Chapter 19 Electric Charge and Electric Field
电磁学
(Electromagnetism)
The combination of electrical and
magnetic phenomena
Chapter 19 Electric Charge and Electric Field
物理学的第二次大综合法拉第 的电磁感应定律：电磁一体麦克斯韦 电磁场统一理论（ 19世纪中叶）
赫兹 在实验中证实电磁波的存在，光是电磁波,
技术上的重要意义：发电机、电动机、无线电技术等,
库仑 定律,电荷与电荷间的相互作用奥斯特 的发现,电流的磁效应，安培发现电流与电流间的相互作用规律,
Chapter 19 Electric Charge and Electric Field
Chapter 19 Electric Charge and
Electric Field
1,Static Electricity; Electric Charge and Its
Conservation; Insulators and Conductors;
Induced Charge
2,Coulomb’s Law
3,The Electric Field and its Calculations
4,Electric Field and Conductors
5,Electric Dipoles
Chapter 19 Electric Charge and Electric Field
New Words and Expressions
static charge 静电荷
quantized 量子化的
elementary charge 基本电荷
conductor 导体
insulator 绝缘体
induce 感应
Coulomb 库仑
point charge 点电荷
permittivity of free space 真空电容率
electric field 静电场
test charge 试验电荷
electric dipole 电偶极子
Chapter 19 Electric Charge and Electric Field
Rub a plastic ruler (a) and bring it close (b) to some
tiny pieces of paper.
19-1&19-2&19-3&19-4,Electric Charge and Its
Conservation; Insulators and conductors;
Induced Charge (P456-460)
1 Static electricity
Chapter 19 Electric Charge and Electric Field
1,Electric charge (电荷 )
It is an intrinsic character of the fundamental
particles making up those objects.
It can be either positive or negative,Charges
with the same sign repel each other and
charges with opposite signs attract each other.
That is,unlike charges attract,like charges
repel (同号相斥,异号相吸 ),p457
一个物体能够吸引轻微的物体，这个物体就带有电荷，也称带电体。
Chapter 19 Electric Charge and Electric Field
The net amount of electric charge produced in
any process is zero.
3,The SI unit of charge is the Coulomb,(p461)
The SI unit of charge is the coulomb (C).
2,Law of conservation of electric charge (p457)
4,Electric charge is quantized (p461)
q=n|e|,where n is a positive or negative
integer,and e is a constant of nature called the
elementary charge (基本电荷 ),1|e|=1.60× 10-19C.
物体带电量都是 基本电荷 的整数倍 。 电荷的这种特性叫电荷的 量子性 (quantized)。
Chapter 19 Electric Charge and Electric Field
Conductors are materials in which some of
negative charge can move freely,
5,Conductors and Insulators (p458)
nonconductors（ insulators），
semiconductors,superconductors
6,The methods to get electric charges p459-460
电荷从一个物体，转移到另一个物体。
1) Charged due to rubbing (摩擦起电 )
Chapter 19 Electric Charge and Electric Field
2) Induced Charge (感应起电 )
A positively charged object is
brought close to a neutral
metal rod,Neutral metal rod
metal rod still neutral,but
with a separation of charge
Charges move and
leave a positive charge
at the opposite end.
It is said to be induced (感应 ).
Chapter 19 Electric Charge and Electric Field
19-5,Coulomb's Law (P460-P464)
Chapter 19 Electric Charge and Electric Field
1773年发表有关材料强度的论文，所提出的计算物体上应力和应变分布情况的方法沿用到现在，是结构工程的理论基础。
1777年开始研究静电和磁力问题。当时法国科学院悬赏征求改良航海指南针中的磁针问题。库仑认为磁针支架在轴上，必然会带来摩擦，提出用细头发丝或丝线悬挂磁针。研究中发现线扭转时的扭力和针转过的角度成比例关系，从而可利用这种装置测出静电力和磁力的大小，这导致他发明扭秤。 1779年对摩擦力进行分析，提出有关润滑剂的科学理论。还设计出水下作业法，类似现代的沉箱。 1785-1789年，用扭秤测量静电力和磁力，导出著名的库仑定律。
库仑 ——法国工程师、物理学家。 1736年 6月 14 日生于法国昂古莱姆。 1806年 8月 23日在巴黎逝世。
早年就读于美西也尔工程学校。离开学校后，进入皇家军事工程队当工程师。法国大革命时期，库仑辞去一切职务，到布卢瓦致力于科学研究。法皇执政统治期间，回到巴黎成为新建的研究院成员。
Chapter 19 Electric Charge and Electric Field
1,Point charge (点电荷 ) (p461)
当带电体的线度与它到其它带电体之间距离或到研究点之间的距离相比足够小时 (d<<r),可忽略其大小,将电荷看成集中于一点的带电体,称 点电荷,
The sizes of objects are much more smaller
than the distance between them.
With the torsion balance (扭称实验 )Coulomb
established the Coulomb’s law of electrostatic
interaction:
2,Coulomb’s Law
Chapter 19 Electric Charge and Electric Field
The force between two point charges at rest
was inversely proportional to the square of the
distance between them and proportional to the
product of the charges.
1q 12r
12r
21F
12F
d21F?
12F
2q?
1q 2q
Chapter 19 Electric Charge and Electric Field
21122
12
21
12 Fer
qqkF
229 CmN109 8 7 5 5.8kSI制
k is a proportionality constant,
（ 为真空电容率 permittivity of free space ）0?
122
12
21
0
12 π4
1 e
r
qqF
0π4
1
k
令
Chapter 19 Electric Charge and Electric Field
Direction (p460)：
The direction of the electric force is always along
the line joining the two objects,If the two charges
have the same sign,the force on either object is
directed away from the other,If the two charges
have opposite signs,the force on one is directed
toward the other.
Chapter 19 Electric Charge and Electric Field
(1) It is an exp,Law,holds both for macroscopic &
microscopic,only holds for,point charge” model.
(2) There are four basic physical quantities for
electromagnetic quantity in the SI system,They
are length (m),mass(kg),time(s),current(A).
(3) principle of superposition p462,The net force
on any one of them will be the vector sum of the
forces due to each of the others.
i
iFF 11
Vector
sum
Description:
Chapter 19 Electric Charge and Electric Field
Example (p462),The electron and proton of a
hydrogen atom are separated (on the average)
by a distance of about 5.3x10-11 m,Find the
magnitude of the electric force that each particle
exerts on the other.
q1 =-1.60x10-19 C,q2 =1.60x10-19 C,
r = 5.3x10-11 m
2
2
22 19
98
22 11
1,6 1 0
8,9 9 1 0 8,2 1 0
5,3 1 0
Nm
ee C
Ce
F k N
r m
From Coulomb’s law
Solution:
Chapter 19 Electric Charge and Electric Field
例,经典的氢原子中电子绕核旋转，质子质量 Mp =
1.67?10-27 kg,电子质量 me= 9.11?10-31 kg,求电子与质子间的库仑力 Fe与万有引力 F引 之比。
解,库仑力大小
2
21
04
1
r
qqF
e 2
2
04
1
r
e
万有引力大小
2
21
r
mmGF?
引 2
mG ep?
ep
e
mm
e
GF
F 2
04
1
引
391026.2
（微观领域中,万有引力比库仑力小得多,可 忽略 不计,）
Chapter 19 Electric Charge and Electric Field
19-6&19-7&19-11 Electric Field (静电场 )
(p464-471,476-477)
Coulomb’s interaction is at a distance,How does
q1,know” of the presence of q2? How the force of
q1 acts on the point charge q2?
实验证实了两静止电荷间存在相互作用的静电力，
但其相互作用是怎样实现的？
电 荷电 场电 荷场是一种特殊形态的物质实物物 质场
Chapter 19 Electric Charge and Electric Field
In the 19th century,British experimental physicist
Michael Faraday proposed the electric field
Charge q1 Electric Field 1 Electric Field
2
Charge q2
1,The Electric Field (P464):
vector field It is similar to gravitational field！
2,The Basic Feature of Electric Field
Giving an acting force to any charge
in it (对放其内的任何电荷都有作用 力 ) ;E?
The electric force does work on moving
charge (电场力对移动电荷作 功 ) V ;
Chapter 19 Electric Charge and Electric Field
3 Definition of electric field (p464)
(1)Test charge(试验电荷 )q0 (P464)
A charge so small that the force it exerts does
not significantly alter the distribution of the
charges that create the field being measured.
描写电场性质的物理量。
试验电荷为点电荷、且足够小,故对原电场几乎无影响
Chapter 19 Electric Charge and Electric Field
0q?
F?
：场源电荷Q?
0q?
：试验电荷
q0
2q0
3q0
nq0
F0
2F0
3F0
nF0
….,…...
场源电荷 Q，场点处检验电荷 q0在电场中受力 F。
0q
F
E
Definition of electric field,The force exerted on a
tiny positive test charge at that point divided by
the magnitude of the test charge q.
F?
0q
F?2
02q
F?3
03q
E
Chapter 19 Electric Charge and Electric Field
1) The electric field depends only on the,field
charges” and their distribution,The presence of
test charge does also not alter the electric field.
Discussion:
2) Electric field is a vector function of space
its SI Unit,N/C V/mor),,,( zyxEE
2）电场中某点的电场强度与试验电荷的电量无关。
1) 是一个矢量,
3) Note:
EqF3） 电荷 在电场中受的静电力q
E?
Chapter 19 Electric Charge and Electric Field
4,The Calculation of Electric Field (P465-P468)
1) Electric Field of A Single Point Charge,(点电荷的电场强度 ) p465
To find the electric
field due to a point
charge q,we put a
positive test charge q0
at that point,From
Coulomb’s law：
Q 0
qr?
E?
r?Q
0q
E?
0q
FE
02
0
0
04
1 r
rq
Qq?
02
04
1 r
r
Q?
Chapter 19 Electric Charge and Electric Field
与 方向一致； rerQqFE?
2
00 π 4
1
讨论
E? r?
与 方向相反；Q<0，
Q>0,E? r?
E? Q? Q?E?
Chapter 19 Electric Charge and Electric Field
2) Superposition applies to electric fields （ 场强叠加原理 ） p466
1q
2q
3q
0q
1r
1F
2r
3r
2F
3F
To find the net electric
field due to more than
one point charge,we
place a positive test
charge q0 near n point
charges.
From the principle of superposition of,F?
i
iFF
Chapter 19 Electric Charge and Electric Field
q
FE
ni
i
i
ni
i
i
q
F
q
F
1
1
definition:sE'?
i
iEE
or
i
ni
i i
i r
r
qE
1
2
04
—— The Principle of superposition of E?
If there is a distribution of electric charges
(whether they are discrete or continuous),the net
electric field is the vector sum of that of all
charges.
Chapter 19 Electric Charge and Electric Field
3) Electric Dipole (电偶极子 ) (P475-477)
Two charged particles of magnitude Q but of
opposite sign separated by a distance d,such a
configuration (结构 ) is called electric dipole (电偶极子 ).
q? q?
0r
Chapter 19 Electric Charge and Electric Field
lqp
Separated by a distance l,the quantity ql is
called the dipole moment (电偶极矩 ) and it is
represented by the symbol p,The dipole
moment can be considered to be a vector,of
magnitude ql,that points from the negative to
the positive charge.
q? q?
p?
0r
Chapter 19 Electric Charge and Electric Field
i.e,The electric field at the
point P,perpendicular
bisector ( 中垂 线 ) to the
dipole.
EEE
Solution:
How to calculate produced by a dipole?E?
电偶极子轴线的中垂线上一点的电场强度,
q? q?
0r
x
y
B
y
Chapter 19 Electric Charge and Electric Field
q? q?
0r
E?
E
E
r?r
x
y
B
y
e
e
er
q
E?
2
0π 4
1
er
q
E?
2
0π 4
1
202 )
2
( ryrrr
rjyire )2( 0
rjyire )2( 0
Chapter 19 Electric Charge and Electric Field
)
2
(
π 4
1 0
3
0
irjy
r
qE
3
0
0
π 4
1
r
iqrEEE
)
2
(
π 4
1 0
3
0
irjy
r
qE
2/3
2
02
0
0 )
4
(
π 4
1
r
y
iqr
0ry
3
0
0
π 4
1
y
iqr
E
3
0π 4
1
y
p?
q? q?
0r
E?
E
E
r?r
x
y
B
y
e
e
Chapter 19 Electric Charge and Electric Field
Torque on a dipole (in external uniform ) p476,E?
s i ns i n q E llF
s inpE?
Ep
0?n e tF?
The torque makes the dipole rotate towards the
direction of the external electric field 使 P 向和 E 尽量一致的方向转,
F
F
q?
q?
0r
E
Chapter 19 Electric Charge and Electric Field
If the electric charge can be treated as being
distributed continuously,we can divide up a charge
distribution into infinitesimal charges dq,each of
which will act as a tiny point charge.
把带电体看作是由许多个电荷元 dq(可视为点电荷 )组成,然后利用场强叠加原理 。
4) Electric Field Calculations for Any Continuous
Charged Distributions (P468-471):
r
r
dqEdE
QQ
4 20
Chapter 19 Electric Charge and Electric Field
Density of Charge (DC):
电荷 体 密度
V
q
d
d
V
r
eE r
V
d
π 4
1
2
0
点 处电场强度P
q
qd
E?dr?
P
Chapter 19 Electric Charge and Electric Field
q
P
sd
电荷 面 密度
s
q
d
d
s
r
eσ
E r
S
d
π 4
1
2
0
q
ld
电荷 线 密度
l
q
d
d
l
r
e
E r
l
d
π 4
1
2
0
E?dr?
E?dr?
P
Chapter 19 Electric Charge and Electric Field
1.建立坐标系。
2.确定电荷密度,
4.确定电荷元的场
02
0
4
1 r
r
dqEd
5.求场强分量 Ex,Ey。
6 求总场
22
yx EEE
, xx dEE yy dEE
体 dq=? dV,
3.求电荷元电量。
体密度?,面密度?,线密度?
面 dq=? dS,线 dq=? dl。
解题思路及应用举例
Chapter 19 Electric Charge and Electric Field
例 1,long line of charge,Determine the magnitude of
the electric field at any point P a distance x from a very
long line of uniformly distributed charge,均匀带电直线长为 2l,带电量 q,求中垂线上一点的电场强度 。 P469
SOLUTION:
l
q
2 dydq
02
0
4
1
r
r
dq
Ed
x
yd
l?
l?
qd
E?d'dq
'dE?
xEd
yEd
'd xE?
r
'd yE
o
y
xy
The charge per unit
length (线电荷密度 )
Chapter 19 Electric Charge and Electric Field
Because of the symmetry
(对称性 ),Ey=0
22
yx EEE xE?
xEdE
l
l dE?c o s
r
xc o s
2/122 )( yxr
r
x
r
dqE l
0 2
04
12
l
yx
x d y
0 2/322
0 )(4
2
o
y
xx
yd
l?
l?
qd
E?d'dq
'dE?
xEd
yEd
'd xE?
r
'd yE
y
Chapter 19 Electric Charge and Electric Field
2/12202 lxx
lE
讨论
1,l >>x,无限长均匀带电直线,assume the wire
is extremely long in both directions.
,222 llx xE
02
2,x>>l,无穷远点场强,222 xlx
2
02 x
lE
2
04
2
x
l
2
04 x
q
相当于点电荷的电场。
查积分表
Chapter 19 Electric Charge and Electric Field
例 2 A ring of charge,A thin,ring-shaped object of
radius a holds a total charge Q distributed
uniformly around it,Determine the electric field
at a point P on its axis,a distance x from the
center,正电荷 均匀分布在半径为 的圆环上,计算在环的轴线上任一点 的电场强度,p468-469
x
q
x
o
P
R
Rq
P
Chapter 19 Electric Charge and Electric Field
x
q
y
x
z
o
P
R
r
rer
l
E?
2
0
d
π 4
1
d
EE d 由对称性有 iEE
x
lq dd )
π 2
(
R
q
SOLUTION:
Chapter 19 Electric Charge and Electric Field
x
q
y
x
z
o
R
r
lq dd
rer
l
E?
2
0
d
π 4
1
d
P
)
π 2
(
R
q
c osdd EEE ll x r
x
r
l
2
0π4
d
R
r
lxπ2
0 3
0π 4
d
2322
0 )(π 4 Rx
qx
Chapter 19 Electric Charge and Electric Field
2322
0 )(π 4 Rx
qx
E
x
q
y
x
z
o
R r
lq dd
P?
E?
讨 论
Rx
（ 1）
2
0π 4 x
qE
（点电荷电场强度）
0,0 0 Ex（ 2）
Rx
x
E
2
2,0
d
d
（ 3） R
2
2
R22?
E
o
x
Chapter 19 Electric Charge and Electric Field
例 3 均匀带电薄圆盘轴线上的电场强度,p470-480
有一半径为,电荷均匀分布的薄圆盘,其电荷面密度为,求通过盘心且垂直盘面的轴线上任意一点处的电场强度,
0R
x
P x
y
z
o
0R
Uniformly charged disk.
Charge is distributed
uniformly over a thin
circular disk of radius R0.
The charge per unit area
is,Calculate the
electric field at a point P
on the axis of the disk.
Chapter 19 Electric Charge and Electric Field
2322
0 )(π 4
Rx
xqE
2
0π Rq
E?d
RRq dπ2d
x
P
R
Rd
2/122 )( Rx?2322
0 )(π 4
dd
Rx
xqE
x?
2322
0 )(
d
2 Rx
RxR
x
y
z
o
0R
解 由例 2
SOLUTION:
Chapter 19 Electric Charge and Electric Field
xEE d
)
11
(
2 2
0
22
0 Rxx
x
E
0R
x
y
z
o E?d
R
P
Rd
0
0 2/322
0 )(
d
2
R
Rx
RRx
2322
0 )(
d
2
d
Rx
RxRE
x
Chapter 19 Electric Charge and Electric Field
0Rx
02?
E
0Rx
2
0π4 x
qE
（点电荷电场强度）
讨 论
2
2
02
1
2
2
0
2
11)1(
x
R
x
R
无限大均匀带电平面的电场强度
)
11
(
2 2
0
22
0 Rxx
x
E
Chapter 19 Electric Charge and Electric Field
Main Steps of Calculating Electric Field:
Step1,Choose differential element of charge dq;
Build up the coordinate system;Step3:
Step2,Calculate set up by the dq ;Ed?
Step4:
E?d
Resolving and find out the scalar
integration for (将 分解,求标量积分 ).
Ed?
E?
Step5,Determine the magnitude and direction of and discuss for its results.
E?
Chapter 19 Electric Charge and Electric Field
19-8 Field lines p471-473
1,Electric field lines
A convenient way to visualize field patterns is
to draw lines in the direction of the electric
field,Such lines are called field lines.（ 形象地描述电场的大小和方向的一组有向曲线 ）
A B
AE
B
E?
Chapter 19 Electric Charge and Electric Field
A B
AE
B
E?
1) Field lines begin on positive charges and
terminate on negative charges,Electric field
vector,is tangent to the electric field lines at
each point in space,（ 某点的电场方向是曲线在该点的切线方向,正?负电荷 ）
E?
2) The number of lines per unit area through a
surface perpendicular to the lines is
proportional to the strength of the electric field
in a given region,E is large when the field lines
are close together and small when far apart.
电力线密处场强大，电力线疏处场强小。
BA EE?
Chapter 19 Electric Charge and Electric Field
S
ψE
d
d
E?
dS
dψ
电场线密度,垂直于 的单位面积的电场线的数目,大小等于,
E?
E?
Chapter 19 Electric Charge and Electric Field
点电荷的电场线
a positive point charge
+
a negative point
charge
Chapter 19 Electric Charge and Electric Field
Two charges of opposite sign
+
Chapter 19 Electric Charge and Electric Field
Two equal positive charge
++
Chapter 19 Electric Charge and Electric Field
Unequal charges,+2q and -q
q?q2
Chapter 19 Electric Charge and Electric Field
Two oppositely charged parallel plates
+ + + + + + + + + + + +
Chapter 19 Electric Charge and Electric Field
2,Rules for drawing electric field lines for any
charge distribution,电力线特点电力线始于正电荷,
终止于负电荷,不会在无电荷处中断,电力线为非闭合曲线 。
1) Lines must begin on positive charges (or at
infinity) and must terminate on negative
charges or in the case of excess charge at
infinity,起于正电荷 （ 或,?” 远 ）,止于负电荷
（ 或,?” 远 ）
Chapter 19 Electric Charge and Electric Field
2） The number of lines drawn leaving a positive
charge or approaching a negative charge is
proportional to the magnitude of the charge.
电场线的多少与电荷量有关
3） No two field lines can cross each other.在没有电荷 任何两条电力线不能相交
1E
2E
Chapter 19 Electric Charge and Electric Field
19-9.Electric Fields and Conductors P473-474
导体内部无宏观电荷的定向移动，导体处在静电平衡状态。
0E
+
+
+
+
+
+
+
+
＇E?
0E
0?E?
1.静电平衡 Static situation
Chapter 19 Electric Charge and Electric Field
00 ＇EEE
导体内电场强度 外电场强度 感应电荷电场强度
1) 导体内部任意一点的场强为 0.
The electric field inside a conductor is zero.
Chapter 19 Electric Charge and Electric Field
2) 静电平衡时，场强方向与导体表面垂直。
The electric field is always perpendicular to the
surface outside of a conductor.
如果场强不垂直于表面，
电场力继续移动电荷，不满足静电平衡条件。
Chapter 19 Electric Charge and Electric Field
in response to this force until they reached
positions where no net force was exerted on
them parallel to the surface,that is,until the
electric field was perpendicular to the surface.
If there were a
component of E parallel
to the surface,electrons
at the surface would
move along the surface
Chapter 19 Electric Charge and Electric Field
1)屏蔽外电场
E?
外电场空腔导体可以屏蔽外电场,使空腔内物体不受外电场影响,这时,整个空腔导体和腔内的电势也必处处相等,
E?
空腔导体屏蔽外电场
2 静电屏蔽 Electrostatic Shielding
Chapter 19 Electric Charge and Electric Field
q?
接地空腔导体将使外部空间不受空腔内的电场影响,
q
2)屏蔽腔内电场
+
+
++
+
+
+
+
q
Chapter 19 Electric Charge and Electric Field
Chapter 19 Electric Charge and Electric Field
Homework,page 480,12
page 481,42; 48; 65
电磁学
(Electromagnetism)
The combination of electrical and
magnetic phenomena
Chapter 19 Electric Charge and Electric Field
物理学的第二次大综合法拉第 的电磁感应定律：电磁一体麦克斯韦 电磁场统一理论（ 19世纪中叶）
赫兹 在实验中证实电磁波的存在，光是电磁波,
技术上的重要意义：发电机、电动机、无线电技术等,
库仑 定律,电荷与电荷间的相互作用奥斯特 的发现,电流的磁效应，安培发现电流与电流间的相互作用规律,
Chapter 19 Electric Charge and Electric Field
Chapter 19 Electric Charge and
Electric Field
1,Static Electricity; Electric Charge and Its
Conservation; Insulators and Conductors;
Induced Charge
2,Coulomb’s Law
3,The Electric Field and its Calculations
4,Electric Field and Conductors
5,Electric Dipoles
Chapter 19 Electric Charge and Electric Field
New Words and Expressions
static charge 静电荷
quantized 量子化的
elementary charge 基本电荷
conductor 导体
insulator 绝缘体
induce 感应
Coulomb 库仑
point charge 点电荷
permittivity of free space 真空电容率
electric field 静电场
test charge 试验电荷
electric dipole 电偶极子
Chapter 19 Electric Charge and Electric Field
Rub a plastic ruler (a) and bring it close (b) to some
tiny pieces of paper.
19-1&19-2&19-3&19-4,Electric Charge and Its
Conservation; Insulators and conductors;
Induced Charge (P456-460)
1 Static electricity
Chapter 19 Electric Charge and Electric Field
1,Electric charge (电荷 )
It is an intrinsic character of the fundamental
particles making up those objects.
It can be either positive or negative,Charges
with the same sign repel each other and
charges with opposite signs attract each other.
That is,unlike charges attract,like charges
repel (同号相斥,异号相吸 ),p457
一个物体能够吸引轻微的物体，这个物体就带有电荷，也称带电体。
Chapter 19 Electric Charge and Electric Field
The net amount of electric charge produced in
any process is zero.
3,The SI unit of charge is the Coulomb,(p461)
The SI unit of charge is the coulomb (C).
2,Law of conservation of electric charge (p457)
4,Electric charge is quantized (p461)
q=n|e|,where n is a positive or negative
integer,and e is a constant of nature called the
elementary charge (基本电荷 ),1|e|=1.60× 10-19C.
物体带电量都是 基本电荷 的整数倍 。 电荷的这种特性叫电荷的 量子性 (quantized)。
Chapter 19 Electric Charge and Electric Field
Conductors are materials in which some of
negative charge can move freely,
5,Conductors and Insulators (p458)
nonconductors（ insulators），
semiconductors,superconductors
6,The methods to get electric charges p459-460
电荷从一个物体，转移到另一个物体。
1) Charged due to rubbing (摩擦起电 )
Chapter 19 Electric Charge and Electric Field
2) Induced Charge (感应起电 )
A positively charged object is
brought close to a neutral
metal rod,Neutral metal rod
metal rod still neutral,but
with a separation of charge
Charges move and
leave a positive charge
at the opposite end.
It is said to be induced (感应 ).
Chapter 19 Electric Charge and Electric Field
19-5,Coulomb's Law (P460-P464)
Chapter 19 Electric Charge and Electric Field
1773年发表有关材料强度的论文，所提出的计算物体上应力和应变分布情况的方法沿用到现在，是结构工程的理论基础。
1777年开始研究静电和磁力问题。当时法国科学院悬赏征求改良航海指南针中的磁针问题。库仑认为磁针支架在轴上，必然会带来摩擦，提出用细头发丝或丝线悬挂磁针。研究中发现线扭转时的扭力和针转过的角度成比例关系，从而可利用这种装置测出静电力和磁力的大小，这导致他发明扭秤。 1779年对摩擦力进行分析，提出有关润滑剂的科学理论。还设计出水下作业法，类似现代的沉箱。 1785-1789年，用扭秤测量静电力和磁力，导出著名的库仑定律。
库仑 ——法国工程师、物理学家。 1736年 6月 14 日生于法国昂古莱姆。 1806年 8月 23日在巴黎逝世。
早年就读于美西也尔工程学校。离开学校后，进入皇家军事工程队当工程师。法国大革命时期，库仑辞去一切职务，到布卢瓦致力于科学研究。法皇执政统治期间，回到巴黎成为新建的研究院成员。
Chapter 19 Electric Charge and Electric Field
1,Point charge (点电荷 ) (p461)
当带电体的线度与它到其它带电体之间距离或到研究点之间的距离相比足够小时 (d<<r),可忽略其大小,将电荷看成集中于一点的带电体,称 点电荷,
The sizes of objects are much more smaller
than the distance between them.
With the torsion balance (扭称实验 )Coulomb
established the Coulomb’s law of electrostatic
interaction:
2,Coulomb’s Law
Chapter 19 Electric Charge and Electric Field
The force between two point charges at rest
was inversely proportional to the square of the
distance between them and proportional to the
product of the charges.
1q 12r
12r
21F
12F
d21F?
12F
2q?
1q 2q
Chapter 19 Electric Charge and Electric Field
21122
12
21
12 Fer
qqkF
229 CmN109 8 7 5 5.8kSI制
k is a proportionality constant,
（ 为真空电容率 permittivity of free space ）0?
122
12
21
0
12 π4
1 e
r
qqF
0π4
1
k
令
Chapter 19 Electric Charge and Electric Field
Direction (p460)：
The direction of the electric force is always along
the line joining the two objects,If the two charges
have the same sign,the force on either object is
directed away from the other,If the two charges
have opposite signs,the force on one is directed
toward the other.
Chapter 19 Electric Charge and Electric Field
(1) It is an exp,Law,holds both for macroscopic &
microscopic,only holds for,point charge” model.
(2) There are four basic physical quantities for
electromagnetic quantity in the SI system,They
are length (m),mass(kg),time(s),current(A).
(3) principle of superposition p462,The net force
on any one of them will be the vector sum of the
forces due to each of the others.
i
iFF 11
Vector
sum
Description:
Chapter 19 Electric Charge and Electric Field
Example (p462),The electron and proton of a
hydrogen atom are separated (on the average)
by a distance of about 5.3x10-11 m,Find the
magnitude of the electric force that each particle
exerts on the other.
q1 =-1.60x10-19 C,q2 =1.60x10-19 C,
r = 5.3x10-11 m
2
2
22 19
98
22 11
1,6 1 0
8,9 9 1 0 8,2 1 0
5,3 1 0
Nm
ee C
Ce
F k N
r m
From Coulomb’s law
Solution:
Chapter 19 Electric Charge and Electric Field
例,经典的氢原子中电子绕核旋转，质子质量 Mp =
1.67?10-27 kg,电子质量 me= 9.11?10-31 kg,求电子与质子间的库仑力 Fe与万有引力 F引 之比。
解,库仑力大小
2
21
04
1
r
qqF
e 2
2
04
1
r
e
万有引力大小
2
21
r
mmGF?
引 2
mG ep?
ep
e
mm
e
GF
F 2
04
1
引
391026.2
（微观领域中,万有引力比库仑力小得多,可 忽略 不计,）
Chapter 19 Electric Charge and Electric Field
19-6&19-7&19-11 Electric Field (静电场 )
(p464-471,476-477)
Coulomb’s interaction is at a distance,How does
q1,know” of the presence of q2? How the force of
q1 acts on the point charge q2?
实验证实了两静止电荷间存在相互作用的静电力，
但其相互作用是怎样实现的？
电 荷电 场电 荷场是一种特殊形态的物质实物物 质场
Chapter 19 Electric Charge and Electric Field
In the 19th century,British experimental physicist
Michael Faraday proposed the electric field
Charge q1 Electric Field 1 Electric Field
2
Charge q2
1,The Electric Field (P464):
vector field It is similar to gravitational field！
2,The Basic Feature of Electric Field
Giving an acting force to any charge
in it (对放其内的任何电荷都有作用 力 ) ;E?
The electric force does work on moving
charge (电场力对移动电荷作 功 ) V ;
Chapter 19 Electric Charge and Electric Field
3 Definition of electric field (p464)
(1)Test charge(试验电荷 )q0 (P464)
A charge so small that the force it exerts does
not significantly alter the distribution of the
charges that create the field being measured.
描写电场性质的物理量。
试验电荷为点电荷、且足够小,故对原电场几乎无影响
Chapter 19 Electric Charge and Electric Field
0q?
F?
：场源电荷Q?
0q?
：试验电荷
q0
2q0
3q0
nq0
F0
2F0
3F0
nF0
….,…...
场源电荷 Q，场点处检验电荷 q0在电场中受力 F。
0q
F
E
Definition of electric field,The force exerted on a
tiny positive test charge at that point divided by
the magnitude of the test charge q.
F?
0q
F?2
02q
F?3
03q
E
Chapter 19 Electric Charge and Electric Field
1) The electric field depends only on the,field
charges” and their distribution,The presence of
test charge does also not alter the electric field.
Discussion:
2) Electric field is a vector function of space
its SI Unit,N/C V/mor),,,( zyxEE
2）电场中某点的电场强度与试验电荷的电量无关。
1) 是一个矢量,
3) Note:
EqF3） 电荷 在电场中受的静电力q
E?
Chapter 19 Electric Charge and Electric Field
4,The Calculation of Electric Field (P465-P468)
1) Electric Field of A Single Point Charge,(点电荷的电场强度 ) p465
To find the electric
field due to a point
charge q,we put a
positive test charge q0
at that point,From
Coulomb’s law：
Q 0
qr?
E?
r?Q
0q
E?
0q
FE
02
0
0
04
1 r
rq
Qq?
02
04
1 r
r
Q?
Chapter 19 Electric Charge and Electric Field
与 方向一致； rerQqFE?
2
00 π 4
1
讨论
E? r?
与 方向相反；Q<0，
Q>0,E? r?
E? Q? Q?E?
Chapter 19 Electric Charge and Electric Field
2) Superposition applies to electric fields （ 场强叠加原理 ） p466
1q
2q
3q
0q
1r
1F
2r
3r
2F
3F
To find the net electric
field due to more than
one point charge,we
place a positive test
charge q0 near n point
charges.
From the principle of superposition of,F?
i
iFF
Chapter 19 Electric Charge and Electric Field
q
FE
ni
i
i
ni
i
i
q
F
q
F
1
1
definition:sE'?
i
iEE
or
i
ni
i i
i r
r
qE
1
2
04
—— The Principle of superposition of E?
If there is a distribution of electric charges
(whether they are discrete or continuous),the net
electric field is the vector sum of that of all
charges.
Chapter 19 Electric Charge and Electric Field
3) Electric Dipole (电偶极子 ) (P475-477)
Two charged particles of magnitude Q but of
opposite sign separated by a distance d,such a
configuration (结构 ) is called electric dipole (电偶极子 ).
q? q?
0r
Chapter 19 Electric Charge and Electric Field
lqp
Separated by a distance l,the quantity ql is
called the dipole moment (电偶极矩 ) and it is
represented by the symbol p,The dipole
moment can be considered to be a vector,of
magnitude ql,that points from the negative to
the positive charge.
q? q?
p?
0r
Chapter 19 Electric Charge and Electric Field
i.e,The electric field at the
point P,perpendicular
bisector ( 中垂 线 ) to the
dipole.
EEE
Solution:
How to calculate produced by a dipole?E?
电偶极子轴线的中垂线上一点的电场强度,
q? q?
0r
x
y
B
y
Chapter 19 Electric Charge and Electric Field
q? q?
0r
E?
E
E
r?r
x
y
B
y
e
e
er
q
E?
2
0π 4
1
er
q
E?
2
0π 4
1
202 )
2
( ryrrr
rjyire )2( 0
rjyire )2( 0
Chapter 19 Electric Charge and Electric Field
)
2
(
π 4
1 0
3
0
irjy
r
qE
3
0
0
π 4
1
r
iqrEEE
)
2
(
π 4
1 0
3
0
irjy
r
qE
2/3
2
02
0
0 )
4
(
π 4
1
r
y
iqr
0ry
3
0
0
π 4
1
y
iqr
E
3
0π 4
1
y
p?
q? q?
0r
E?
E
E
r?r
x
y
B
y
e
e
Chapter 19 Electric Charge and Electric Field
Torque on a dipole (in external uniform ) p476,E?
s i ns i n q E llF
s inpE?
Ep
0?n e tF?
The torque makes the dipole rotate towards the
direction of the external electric field 使 P 向和 E 尽量一致的方向转,
F
F
q?
q?
0r
E
Chapter 19 Electric Charge and Electric Field
If the electric charge can be treated as being
distributed continuously,we can divide up a charge
distribution into infinitesimal charges dq,each of
which will act as a tiny point charge.
把带电体看作是由许多个电荷元 dq(可视为点电荷 )组成,然后利用场强叠加原理 。
4) Electric Field Calculations for Any Continuous
Charged Distributions (P468-471):
r
r
dqEdE
4 20
Chapter 19 Electric Charge and Electric Field
Density of Charge (DC):
电荷 体 密度
V
q
d
d
V
r
eE r
V
d
π 4
1
2
0
点 处电场强度P
q
qd
E?dr?
P
Chapter 19 Electric Charge and Electric Field
q
P
sd
电荷 面 密度
s
q
d
d
s
r
eσ
E r
S
d
π 4
1
2
0
q
ld
电荷 线 密度
l
q
d
d
l
r
e
E r
l
d
π 4
1
2
0
E?dr?
E?dr?
P
Chapter 19 Electric Charge and Electric Field
1.建立坐标系。
2.确定电荷密度,
4.确定电荷元的场
02
0
4
1 r
r
dqEd
5.求场强分量 Ex,Ey。
6 求总场
22
yx EEE
, xx dEE yy dEE
体 dq=? dV,
3.求电荷元电量。
体密度?,面密度?,线密度?
面 dq=? dS,线 dq=? dl。
解题思路及应用举例
Chapter 19 Electric Charge and Electric Field
例 1,long line of charge,Determine the magnitude of
the electric field at any point P a distance x from a very
long line of uniformly distributed charge,均匀带电直线长为 2l,带电量 q,求中垂线上一点的电场强度 。 P469
SOLUTION:
l
q
2 dydq
02
0
4
1
r
r
dq
Ed
x
yd
l?
l?
qd
E?d'dq
'dE?
xEd
yEd
'd xE?
r
'd yE
o
y
xy
The charge per unit
length (线电荷密度 )
Chapter 19 Electric Charge and Electric Field
Because of the symmetry
(对称性 ),Ey=0
22
yx EEE xE?
xEdE
l
l dE?c o s
r
xc o s
2/122 )( yxr
r
x
r
dqE l
0 2
04
12
l
yx
x d y
0 2/322
0 )(4
2
o
y
xx
yd
l?
l?
qd
E?d'dq
'dE?
xEd
yEd
'd xE?
r
'd yE
y
Chapter 19 Electric Charge and Electric Field
2/12202 lxx
lE
讨论
1,l >>x,无限长均匀带电直线,assume the wire
is extremely long in both directions.
,222 llx xE
02
2,x>>l,无穷远点场强,222 xlx
2
02 x
lE
2
04
2
x
l
2
04 x
q
相当于点电荷的电场。
查积分表
Chapter 19 Electric Charge and Electric Field
例 2 A ring of charge,A thin,ring-shaped object of
radius a holds a total charge Q distributed
uniformly around it,Determine the electric field
at a point P on its axis,a distance x from the
center,正电荷 均匀分布在半径为 的圆环上,计算在环的轴线上任一点 的电场强度,p468-469
x
q
x
o
P
R
Rq
P
Chapter 19 Electric Charge and Electric Field
x
q
y
x
z
o
P
R
r
rer
l
E?
2
0
d
π 4
1
d
EE d 由对称性有 iEE
x
lq dd )
π 2
(
R
q
SOLUTION:
Chapter 19 Electric Charge and Electric Field
x
q
y
x
z
o
R
r
lq dd
rer
l
E?
2
0
d
π 4
1
d
P
)
π 2
(
R
q
c osdd EEE ll x r
x
r
l
2
0π4
d
R
r
lxπ2
0 3
0π 4
d
2322
0 )(π 4 Rx
qx
Chapter 19 Electric Charge and Electric Field
2322
0 )(π 4 Rx
qx
E
x
q
y
x
z
o
R r
lq dd
P?
E?
讨 论
Rx
（ 1）
2
0π 4 x
qE
（点电荷电场强度）
0,0 0 Ex（ 2）
Rx
x
E
2
2,0
d
d
（ 3） R
2
2
R22?
E
o
x
Chapter 19 Electric Charge and Electric Field
例 3 均匀带电薄圆盘轴线上的电场强度,p470-480
有一半径为,电荷均匀分布的薄圆盘,其电荷面密度为,求通过盘心且垂直盘面的轴线上任意一点处的电场强度,
0R
x
P x
y
z
o
0R
Uniformly charged disk.
Charge is distributed
uniformly over a thin
circular disk of radius R0.
The charge per unit area
is,Calculate the
electric field at a point P
on the axis of the disk.
Chapter 19 Electric Charge and Electric Field
2322
0 )(π 4
Rx
xqE
2
0π Rq
E?d
RRq dπ2d
x
P
R
Rd
2/122 )( Rx?2322
0 )(π 4
dd
Rx
xqE
x?
2322
0 )(
d
2 Rx
RxR
x
y
z
o
0R
解 由例 2
SOLUTION:
Chapter 19 Electric Charge and Electric Field
xEE d
)
11
(
2 2
0
22
0 Rxx
x
E
0R
x
y
z
o E?d
R
P
Rd
0
0 2/322
0 )(
d
2
R
Rx
RRx
2322
0 )(
d
2
d
Rx
RxRE
x
Chapter 19 Electric Charge and Electric Field
0Rx
02?
E
0Rx
2
0π4 x
qE
（点电荷电场强度）
讨 论
2
2
02
1
2
2
0
2
11)1(
x
R
x
R
无限大均匀带电平面的电场强度
)
11
(
2 2
0
22
0 Rxx
x
E
Chapter 19 Electric Charge and Electric Field
Main Steps of Calculating Electric Field:
Step1,Choose differential element of charge dq;
Build up the coordinate system;Step3:
Step2,Calculate set up by the dq ;Ed?
Step4:
E?d
Resolving and find out the scalar
integration for (将 分解,求标量积分 ).
Ed?
E?
Step5,Determine the magnitude and direction of and discuss for its results.
E?
Chapter 19 Electric Charge and Electric Field
19-8 Field lines p471-473
1,Electric field lines
A convenient way to visualize field patterns is
to draw lines in the direction of the electric
field,Such lines are called field lines.（ 形象地描述电场的大小和方向的一组有向曲线 ）
A B
AE
B
E?
Chapter 19 Electric Charge and Electric Field
A B
AE
B
E?
1) Field lines begin on positive charges and
terminate on negative charges,Electric field
vector,is tangent to the electric field lines at
each point in space,（ 某点的电场方向是曲线在该点的切线方向,正?负电荷 ）
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2) The number of lines per unit area through a
surface perpendicular to the lines is
proportional to the strength of the electric field
in a given region,E is large when the field lines
are close together and small when far apart.
电力线密处场强大，电力线疏处场强小。
BA EE?
Chapter 19 Electric Charge and Electric Field
S
ψE
d
d
E?
dS
dψ
电场线密度,垂直于 的单位面积的电场线的数目,大小等于,
E?
E?
Chapter 19 Electric Charge and Electric Field
点电荷的电场线
a positive point charge
+
a negative point
charge
Chapter 19 Electric Charge and Electric Field
Two charges of opposite sign
+
Chapter 19 Electric Charge and Electric Field
Two equal positive charge
++
Chapter 19 Electric Charge and Electric Field
Unequal charges,+2q and -q
q?q2
Chapter 19 Electric Charge and Electric Field
Two oppositely charged parallel plates
+ + + + + + + + + + + +
Chapter 19 Electric Charge and Electric Field
2,Rules for drawing electric field lines for any
charge distribution,电力线特点电力线始于正电荷,
终止于负电荷,不会在无电荷处中断,电力线为非闭合曲线 。
1) Lines must begin on positive charges (or at
infinity) and must terminate on negative
charges or in the case of excess charge at
infinity,起于正电荷 （ 或,?” 远 ）,止于负电荷
（ 或,?” 远 ）
Chapter 19 Electric Charge and Electric Field
2） The number of lines drawn leaving a positive
charge or approaching a negative charge is
proportional to the magnitude of the charge.
电场线的多少与电荷量有关
3） No two field lines can cross each other.在没有电荷 任何两条电力线不能相交
1E
2E
Chapter 19 Electric Charge and Electric Field
19-9.Electric Fields and Conductors P473-474
导体内部无宏观电荷的定向移动，导体处在静电平衡状态。
0E
+
+
+
+
+
+
+
+
＇E?
0E
0?E?
1.静电平衡 Static situation
Chapter 19 Electric Charge and Electric Field
00 ＇EEE
导体内电场强度 外电场强度 感应电荷电场强度
1) 导体内部任意一点的场强为 0.
The electric field inside a conductor is zero.
Chapter 19 Electric Charge and Electric Field
2) 静电平衡时，场强方向与导体表面垂直。
The electric field is always perpendicular to the
surface outside of a conductor.
如果场强不垂直于表面，
电场力继续移动电荷，不满足静电平衡条件。
Chapter 19 Electric Charge and Electric Field
in response to this force until they reached
positions where no net force was exerted on
them parallel to the surface,that is,until the
electric field was perpendicular to the surface.
If there were a
component of E parallel
to the surface,electrons
at the surface would
move along the surface
Chapter 19 Electric Charge and Electric Field
1)屏蔽外电场
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外电场空腔导体可以屏蔽外电场,使空腔内物体不受外电场影响,这时,整个空腔导体和腔内的电势也必处处相等,
E?
空腔导体屏蔽外电场
2 静电屏蔽 Electrostatic Shielding
Chapter 19 Electric Charge and Electric Field
q?
接地空腔导体将使外部空间不受空腔内的电场影响,
q
2)屏蔽腔内电场
+
+
++
+
+
+
+
q
Chapter 19 Electric Charge and Electric Field
Chapter 19 Electric Charge and Electric Field
Homework,page 480,12
page 481,42; 48; 65
