• 沒有找到結果。

# 100 學年上學期高二物 理

N/A
N/A
Protected

Share "100 學年上學期高二物 理"

Copied!
26
0
0

(1)

(2)

3 Gauss’ Law

(3)

### lightning strike ?

(4)

3-1 A New Look at Coulomb’s Law

Using Gauss’s law to take advantage of special

symmetry situations

Gaussian surfaces

(5)

3-2 Flux (

### 通量 / 流量 )

For a fluid

A v

vA A

v  

( cos ) cos

m/s × m2 = m3/s

(6)
(7)

3-3 Flux of an Electric Field

For a flat surface

For a arbitrary (asymmetric) surface

A E

EA A

E  

( cos ) cos

### 

E A E dA

(8)

An

arbitrary Gaussian surface

(9)

Ex.3-1 A cylindrical Gaussian surface

0

0

### 

EA EA

A d E

A d E

A d E

A d E

c b

a

(10)

Ex.3-2 A nonuniform electric field and a Gaussian cube

3 .0 ˆˆ 4 .0 ˆ

(3 .0 ˆˆˆ 4 .0 ) ( )

r

E x i j

d A d A i

E d A

x i j d A i

 

### 

(11)

2

(3.0 ˆˆˆ 4.0 ) ( )

[(3.0 )( ) ˆˆˆˆ (4.0)( ) )

(3.0 0) 3.0

3.0 3.0 9.0 36 /

r E dA

xi j dAi

x dA i i dA j i

xdA xdA

dA dA N m C

 

 

(12)

2

left face: ˆ

3.0 1.0 3.0 12 /

l

dA dAi

dA dA N m C

 

 

### 

 

2

(3.0 ˆˆˆ 4.0 ) ( )

[(3.0 )( ) ˆˆˆˆ (4.0)( )( )]

(0 4.0 ) 4.0 16 /

t xi j dAj

x dA i j dA j j

dA dA N m C

 

 

(13)

3-4 Gauss’ Law

Flux 

enclosed charge

q enc

A d E

## 

0 0

(14)

3-5 Gauss’ Law and Coulomb’ Law

From G.L. to C.L.

2 0

2 0

0

0 0

4 1

) 4

(

r E q

q r

E

q dA

E

q EdA

A d E



### 

(15)

3-6 A Charged Isolated Conductor

The external electric field

qenc

A d

E

### 

0

0 0

,

E A

EA

EA A

q enc

(16)
(17)

3-7 Applying Gauss’ Law:

Cylindrical Symmetry

E r

h rh

E

rh A

h q enc

0 0

2 2

2

= ,



(18)

Ex.3-5 A lightning strike

m r E

6

) 10

3 ( 2

10 1

2

6 0

3 0





(19)

3-8 Applying Gauss’ Law:

Planar Symmetry

0

0 ( ) 2

E A

EA EA

EdA A

d E

(20)

Two Conducting Plates

E  2 1

0 0

(21)

ex.3-6

Two‖nonconducting sheets

(22)

3-9 Applying Gauss’

Law: Spherical Symmetry

) (

0

) 4 (

1

2 0

R r

E

R r r

E q



The Shell Theorems

(23)

A spherical distribution

) 4 (

1

2 0

R r r

E q



(24)

Ex.3-7 The electric field vs. r

C r N

E q

C e

Ze q

/ 10

3.0 4 =

1

10 264

. 1 )

79 (

21 2

0

17



(25)

R r q r

E q

R q r

q R

r q

q

4 ) 4 (

1 3 43

4

3 0

2 0

3 3 3

3





(26)

0 0

0

0 0

0

1

e n c e n c

S V

e n c

E d A q E d A q

E d A E d V

E d V q d V

E

 

  

 

  

 

 

3-10 Gauss’ Law in Differential Form

Total charge

Charge density Divergence

Basic Law of the Hong Kong Special Administrative Region of the People’s Republic of

(1) principle of legality - everything must be done according to law (2) separation of powers - disputes as to legality of law (made by legislature) and government acts (by

1.8 Teachers should take every opportunity to attend seminars and training courses on special education to get a better understanding of the students’ special needs and

What is the danger if your hair suddenly stands up?... Lightning bolt

• Using Gauss’s law to take advantage of special. symmetry