expt. 2: Electrostatic Force Hour 2: Capacitors
1P07 -
Class 07: Outline
Hour 1:Conductors & Insulators Expt. 2: Electrostatic Force
Hour 2:Capacitors
2P07 -
Last Time:Gausss Law
3P07 -
Gausss Law
0closedsurface S
encE
Qd = = E AGGw
In practice, use symmetry: Spherical (r) Cylindrical (r, A) Planar (Pillbox, A)
4P07 -
Conductors
5P07 -
Conductors and InsulatorsA conductor contains charges that are free to move (electrons are weakly bound to atoms)Example: metals
An insulator contains charges that are NOT free to move (electrons are strongly bound to atoms)Examples: plastic, paper, wood
6P07 -
Conductors
Conductors have free charges E must be zero inside the conductor Conductors are equipotential objects
E
Neutral Conductor
----
++++
7P07 -
Equipotentials
8P07 -
Topographic Maps
9P07 -
Equipotential Curves
All points on equipotential curve are at same potential.Each curve represented by V(x,y) = constant
10P07 -
PRS Question:Walking down a mountain
11P07 -
Direction of Electric Field E
E is perpendicular to all equipotentials
Constant E field Point Charge Electric dipole
12P07 -
Properties of Equipotentials
E field lines point from high to low potential E field lines perpendicular to equipotentials
Have no component along equipotential No work to move along equipotential
13P07 -
Conductors in Equilibrium
Conductors are equipotential objects:1) E = 0 inside2) Net charge inside is 03) E perpendicular to surface 4) Excess charge on surface
0=E
14P07 -
Conductors in EquilibriumPut a net positive charge anywhere inside a
conductor, and it will move to the surface to get as far away as possible from the other charges of like sign.
http://ocw.mit.edu/ans7870/8/8.02T/f04/visualizations/electrostatics/34-pentagon/34-pentagon320.html
15P07 -
Expt. 2: Electrostatic Force
16P07 -
Expt. 2: Electrostatic Force
http://ocw.mit.edu/ans7870/8/8.02T/f04/visualizations/electrostatics/36-electrostaticforce/36-esforce320.html
17P07 -
Experiment 2:Electrostatic Force
P07 -
Capacitors and Capacitance
P07 -
Capacitors: Store Electric EnergyCapacitor: two isolated conductors with equal and opposite charges Q and potential difference V between them.
QCV
= Units: Coulombs/Volt or
Farads
20P07 -
Parallel Plate Capacitor
0=E
0=E
Q A+ =
Q A =
d?E =
21P07 -
Parallel Plate CapacitorWhen you put opposite charges on plates, charges move to the inner surfaces of the plates to get as close as possible to charges of the opposite sign
http://ocw.mit.edu/ans7870/8/8.02T/f04/visualizations/electrostatics/35-capacitor/35-capacitor320.html
22P07 -
Calculating E (Gausss Law)
0S
inqd = E AGGw
00
AQE ==( )
0
GaussGauss
AE A =
Note: We only consider a single sheet! Doesnt the other sheet matter?
23P07 -
Alternate Calculation Method
+ + + + + + + + + + + + + +Top Sheet:02
E =
02E =
- - - - - - - - - - - - - -Bottom Sheet: 02
E =
02E =
0 0 0 02 2QEA
= + = =
24P07 -
Parallel Plate Capacitor
top
bottom
V d = E SGG0
Q dA=Ed= d
AVQC 0==
C depends only on geometric factors A and d
25P07 -
Demonstration:Big Capacitor
26P07 -
Spherical CapacitorTwo concentric spherical shells of radii a and b
What is E?
Gausss Law E 0 only for a < r < b, where it looks like a point charge:
rE 4 20rQ
=G
27P07 -
Spherical Capacitor
For an isolated spherical conductor of radius a:
20
4
b
a
Q drr= r r
( )11 04 == baVQC
outside
inside
V d = E SGG0
1 14Q
b a =
Is this positive or negative? Why?
aC 04=
28P07 -
Capacitance of EarthFor an isolated spherical conductor of radius a:
aC 04=mF1085.8 120
= m104.6 6=amF7.0F107 4 == C
A Farad is REALLY BIG! We usually use pF (10-12) or nF (10-9)
29P07 -
1 Farad Capacitor
How much charge?
( )( )1F 12 V12C
Q C V= ==
30P07 -
PRS Question:Changing C Dimensions
31P07 -
Demonstration:Changing C Dimensions
32P07 -
Energy Stored in Capacitor
33P07 -
Energy To Charge Capacitor
1. Capacitor starts uncharged.2. Carry +dq from bottom to top.
Now top has charge q = +dq, bottom -dq3. Repeat4. Finish when top has charge q = +Q, bottom -Q
+q
-q
34P07 -
Work Done Charging CapacitorAt some point top plate has +q, bottom has q
Potential difference is V = q / CWork done lifting another dq is dW = dq V
+q
-q
35P07 -
Work Done Charging CapacitorSo work done to move dq is:
dW dq V= 1qdq q dqC C
= =Total energy to charge to q = Q:
0
1 QW dW qdqC
= = +q-q
212Q
C=
36P07 -
Energy Stored in CapacitorQCV
= Since
22
21
21
2VCVQ
CQU ===
Where is the energy stored???
37P07 -
Energy Stored in Capacitor
Energy stored in the E field!
ando AC V Edd
= =Parallel-plate capacitor:21
2U CV= ( ) 221 ( )
2 2o oA EEd Add = = ( )Eu volume=
2
field energy density2o
EEu E = =
38P07 -
1 Farad Capacitor - EnergyHow much energy?
( )( )2
2
121 1F 12 V272 J
U C V= ==
Compare to capacitor charged to 3kV:
( )( )( )( )
22
24 3
1 1 100F 3kV2 21 1 10 F 3 10 V 450 J2
U C V
= == =
39P07 -
PRS Question:Changing C Dimensions
Energy Stored
40P07 -
Demonstration:Dissectible Capacitor
1P8-
Class 08: Outline
Hour 1:Last Time: ConductorsExpt. 3: Faraday Ice Pail
Hour 2:Capacitors & Dielectrics
2P8-
Last Time:Conductors
3P8-
Conductors in Equilibrium
Conductors are equipotential objects:1) E = 0 inside2) Net charge inside is 03) E perpendicular to surface 4) Excess charge on surface
0=E
4P8-
Conductors as Shields
5P8-
Hollow Conductors
Charge placed INSIDE induces balancing charge INSIDE
+q-- -
-
++
+
-
-- -
--
-+
+
++ +
6P8-
Hollow Conductors
Charge placed OUTSIDE induces charge separation on OUTSIDE
+q
----
+
+
+E=0
7P8-
PRS Setup
I1
I2O1
O2What happens if we put Q in the center?
8P8-
PRS Questions:Point Charge
Inside Conductor
9P8-
Demonstration:Conductive Shielding
10P8-
Visualization: Inductive Charging
http://ocw.mit.edu/ans7870/8/8.02T/f04/visualizations/electrostatics/40-chargebyinduction/40-chargebyinduction.html
11P8-
Experiment 3:Faraday Ice Pail
12P8-
Last Time:Capacitors
P8-
Capacitors: Store Electric Energy
QCV
=
To calculate:1) Put on arbitrary Q 2) Calculate E3) Calculate V
Parallel Plate Capacitor:
0ACd=
14P8-
Batteries & Elementary Circuits
15P8-
Ideal Battery
Fixes potential difference between its terminalsSources as much charge as necessary to do so
Think: Makes a mountain
16P8-
Batteries in Series
V1 V2
Net voltage change is V = V1 + V2
Think: Two Mountains Stacked
17P8-
Batteries in Parallel
Net voltage still VDont do this!
18P8-
Capacitors in Parallel
19P8-
Capacitors in Parallel
Same potential!
1 21 2,
Q QC CV V
= =
20P8-
Equivalent Capacitance
?
( )1 2 1 2
1 2
Q Q Q C V C VC C V
= + = + = +
1 2eqQC C CV
= = +
21P8-
Capacitors in Series
Different Voltages NowWhat about Q?
22P8-
Capacitors in Series
23P8-
Equivalent Capacitance
1 21 2
Q QV , VC C
= =
1 2V V V = + (voltage adds in series)
1 2eq
Q Q QVC C C
= = +
1 2
1 1 1
eqC C C= +
24P8-
PRS Question:Capacitors in Series and Parallel
25P8-
Dielectrics
26P8-
Demonstration:Dielectric in Capacitor
27P8-
DielectricsA dielectric is a non-conductor or insulatorExamples: rubber, glass, waxed paper
When placed in a charged capacitor, the dielectric reduces the potential difference between the two plates
HOW???
28P8-
Molecular View of Dielectrics
Polar Dielectrics : Dielectrics with permanent electric dipole moments Example: Water
29P8-
Molecular View of Dielectrics
Non-Polar DielectricsDielectrics with induced electric dipole momentsExample: CH4
30P8-
Dielectric in Capacitor
Potential difference decreases because dielectric polarization decreases Electric Field!
31P8-
Gausss Law for Dielectrics
Upon inserting dielectric, a charge density is induced at its surface
0S
insideqd EA = = E AGGw
0
' =E( )
0
' A =
What is ?
32P8-
Dielectric Constant Dielectric weakens original field by a factor
0
0 0
' EE = = 1' 1
=
Gausss Law with dielectrics:
0S
freeinsideqd = E A
GGDielectric constantsVacuum 1.0Paper 3.7Pyrex Glass 5.6Water 80
33P8-
Dielectric in a CapacitorQ0= constant after battery is disconnected
0VV =Upon inserting a dielectric:
0 00
0 0/Q QQC C
V V V = = = =
34P8-
Dielectric in a CapacitorV0 = constant when battery remains connected
Upon inserting a dielectric: 0Q Q=0
00
QQC CV V
= = =
35P8-
PRS Questions:Dielectric in a Capacitor
36P8-
Group: Partially Filled Capacitor
What is the capacitance of this capacitor?
presentati_w03d1.pdfClass 07: OutlineConductorsConductors and InsulatorsConductorsEquipotentialsTopographic MapsEquipotential CurvesPRS Question:Walking down a mountainDirection of Electric Field EProperties of EquipotentialsConductors in EquilibriumConductors in EquilibriumExpt. 2: Electrostatic ForceExpt. 2: Electrostatic ForceExperiment 2:Electrostatic ForceCapacitors and CapacitanceCapacitors: Store Electric EnergyParallel Plate CapacitorParallel Plate CapacitorAlternate Calculation MethodParallel Plate CapacitorDemonstration:Big CapacitorSpherical CapacitorSpherical CapacitorCapacitance of Earth1 Farad CapacitorPRS Question:Changing C DimensionsDemonstration:Changing C DimensionsEnergy Stored in CapacitorEnergy To Charge CapacitorWork Done Charging CapacitorWork Done Charging CapacitorEnergy Stored in CapacitorEnergy Stored in Capacitor1 Farad Capacitor - EnergyPRS Question:Changing C DimensionsEnergy StoredDemonstration:Dissectible Capacitor
presentati_w03d2.pdfClass 08: OutlineLast Time:ConductorsConductors in EquilibriumConductors as ShieldsHollow ConductorsHollow ConductorsPRS SetupPRS Questions:Point Charge Inside ConductorDemonstration:Conductive ShieldingVisualization: Inductive ChargingExperiment 3:Faraday Ice PailLast Time:CapacitorsCapacitors: Store Electric EnergyBatteries & Elementary CircuitsIdeal BatteryBatteries in SeriesBatteries in ParallelCapacitors in ParallelCapacitors in ParallelEquivalent CapacitanceCapacitors in SeriesCapacitors in SeriesEquivalent CapacitancePRS Question:Capacitors in Series and ParallelDielectricsDemonstration:Dielectric in CapacitorDielectricsMolecular View of DielectricsMolecular View of DielectricsDielectric in CapacitorDielectric Constant kDielectric in a CapacitorDielectric in a CapacitorPRS Questions:Dielectric in a CapacitorGroup: Partially Filled Capacitor