PHY121 Summer Session II, 2006 Most of information is available at:...

PHY121 Summer Session II, 2006

• Most of information is available at: http://nngroup.physics.sunysb.edu/~chiaki/PHY122-06. It will be frequently updated.• Homework assignments for each chapter due a week later (normally) and are delivered through WebAssign. Once the deadline has passed you cannot input answers on WebAssign. To gain access to WebAssign, you need to obtain access code and go to http://www.webassign.net. Your login username, institution name and password are: initial of your first name plus last name (such as cyanagisawa), sunysb, and the same as your username, respectively.

• In addition to homework assignments, there is a reading requirement of each chapter, which is very important.

• The lab session will start next Monday (June 5), for the first class go to A-117 at Physics Building. Your TAs will divide each group into two classes in alphabetic order.

Instructor : Chiaki Yanagisawa

http://nngroup.physics.sunysb.edu/~chiaki/PHY122-06

http://www.webassign.net/

• There will be recitation classes currently planned to be on Fridays at: 9:30 am - 10:15 am, 10:30 am - 11:15 am 3:00 pm - 3:45 pm, 4:00 pm - 4:45 pm. The location will be announced and the times are subject to change. In the recitation classes, quizzes will be given.

• There will be Office Hours by TAs and the times and locations will be announced.

• Questions about homework problems should be addressed during Office hours.• Certain important announcements will be announce during the lectures and MOST of THEM (NOT ALL) will be posted on the web.

• Find information about which you want to know on the web or during the lectures as much as possible.

Chapter 15: Electric Forces and Electric Fields

Properties of electric charges

Two opposite signed charges attract each other

Two equally signed charges repel each other

When a plastic rod is rubbed with a piece of fur, the rod is “positively” charged

When a glass rod is rubbed with a piece of silk, the rod is “negatively” charged

Electric charge is conserved

Homework on WebAssign to be set up: 14,22,40,53,64

Particle Physics

Model of Atoms

electrons e-

nucleus

Old view

Semi-modern view

Modern view

nucleusquarks

prot

on

What is the world made of?

Electric charge (cont’d)


Origin of electric charge • Nature’s basic carriers of positive charge are protons, which, along with neutron, are located in the nuclei of atoms, while the basic carriers of negative charge are electrons which orbit around the nucleus of an atoms. Atoms are in general electrically neutral.

• It is easier to take off electron(s) from an atom than proton(s). By stripping off an electron from the atom, the atom becomes positively charged, while an atom that the stripped off electron is relocated to becomes negatively charged.

• In 1909 Millikan discovered that if an object is charged, its charge is always a multiple of a fundamental unit of charge, designated by the symbol : the electric charge is quantized.

The value of in the SI unit is 1.60219x10-19 coulomb C.

• Electron: Considered a point object with radius less than 10-18 meters with electric charge e= -1.6 x 10 -19 Coulombs (SI units) and mass me= 9.11 x 10 - 31 kg

• Proton: It has a finite size with charge +e, mass mp= 1.67 x 10-27 kg and with radius– 0.805 +/-0.011 x 10-15 m scattering experiment– 0.890 +/-0.014 x 10-15 m Lamb shift experiment

• Neutron: Similar size as proton, but with total charge = 0 and mass mn=– Positive and negative charges exists inside the neutron

• Pions: Smaller than proton. Three types: + e, - e, 0 charge.– 0.66 +/- 0.01 x 10-15 m

• Quarks: Point objects. Confined to the proton, neutron, pions, and so forth.– Not free– Proton (uud) charge = 2/3e + 2/3e -1/3e = +e– Neutron (udd) charge = 2/3e -1/3e -1/3e = 0

– An isolated quark has never been found

Electric charges


• Two kinds of charges: Positive and Negative• Like charges repel - unlike charges attract• Charge is conserved and quantized

1. Electric charge is always a multiple of the fundamental unit of charge, denoted by e.

2. In 1909 Robert Millikan was the first to measure e. Its value is e = 1.602 x 10−19 C (coulombs).

3. Symbols Q or q are standard for charge.

4. Always Q = Ne where N is an integer

5. Charges: proton, + e ; electron, − e ; neutron, 0 ; omega, − 3e ; quarks, ± 1/3 e or ± 2/3 e – how come? – quarks always exist in groups with the N×e rule applying to the group as a whole.


Insulators and Conductors

Definition • In conductors, electric charges move freely in response to an electric force. All other materials are called insulators.

Insulators : glass, rubber, etc.

When an insulator is charged by rubbing, only the rubbed areabecomes charged, and there is no tendency for the charge tomove into other regions of the material.

Conductors : copper, aluminum, silver, etc.

When a small area of a conductor is charged, the charge readilydistributes itself over the entire surface of the material.

Semiconductors : silicon, germanium, etc.

Electrical properties of semiconductor materials are somewherebetween insulators and conductors.


Charging a material • Charging by contact


Charging a material • Charging by induction

Induction : A process in which a donor material gives opposite signed charges to another material without losing any of donor’s charges


Insulator• Polarization

• Polarization in an insulator by induction

+ +

-

Coulomb’s Law

Coulomb’s law- The magnitude of the electric force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them

221

r

qqkF e

r : distance between two chargesq1,q2 : chargeske : Coulomb constant 8.9875 x109

Nm/C2

- The directions of the forces the two charges exert on each other are always along the line joining them.- When two charges have the same sign, the forces are repulsive.- When two charges have opposite signs, the forces are attractive.

+ +r

q1 q2

- -r

q1 q2

+ -r

q1 q2

F21 F12 F21 F12 F12F21

Coulomb’s Law

Coulomb’s law and units

221

r

qqkF e

229

229

229

C/mN100.9

C/mN10988.8

C/mN109875.8

ek

s/m102.99792458c 8

)mN/(C10854.8;4

1

c)C/sN10(

22120

0

2227

ek

SI unit

Exact by definition

C10)63(602176462.1 19echarge of a proton

C10nC1 C, 10 1 -96 C

r : distance between two charges (m)q1,q2 : charges (C)ke : Coulomb’s constant

Coulomb’s Law

Example : Electric forces vs. gravitational forces

2

2

04

1

r

qFe

2

2

r

mGFg

electric force

gravitational force

+ +r

q q

35

227

219

2211

229

2

2

0

101.3

)kg1064.6(

C)102.3(

kg/mN1067.6

C/mN100.9

4

1

m

q

GF

F

g

e

Gravitational force is tiny compared with electric force!

kg1064.6

102.3227

19

m

Ceq

+ +0

0protonneutron

particle

Coulomb’s law

Example : Forces between two charges

12

2

9-9229

2

21

012

N 019.0

m)030.0(

C)10C)(751025()C/mN100.9(

4

1

F

r

qqF

nC75nC,25 21 qq

+ -r

F12F21

cm0.3r

1221 FF

Coulomb’s law

Superposition of forces Principle of superposition

When two charges exert forces simultaneously on a third charge,the total force acting on that charge is the vector sum of the forcesthat the two charges would exert individually.

Example : Vector addition of electric forces on a line

+ -2.0 cm

F13F23

+

q1q2q3

4.0 cm

Coulomb’s Law

Example 15.2: May the force be zero

+2.0 cm-x

F13F23

+

q1q3q2

2.0 cm

-x

Three charges lie along the x-axis asin Fig. The positive charge q1=15 C isat x=2.0 cm, and the positive chargeq2=6.0 C is at the origin. Where musta negative charge q3 be placed on thex-axis so that the resultant electric forceon it is zero?

Coulomb’s law

Example : Vector addition of electric forces in a plane

N29.0

m)50.0(

C)10C)(2.0100.4()C/mN100.9(

4

1

2

6-6229

21

1

01

Q

Qr

QqF

+

+

+

0.50 m

0.50 m

0.40 m

0.30 m

0.30 m

q1=2.0 C

q1=2.0 C

Q=2.0 C

QF1

xQF )( 1

yQF )( 1

N23.00.50m

0.40mN)29.0(cos)()( 11 QxQ FF

N17.00.50m

0.30mN)29.0(sin)()( 11 QyQ FF

0N17.0N17.0

N0.460.23NN23.0

y

x

F

F

Electric Field

Electric field and electric forces

++ +

++++

++

A B

0F

0F

0q+ +

++++

++

A

P

remove body B

•Existence of a charged body A modifies property of space and produces an “electric field”. •When a charged body B is removed, although the force exerted on the body B disappeared, the electric field by the body A remains.

•The electric force on a charged body is exerted by the electric field created by other charged bodies.

Electric field and electric forces (cont’d)

+ ++

+++++

A Test charge

0F

0F

0q+ +

++++

++

A

P

placing a test charge

• To find out experimentally whether there is an electric field at a particular point, we place a small charged body (test charge) at the point.• Electric field is defined by

0

0

q

FE

(N/C in SI units)

• The force on a charge q: EqF

Electric Field

Electric field of a point charge

+ -rrr /ˆ

r̂ r̂

P P

q0 q0

q q

S S

E

E

2

0

00 4

1

r

qqF

0

0

q

FE

+

rr

qE ˆ

4

12

0

+

r̂ P

q0

q

S

E

'E

P’

'r̂

'' EErr

Electric Field

unit vector

Electric Field Lines

An electric field line is an imaginary line or curve drawn through a region of space so that its tangent at any point is in the direction of the electric-field vector at that point.

Electric field lines show the direction of at each point, and their spacing gives a general idea of the magnitude of at each point.

E

E

Where is strong, electric field lines are drawn bunched closely together; where is weaker, they are farther apart.

E

E

At any particular point, the electric field has a unique direction so that only one field line can pass through each point of the field. Field lines never intersect.

• E-field lines begin on + charges and end on - charges. (or infinity)• They enter or leave charge symmetrically.• The number of lines entering or leaving a charge is proportional to

the charge.• The density of lines indicates the strength of E at that point.• At large distances from a system of charges, the lines become

isotropic and radial as from a single point charge equal to the net charge of the system.

• No two field lines can cross.

Field line drawing rules:


Electric Field Lines Field line examples


Field line examples (cont’d)

An electric dipole is a pair of point charges with equal magnitude and opposite sign separated by a distance d.

q qqd

d

electric dipole moment

Water molecule and its electric dipole


Millikan’s experiment

Millikan Oil-Drop Experiment

Dif v<0 (i.e. Eq<mg) D

if v>0 (i.e. Eq>mg)

drag force

If the oil drop moves downward, the drag force points upward.When Eq=mg+D, the drop reaches the terminal velocity. Knowingthe terminal velocity, mass of the drop, and the magnitude of theelectric field, the charge of the drop can be measured.

E=0 When the drag force, which is proportional to the velocity of the drop, becomes equal to mg, the drop reaches the terminal velocity.

E=0

Some definitions

Electric Flux and Guass’s Law

Closed surface : A closed surface has an inside and outside.Electric flux : A measure of how much the electric field vectors penetrate through a given surface.

Electric fluxA (area)

nAA ˆ E

E

electric flux: EAE

AEAEEAE

coselectric flux:

plane thelar toperpendicuector Unit v

runit vecto Normal : n̂

nAA ˆ

Calculating Electric Flux

Example : Electric flux through a cube

1n̂2n̂3n̂

4n̂

5n̂

6n̂

L

E

221 180cosˆ

1ELELAnEE

222 0cosˆ

2ELELAnEE

090cos2

6543 ELEEEE

06

1

i

i EE i

Calculating Electric Flux

Example : Electric flux through a sphere

+

+q

r=0.20 m

Ad

q=3.0 CA=2r2

C/mN104.3

m) )(0.20N/C)(4 1075.6(

N/C1075.6

(0.20m)

C100.3)C/mN100.9(

4

//ˆ//,

25

25E

5

2

6229

20

EA

r

qE

AdnEEE

Gauss’s Law

Preview: The total electric flux through any closed surface (a surface enclosing a definite volume) is proportional to the total (net) electric charge insidethe surface.

Case 1: Field of a single positive charge q

+

q

r=R

E

E

204

1

R

qE

A sphere with r=R

at r=R

surfaceE

0

2

0

)4(4

1

q

RR

qEAE

The flux is independent of the radius R ofthe surface.

Gauss’s Law

Case 2: More general case with a charge +q

+

q

E

A

+

EcosE

EnE

A

cos)( Asurface perpendicularto E

AEAEE cos

0q

E

Gauss’s Law Case 3: An closed surface without any charge inside

0E

+

Electric field lines that go in come out.Electric field lines can begin or end insidea region of space only when there is chargein that region.

Gauss’s law

The total electric flux through a closed surface is equal to the total(net) electric charge inside the surface divided by

i ii iinside

insideE EEqQ

Q ,;

0

Applications of Gauss’s Law

Example 15.8: Field of an infinite plane sheet of charge

++

+

+

+

+

+++ +

+

density charge:

Gaussian surface

E E

EEE sheet the

AQinside

0

)(2A

EAE

02

E

two end surfaces

Note: 0

2 0

xEx

0 2 0

xEx

Gauss’s Law

Example : Field between oppositely charged parallel conducting plane

+++++++++

---------

plate 1 plate 2

2E

1E

1E

1E

E

2E

2E

ab

c

S1

S2 S3

S4

Solution 1:

No electric fluxon these surfaces

surface)left (0

surface)(right :00

1

E

EA

EAS

surface)right (0

surface)(left :00

4

E

EA

EAS

Solution 2:

inward flux

outward flux

At Point a : 02121

EEEEE

b :

c :

0021 2

2

EEE

02121

EEEEE

Trajectory of a charged particle in a uniform electric field

Application of Gauss’s Law


Example : Field of an infinite line of charges

line chargedensity

Gaussian surfacechosen according to symmetry

EEE ,

Ad

enclQ

surfaceGaussian lcylindrica on theEE

0

)2(

rEE

rE

02

1


Example : Field of a uniformly charged sphere Gaussian surface

r=R

R

++

++

+ +

++

+ +

+

+

3

34

density charge

R

Q

03 /)

3

4(: rEARr

30

032

4

1

/)3

4()4(

R

QrE

rrE

204

1:

R

QERr

20

0

2

4

1

)4(:

r

QE

QrErR


Example 15.7 : Field of a charged spherical shellGaussian surface

+ +

++

+ +

+

+00)4(:

0

2 EQ

rEEAar inside

2000

2

4

1)4(:

r

QE

QQrErb inside

ab

Total charge on the shell = Q

Applications of Gauss’s Law Charge distribution and field

• The charge distribution the field

• The symmetry can simplify the procedure of application

Electric field by a charge distribution on a conductor

• When excess charge is placed on a solid conductor and is at rest, it resides entirely on the surface, not in the interior of the material (excess charge = charge other than the ions and free electrons that make up the material conductor

A Gaussian surface inside conductor

Charges on surface

Conductor


Electric field by a charge distribution on a conductor (cont’d)

A Gaussian surface inside condactor

Charges on surface

Conductor

• Draw a Gaussian surface inside of the conductor• E=0 everywhere on this surface (inside conductor)• The net charge inside the surface is zero• There can be no excess charge at any point within a solid conductor• Any excess charge must reside on the conductor’s surface• E on the surface is perpendicular to the surface

Gauss’s law

E at every point in the interior of a conducting materialis zero in an electrostatic situation (all charges are at rest).If E were non-zero, then the charges would move

Charges on Conductors

Case 1: charge on a solid conductor resides entirely on its outer surface in an electrostatic situation

++

++

++++

+++++ + +

+

Case 2: charge on a conductor with a cavity

++

++

++++

+++++ + +

+ Gauss surface

The electric field at every point within a conductoris zero and any excess charge on a solid conductor is located entirely on its surface.

If there is no charge within the cavity, the netcharge on the surface of the cavity is zero.

Charges on Conductors

Case 3: charge on a conductor with a cavity and a charge q inside the cavity

++

++

++++

+++++ + +

+

Gauss surface

+--- --

--

• The conductor is uncharged and insulated from charge q.• The total charge inside the Gauss surface should be zero from Gauss’ law and E=0 on this surface. Therefore there must be a charge –q distributed on the surface of the cavity.• The similar argument can be used for the case where the conductor originally had a charge qC. In this case the total charge on the outer surface must be q+qC after charge q is inserted in cavity.

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