22-1 Electromagnetism The new science of electromagnetism(the combination Of electrical and magnetic...

22-1 Electromagnetism

The new science of electromagnetism(the combination Of electrical and magnetic phenomena) wasdeveloped.

22 Electric Charge

1 Electric Charge is an intrinsic characteristic of the fundamental particles making up those objects.

2 Two kinds of charge: positive charge and negative charge. The object contains equal amounts of these two kinds of charge is said to be electrically neutral.

22-2 Electric Charge

Charge with the same electrical sign repel eachother, and chargeswith opposite electrical signs attract each other.

Such as metals,tap water,andhuman body,some of the negative charge can move rather freely.

Conductors:

Insulators: Such as glass,chemically pure water ,and plastic,noneof the charge can move freely.

22-3 Conductors and Insulators

Semiconductor: Such as silicon and germanium,are material that are intermediate between conductors and Insulators.

Superconductors: They present no resistance to the movement of electric charge through them.

atom

nucleus

negative charge electrons

positively charge proton

electrically neutralneutron

The properties of conductors and insulates are due to the structure and electrical nature atoms.

CHECKPOINTCHECKPOINT

How can we knowthe electrostatic force between small electric chargeq1 and q2 at rest andseparated by adistance r at this 3situations?

22-4 Coulomb’s Law

221 ||||

r

qqkF

221 ||||

r

qqkF

K is a constant.For practical reasons,theSI unit of charge is derived from the SI unit of electric current,the ampere(A).

The SI unit of charge is the coulomb (C). It is defined in terms of the unit of the unit of current ,the ampere (A),as the charge passing a particular point in 1 second when there is a current of 1 ampere at that point.

The Coulomb and Ampere

For historical reasons (and because doingso simplifies many other formulas),the electrostatic constant k of Eq.22-1 is usually written 1/4πε0.The Coulomb’slaw becomes

221

0

||||

4

1

r

qqF

πε

221

0

||||

4

1

r

qqF

πε

Coulomb’s law describes the electrostatic force between small (point) electric charge q1 and q2 atrest (or nearly at rest) and separated by a distance r

221

0

||||

4

1

r

qqF

πε

221

0

||||

4

1

r

qqF

πε

Here:ε0=8.85×10 － 12C2/Nm2 1/4 πε0=k=8.99×109Nm2/C2

The force of attraction or repulsion between point charges at rest acts along the line joining the two charges.

How about the situation if there are more then two charges are present?

A shell of uniform charge attracts or repels a repels a charged particle that is outside the shell as if all the shell’s charge were concentrated at its center.

The two shell theorems for electrostatics are:

If a charged particle is located inside a shell of uniform charge,there is no net electrostatic force on the particle from the shell.

Sample Problem 22-1

N

m

CC

cmN

R

qqF

24

2

1919

229

221

012

1015.1

)0200.0(

)1020.3)(1060.1(

)/1099.8(

||||

4

1

N

m

CC

cmN

R

qqF

24

2

1919

229

221

012

1015.1

)0200.0(

)1020.3)(1060.1(

)/1099.8(

||||

4

1

(a)

Step one:Step one:

Step two:Step two: iNF ˆ1015.1 2412

iNF ˆ1015.1 2412

(b)

Step one:Step one:

Step two:Step two:

N

m

CC

CmN

R

qqF

24

22

1919

229

231

013

1005.2

0200.043

1020.31060.1

/1099.8

434

1

N

m

CC

CmN

R

qqF

24

22

1919

229

231

013

1005.2

0200.043

1020.31060.1

/1099.8

434

1

iNF ˆ1005.2 2413

iNF ˆ1005.2 2413

iN

iNiN

FFF net

ˆ1000.9

ˆ1005.2ˆ1015.125

2424

1312,1

iN

iNiN

FFF net

ˆ1000.9

ˆ1005.2ˆ1015.125

2424

1312,1

9.00×10 － 25 and 00

Second key idea

NR

qqF 24

2

41

014 1005.2

)43

(

||||

4

1 N

R

qqF 24

2

41

014 1005.2

)43

(

||||

4

1

1412,1 FFF net

1412,1 FFF net

(c)

Method 1

Step one:Step one:

Step two:Step two:

Step three:Step three:

jFiFF ˆsinˆcos 141414

jFiFF ˆsinˆcos 141414

jNiNF ˆ10775.1ˆ10025.1 242414

jNiNF ˆ10775.1ˆ10025.1 242414

jNiN

jNiN

iN

FFF net

ˆ1078.1ˆ1025.1

ˆ10775.1ˆ10025.1

ˆ1015.1

2425

2424

24

1412,1

jNiN

jNiN

iN

FFF net

ˆ1078.1ˆ1025.1

ˆ10775.1ˆ10025.1

ˆ1015.1

2425

2424

24

1412,1

Method 2

Step one:Step one:

Step two:Step two:

N

NN

FFFFF xxxnet

25

02424

01412,14,12,,1

1025.1

60cos1005.21015.1

60cos

N

NN

FFFFF xxxnet

25

02424

01412,14,12,,1

1025.1

60cos1005.21015.1

60cos

N

N

FFFF yyynet

24

024

014,14,12,,1

1078.1

60sin1005.2

60sin0

N

N

FFFF yyynet

24

024

014,14,12,,1

1078.1

60sin1005.2

60sin0

Step three:Step three:

Step four:Step four:

N

FFF ynetxnetnet

24

2,,1

2,,1,1

1078.1

0

,,1

,,11 0.86tan

xnet

ynet

F

F 0

,,1

,,11 0.86tan

xnet

ynet

F

F

000 0.941800.86 000 0.941800.86

“electrical fluid” is also not continuous but is made up of multiples of a certain elementary charge. Any positive or negative charge q that can be detected can be written as and the elementary charge has the value:

q=n e, n=±1,±2,±3,…,

e=1.60×10-19 C.

22-5 Charge Is Quantized

Particle Symbol Charge

Electron e or e- -e

Proton P +e

Neutron n 0

When a physical quantity such as charge can have only discrete values rather then any value, we say that the quantity is quantized.

Sample Problem 22-4Sample Problem 22-4

(a)

N

m

CCmN

r

eF

14

100.4

1060.1/1099.8

4

1

215

219229

2

2

0

N

m

CCmN

r

eF

14

100.4

1060.1/1099.8

4

1

215

219229

2

2

0

(b)

N

m

kgkgmN

r

mGF p

35

215

2272211

2

2

102.1

100.4

1067.1/1067.6

N

m

kgkgmN

r

mGF p

35

215

2272211

2

2

102.1

100.4

1067.1/1067.6

Initially sphere A has a charge of –50e and sphere B has a chargeof +20e.The spheres are made ofconducting and are identical in size.If the spheres then touch,what is theresulting charge on sphere A?

QuestionQuestion

This hypothesis of conservation of charge has stood up under close examination, both for large-scale charge bodies and for atoms, nuclei, and elementary particles.

22-6 Charge is conserved