2 電場
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2-1 電場的定義
•電力: q與q
0之間的電力 orq在q0所建立的電場中受到的電力
m) (V
(N/C)
0
q E F
2-2電力線 Lines of force
點電荷
帶電平板
二正電荷與電雙極
q
02-3 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.
Example 21.6 Electric-field vector of a
point charge
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電雙極
] 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
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
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.
Force and torque on a dipole
• Figure 21.31 below left shows the force on a dipole in an electric field.
electric dipole moment
Potential energy of a dipole
) (
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
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
• If z » R, z
2 R
2 z
2charge) point
a (like
4 1
) (
4
2 0
2 / 3 2 2
0
z q
R z
E qz
極限情形
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
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
Field of a charged line segment
Limiting cases
• For x >> a
• For very long segment (a >> x )
→
→
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.
Example 21.7 Electron in a
uniform field
Solution
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
