Download Ch27 The Electric Field

講者： 許永昌 老師
1
Contents
 Electric Field created by charge :
 Discrete  continuous




Idea:
.
Picturing the electric field by
Discrete:
Continuous:
 Problem solving strategy
 Important Examples:
,
.
,
,
, and
.
 Motion of charged particles in the field:
 Uniform Electric Field: Parallel-Plate Capacitor
 Non-uniform Electric Field
2
Electric Field created by charge
(請預
讀P818~P821)
 Electric field created by a
 E
:
1
q
rˆ.
2
4 0 r
 Electric field created by a group of charges:
 Fon q '  F1 on q '  F2 on q '  ...,
Enet 

Fon q '

F1 on q '

F2 on q '
 ...  E1  E2  ...
q'
q'
q'
這兩條方程是本章所有計算的出發點。
3
Limiting Case
 Electric Field is
 A function of
,
 Related to the
.
 Limiting Case:
 Very far or very close to an charged object.
 Change the size of the charged object to be infinitely
small or large.
 Etc.
1 Qnet
 Example: The electric field at r is E 
rˆ.
2
4 0 r
4
Exercise
 Try to use the Problem-Solving Strategy (P820) to find
the electric field of three equal point charges on the x+
axis.
d
d
+
+
Ex=?
 Limiting Case? x0 and x>>0.
5
Electric Field of a Dipole (請預讀
P822~P823)
Electric_field_of_a_dipole.m
 There are two kinds of electric dipoles:
 Permanent electric dipole: H2O, …
 Induced electric dipole:
O2,…
2
1.5
1
0.5
0
-0.5
-1
-1.5
-2
1.5
2kp
E 3
r
1
0.5
0
-0.5
-1
-1.5
-1.5
-1
-0.5
0
0.5
1
2
1.5
+
s
-
E
:
Prove it.
kp
r3
 qs, from the negative

p

to the positive charge 

Dipole moment p.
6
Picturing the Electric Field (請預讀
P824)
 Electric Field lines is one kind of representation of
electric field.
 The concept is the similar to the
and
we discussed in P460, Ch15.
Will be discussed
in Ch18.
7
Electric Field lines
 It
tell you the exact magnitude of electric field.
 It is a good conceptual tool.
8
Homework
 Student Workbook:
 2, 4, 7, 11, 12
9
Electric Field of a Continuous
Charge Distribution (請預讀P825~P828)
 We need the concept of
Q
 Linear Charge density: l  lim .
L 0
:
L
Q
h

lim
.
 Surface Charge density:
A 0 A
 DQ=hDA.
Q
 Volume Charge density:r  lim .
V 0 V
 DQ=rDV.

DQ=lDL.
Q, #1
a
b
#2
#3
:
 The surface charge density of object 1?
 The original one broken into the smaller ones. Compare
the surface charge densities h1, h2 and h3.
10
Problem solving Strategy(請預讀P826)
: For the pictorial representation.
 Draw a picture and establish a
system.
 Divide the total charge Q into
.
 Draw the electric field vector at desired point for
of charge. (純粹為了方便找到必要的參數) This will help
you
that need to be calculated.
 Look for
of the charge distribution that simplify the
field.
:
 Use the concept of superposition to find the
 Translate the sum into an

from a sum.
(dQ=ldx).
Q: How to do the integration for a vector field?
 此處困難點常常是在於不曉得怎麼寫出相應的積分。
11
Homework
 Student Workbook:
 15, 16, 18, 19, 20
12
Electric Field of Lines (請預讀P827~P828)
Visualize
1.
1.
2.
3.
Known
Coordinate (considered with symmetry) Length
Charge
Separate the object into small pieces
Plot some electric fields on the desired point.
L
Q
2. Solving
x
1.  Ei  x  Ei cos   Ei
2.
3.
Enet
yi2  x 2
N
N
i 1
i 1
 xˆ   Ei  x  xˆ 
N
Enet  xˆ 
i 1
 xˆ
k lDyi
y
2
i
 x2
 2
 yi2  x2 
yi2  x 2
kQ
x x2  L
k DQi
x

2
.
,
L
2
L

2
 xˆ 
y
x
yi2  x 2
kxl
2
 x2

3
.
dy
2
+
+
+
+
+
+
+
+
x

13
Limit case of a line
 Electric field on the x axis: Enet  xˆ
kQ
 2
x x2  L
 If x>>L,
2
.
kQ
xˆ . It behaves as a charge Q. Reasonable.
x2
2kQ
2k l

xˆ 
xˆ . Enet l and  1/x.
xL
x
Enet 
 If x<<L, Enet
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Exercise
 Please find the electric field at point p.
l
p
L
r
15
The electric field of a ring and a
disk(請預讀P829~P832)
Visualize
1.
1.
2.
3.
Coordinate (considered with symmetry)
Separate the object into small pieces
Plot some electric fields on the desired point.
2. Solving
 線和面的計算原理相同
都用到superposition.
 Ring:  E   kzQ .

z
z2  r2

z
3/ 2
r
 Disk:
E  
N
z
i 1

kzDQi
z  ri
2
2

3/ 2

DQi h 2 ri Dri

R
0
Dr
kzh 2 rdr

z2  r2

3/ 2
h z
z

  2
2 0  z
z  R2

.

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Limiting case of a disk
 Electric field of a disk, z>0 part:  E z  h 1 
2 0 
 z>> R (far enough),
E

z
h 
1

1
2
2 0 
1

R
/
z



h R2
Q


.
2
2
4 0 z
4 0 z

.
2
2
z R 
z

2
  h 1  1  1 R  
 2 0   2 z 2  

(當第一階近似為零，就要再找下一階)
 0<z<<R (close enough),
E

z

 h 
h 
z
z h

1

.
1  2



2
2 0 
2

R
2



z R 
0
0
It is a constant!
17
The electric field of a uniform
charged sphere (請預讀P833)
 This problem is analogous to wanting to know the
gravitational field of a spherical planet or star.
 We will discuss it in Ch28 in detail.
 Esphere, outside  kQ rˆ.  r  R 
r2
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The Parallel-Plate Capacitor (請預讀
P834)
 Therefore, we create an
.
+
+
+
+
+
+
E 
h
2 0
E 
: Can we that the right plate
the electric field to the right of the capacitor?
+
+
+
+
+
+
h
0
19
Homework
 Student Workbook:
 22, 25, 27, 28
20
Motion of a charged particle in an
Electric Field (請預讀P835~P840)
 We said that some charges, the
, create
an electric field.
then
to that
electric field. Now we turn our attention to the second
half of the interaction.
 The force exerted by a electric field on a charge q particle
is Fon q  qE.
+
21
Exercises
a capacitor. Sketch the particle’s trajectory if
the particle’s initial velocity is (a) zero, (b)
straight down, and (c) to the right.
+
+
+
+
+
+
+
 How about a negatively charged particle?
-
 A positively charged particle is in the center of
 A charged particle is doing the uniform
circular motion around a uniform charged
infinite long line. Please find its velocity.
 Hint:
+ r
q/m
l
 free-body diagram  Fnet Newton’s 2nd Law
 a Trajectory.
22
Motion of a dipole in an Electric
field (請預讀P839~P840)
 Dipoles in a Uniform Field:
 Net force:
Fnet=0.
  p  E.
 Torque:
 Dipoles in a Nonuniform Field:
 Net force:
Fnet0.

A dipole will experience a net force toward any charged object
23
Homework
 Student Workbook:
 29, 30, 32, 34, 35, 36
 Student Textbook:
 47, 53
 自行製造 Terms and Notation 的卡片
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