Contents 2 電場

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2 電場

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Contents

2-1電場的定義

2-2電力線 Lines of force

• 2-3 Electric-field vector of a point charge

2-4 電場的計算

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2-1 電場的定義

•電力: q與q

0之間的電力 or

q在q0所建立的電場中受到的電力

m) (V

(N/C)

0

q E F

 

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2-2電力線 Lines of force

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點電荷

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帶電平板

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二正電荷與電雙極

q

0

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2-3 Electric-field vector of a point charge

• Follow Example 21.6 to see the

vector nature of the

electric field. Use

Figure 21.19 at the

right.

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Example 21.6 Electric-field vector of a

point charge

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2-4 電場的計算

電雙極

均勻帶電圓環

均勻帶電圓盤

• Field of a charged line segment

• Electron in a uniform field

The electric field on an oil drop

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電雙極

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] 2 )

1 ( 2 )

1 4 [(

) 2 / (

4 1 )

2 / (

4 1

4 1 4

1

2 2

2 0

2 0

2 0

2 0

2 0

 

 

z d z

d z

q

d z

q d

z

q

r q r

q E E

E











兩電荷的電場相加

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dipole) (electric

2 1

2 1 2

4

...)]

1 ( ...)

1 4 [(

...)]

)

! 1 ( 2 1 2

( ) ...)

! 1 ( 2 1 2

4 [(

3 0

3 0

2 0

2 0

2 0

z E p

z qd z

d z

q

z d z

d z

q

z d z

d z

q











) (

moment dipole

elcectric 電雙極矩

p

電雙極的電場

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Electric dipoles

An electric dipole is a pair of point

charges having

equal but opposite sign and separated by a distance.

Figure 21.30 at the right illustrates the water molecule,

which forms an electric dipole.

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Force and torque on a dipole

• Figure 21.31 below left shows the force on a dipole in an electric field.

electric dipole moment

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Potential energy of a dipole

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) (

4 1

4 1 4

1

2 2

0

2 0

2 0

R z

dE ds

r ds r

dE dq

ds dq

 







均勻帶電圓環

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2 / 3 2 2

0 2

/ 3 2 2

0

2 2 0

/ 3 2 2

0

2 / 3 2 2

0

2 / 1 2 2

) (

4 )

( 4

) 2

(

) (

cos 4

) (

cos 4

) cos (

, cos

R z

qz R

z

R z

R ds z

dE z E

R ds z

dE z

R z

z r

dE z dE

R

 

 

 

 

 

 







 



 

均勻帶電圓環的電場

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• If z » R, z

2

R

2

z

2

charge) point

a (like

4 1

) (

4

2 0

2 / 3 2 2

0

z q

R z

E qz





 

極限情形

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rdr dA

dq     2 

 

 

R

z r r dr

dE z E

r z

rdr dE z

r z

rdr dE z

0

2 / 3 2

2 0

2 / 3 2 2

0

2 / 3 2 2

0

) 2 ( )

4 (

) (

2 4

) (

4

2



均勻帶電圓盤

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2 0 0 2

0 2 / 1 2

2

0

0

2 / 3 2

2 0

) 2 1

2 (

2 ] / 1

) [ (

4

) 2 ( )

4 (

 

 

 

R z

z r z

z

dr r

r z z

dE E

R R

均勻帶電圓盤的電場

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Field of a charged line segment

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Limiting cases

For x >> a

For very long segment (a >> x )

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Electron in a uniform field

• Example 21.7 requires us to find the force on a charge that is in a known electric field. Follow this example using Figure 21.20 below.

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Example 21.7 Electron in a

uniform field

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Solution

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The electric field on an oil drop

C e N

g E R

F E

e g

R

F

g e

/ 10

65 . 9 1

4

) 3 3 (

4

6 3

3

A drop of R = 2.76m has 3

excess electrons,  = 920kg/m

3

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Figure

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References

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