P09 - 1 WARNING: Exam 1 Week from Thursday. P09 - 2 Class 09: Outline Hour 1: Conductors & Insulators Expt. 4: Electrostatic Force Hour 2: Capacitors.

1P09 -

WARNING:

Exam 1 Week from Thursday

2P09 -

Class 09: Outline

Hour 1:

Conductors & Insulators

Expt. 4: Electrostatic Force

Hour 2:

Capacitors

3P09 -

Last Time:Gauss’s Law

4P09 -

Gauss’s Law

0Ssurface

closed Q

dE AE

In practice, use symmetry:

• Spherical (r)

• Cylindrical (r, )

• Planar (Pillbox, A)

5P09 -

Conductors

6P09 -

Conductors and Insulators

A 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

7P09 -

Conductors

Conductors have free charges

E must be zero inside the conductor

Conductors are equipotential objects

8P09 -

Conductors in Equilibrium

Conductors are equipotential objects:

1) E = 0 inside

2) Net charge inside is 0

3) E perpendicular to surface

4) Excess charge on surface

0E

9P09 -

Conductors as Shields

10P09 -

Hollow Conductors

Charge placed INSIDE induces balancing charge INSIDE

+q-- -

-

+

+

+

-

-- -

--

-+

+

+

+ +

11P09 -

Hollow Conductors

Charge placed OUTSIDE induces charge separation on OUTSIDE

+q

----

+

+

+

E=0

12P09 -

PRS Setup

I1

I2

O1

O2

What happens if we put Q in the center?

13P09 -

PRS Questions:Point Charge

Inside Conductor

14P09 -

Demonstration:Conductive Shielding

15P09 -

Field Enhancement

2

2

1

1

r

qk

r

qkV ee

12

1

11 r

V

r

qkE e

22 r

VE

E field is enhanced at sharp points!

16P09 -

Demonstration:Field Enhancement

17P09 -

Experiment 4:Electrostatic Force

18P09 -

Demonstration:Capacitor

P09 -

Capacitors and Capacitance

P09 -

Capacitors: Store Electric Energy

Capacitor: two isolated conductors with equal and opposite charges Q and potential difference V between them.

Units: Coulombs/Volt or Farads

QC

V

21P09 -

Parallel Plate Capacitor

0E

0EQ A

d?E

22P09 -

Calculating E (Gauss’s Law)

0S

inqd

E A

00

A

QE

0

GaussGauss

AE A

Alternatively could have superimposed two sheets

23P09 -

Parallel Plate Capacitor

C depends only on geometric factors A and d

top

bottom

V d E S

d

A

V

QC 0

0

Qd

AEd

24P09 -

Spherical CapacitorTwo concentric spherical shells of radii a and b

Gauss’s Law E ≠ 0 only for a < r < b, where it looks like a point charge:

rE ˆ4 2

0r

Q

What is E?

25P09 -

Spherical Capacitor

For an isolated spherical conductor of radius a:

20

ˆˆ

4

b

a

Qdr

r

rr

1104

baV

QC

aC 04

outside

inside

V d E S

0

1 1

4

Q

b a

Is this positive or negative? Why?

26P09 -

Capacitance of Earth

For an isolated spherical conductor of radius a:

aC 04

mF1085.8 120

m104.6 6a

mF7.0F107 4 C

A Farad is REALLY BIG! We usually use pF (10-12) or nF (10-9)

27P09 -

PRS Question:Changing C Dimensions

28P09 -

Demonstration:Changing C Dimensions

29P09 -

Energy Stored in Capacitor

30P09 -

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

31P09 -

Work Done Charging Capacitor

At some point top plate has +q, bottom has –qPotential difference is V = q / CWork done lifting another dq is dW = dq V

32P09 -

So work done to move dq is:

Total energy to charge to q = Q:

Work Done Charging Capacitor

dW dq V

0

1Q

W dW qdqC

1qdq q dqC C

21

2

Q

C

33P09 -

Energy Stored in Capacitor

QC

V

Since

22

2

1

2

1

2VCVQ

C

QU

Where is the energy stored???

34P09 -

Energy Stored in Capacitor

2

field energy density2o

E

Eu E

21

2U CV

Parallel-plate capacitor: andoAC V Edd

Energy stored in the E field!

2

21( )

2 2o oA E

Ed Add

( )Eu volume

35P09 -

PRS Question:Changing C Dimensions

Energy Stored

36P09 -

Batteries & Elementary Circuits

37P09 -

Ideal Battery

Fixes potential difference between its terminals

Sources as much charge as necessary to do so

Think: Makes a mountain

38P09 -

Batteries in Series

V1 V2

Net voltage change is V = V1 + V2

Think: Two Mountains Stacked

39P09 -

Batteries in Parallel

Net voltage still V

Don’t do this!

40P09 -

Capacitors in Parallel

41P09 -

Capacitors in Parallel

1 21 2,

Q QC C

V V

Same potential!

42P09 -

Equivalent Capacitance

1 2 1 2

1 2

Q Q Q C V C V

C C V

1 2eq

QC C C

V

?

43P09 -

Capacitors in Series

Different Voltages Now

What about Q?

44P09 -

Capacitors in Series

45P09 -

Equivalent Capacitance

1 21 2

Q QV , V

C C

1 2V V V

1 2eq

Q Q QV

C C C

1 2

1 1 1

eqC C C

(voltage adds in series)

46P09 -

Dielectrics

47P09 -

Demonstration:Dielectric in Capacitor

48P09 -

Dielectrics

A dielectric is a non-conductor or insulator

Examples: rubber, glass, waxed paper

When placed in a charged capacitor, the dielectric reduces the potential difference between the two plates

HOW???

49P09 -

Molecular View of Dielectrics

Polar Dielectrics :

Dielectrics with permanent electric dipole moments

Example: Water

50P09 -

Molecular View of Dielectrics

Non-Polar Dielectrics

Dielectrics with induced electric dipole moments

Example: CH4

51P09 -

Dielectric in Capacitor

Potential difference decreases because dielectric polarization decreases Electric Field!

52P09 -

Gauss’s Law for Dielectrics

Upon inserting dielectric, a charge density ’ is induced at its surface

0S

inqd EA

E A

0

'

E

What is ’?

0

' A

53P09 -

Dielectric Constant Dielectric weakens original field by a factor

Gauss’s Law with dielectrics:

0

0 0

' EE

0S inqd AE

Dielectric constants

Vacuum 1.0

Paper 3.7

Pyrex Glass 5.6

Water 80

1

' 1

54P09 -

Dielectric in a CapacitorQ0= constant after battery is disconnected

0VV

Upon inserting a dielectric:

0 00

0 0/

Q QQC C

V V V

55P09 -

Dielectric in a Capacitor

V0 = constant when battery remains connected

Upon inserting a dielectric: 0Q Q

00

0

QQC C

V V

56P09 -

PRS Questions:Dielectric in a Capacitor

57P09 -

Group: Partially Filled Capacitor

What is the capacitance of this capacitor?