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