Chapter 17 Electric Charge and Electric Field Chapter 17 Electric Charge and Electric Field.
Electric field Chapter 22 Week-2 Electric Fields In this chapter we will introduce the concept of an...
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Transcript of Electric field Chapter 22 Week-2 Electric Fields In this chapter we will introduce the concept of an...
![Page 1: Electric field Chapter 22 Week-2 Electric Fields In this chapter we will introduce the concept of an electric field. As long as charges are stationary.](https://reader036.fdocuments.us/reader036/viewer/2022062408/56649f145503460f94c28662/html5/thumbnails/1.jpg)
Electric field Chapter 22
Week-2
![Page 2: Electric field Chapter 22 Week-2 Electric Fields In this chapter we will introduce the concept of an electric field. As long as charges are stationary.](https://reader036.fdocuments.us/reader036/viewer/2022062408/56649f145503460f94c28662/html5/thumbnails/2.jpg)
Electric FieldsIn this chapter we will introduce the concept of an electric field. As long as charges are stationary Coulomb’s law described adequately the forces among charges. If the charges are not stationary we must use an alternative approach by introducing the electric field (symbol ). In connection with the electric field, the following topics will be covered:
-Calculate the electric field generated by a point charge.
-Using the principle of superposition determine the electric field created by a collection of point charges as well as continuous charge distributions.
-Once the electric field at a point P is known we will be calculate the electric force on any charge placed at P -Define the notion of an “electric dipole”. Determine the net force , the net torque, exerted on an electric dipole by a uniform electric field, as well as the dipole potential energy.
E
(22-1)
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Fields Imagine an object is placed at a particular point in
space. When placed there, the object experiences a force F. We may not know WHY there is a force on the object,
although we usually will. Suppose further that if we double some property of
the object (mass, charge, …) then the force is found to double as well.
Then the object is said to be in a force field. The strength of the field (field strength) is defined as
the ratio of the force to the property that we are dealing with.
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Electric Field
If a charge Q is in an electric field E then it will experience a force F.
The Electric Field is defined as the force per unit charge at the point.
Electric fields are caused by charges and consequently we can use Coulombs law to calculate it.
For multiple charges, add the fields as VECTORS.
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Two Charges
unitunit rrF
E22
0
00
1
r
qk
r
qqk
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Doing it
Q
r
q
A Charge
The spot where we wantto know the Electric Field
unit
unit
r
Qk
q
r
qQk
rF
E
rF
2
2
F
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General-
unitjj
jjj
unit
unit
r
Qk
q
General
r
Qk
q
r
qQk
,2
2
2
rF
EE
rF
E
rF
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Force Field
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![Page 10: Electric field Chapter 22 Week-2 Electric Fields In this chapter we will introduce the concept of an electric field. As long as charges are stationary.](https://reader036.fdocuments.us/reader036/viewer/2022062408/56649f145503460f94c28662/html5/thumbnails/10.jpg)
q
qo
r
P
E
2
1
4 o
qE
r
Consider the positive charge shown in
the figure. At point P a distance from
we place the test charge . The force
exerted on by is equal to: o
o o
q
r
q q
q q
Electric field generated by a point charge
2
2 2
1
4
1 1
4 4
The magnitude of is a positive number
In terms of direction, points radially
as shown in then figure.
If q were a negative charge the magnitude
o
o
o
o
o o o o
q qF
r
q q qFE
q q r r
E
E
outwards
f remains the same. The direction
of points radially instead
E
E inwards
(22-4)
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O O
The net electric electric field generated by a group of point charges is equal
to the vector sum of the electric field vectors ge
E
Electric field generated by a group of point charges. Superposition
1 2 3
1 2 3
1 1 3
1 2
nerated by each charge.
In the example shown in the figure
Here , , and are the electric field vectors
generated by , , and , respectively
Note , , an: d
E E E E
E E E
q q q
E E
1 2 3 1 2 3 1 3
3
2
must be added as vectors
, , x x x x y y y y z z z zE E E
E
E E E E E E E E E
(22-5)
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What is the electric field at the center of the square array?
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d
+ q
- q
-q
+q/2 +q/2
A system of two equal charges of opposite sign
placed at a distance is known as an "electric
dipole". For every electric dipole we associate
a vector known as "the electric dipol
q d
Electric Dipole
e moment"
(symbol )defined as follows:
The magnitude
The direction of is along the line that connects
the two charges and points from - to .
Many molecules have a built-in electric dip
p
p qd
p
q q
2
ole
moment. An example is the water molecule (H O)
The bonding between the O atom and the two H
atoms involves the sharing of 10 valence electrons
(8 from O and 1 from each H atom)
(22-6)
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(22-7)
We will determine the electric field generated by the
electric dipole shown in the figure using the principle of
superposition. The positive charge ge
E
Electric field generated by an electric dipole
( ) 2
( ) 2
( ) ( )
2
nerates at P an electric
1field whose magnitude The negative charge
4
1creates an electric field with magnitude
4
The net electric field at P is:
1
4
o
o
o
qE
r
qE
r
E E E
q qE
r
2 22
2 2
2
2 3 3
1
4 / 2 / 2
1 1 We assume: 14 2 2 2
1 1 =4 22
1
o
o
o o o
q q
r z d z d
q d d dE
z z z z
q d d qdE
z z z z
p
z
21 1 2x x
<<
=
![Page 15: Electric field Chapter 22 Week-2 Electric Fields In this chapter we will introduce the concept of an electric field. As long as charges are stationary.](https://reader036.fdocuments.us/reader036/viewer/2022062408/56649f145503460f94c28662/html5/thumbnails/15.jpg)
Kinds of continuously distributed charges
Line of charge = the charge per unit length. dq=ds (ds= differential of length along the line)
Area = charge per unit area dq=dA dA = dxdy (rectangular coordinates) dA= 2rdr for elemental ring of charge
Volume =charge per unit volume dq=dV dV=dxdydz or 4r2dr or some other expressions we will
look at later.
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Continuous Charge Distribution
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Symmetry
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Let’s Do it Real Time
Concept – Charge perunit length
dq= ds
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The math
)sin(2
)cos(2
)cos()2(
)cos()2(
0
0
0
02
02
0
0
0
r
kd
r
kE
r
rdkE
r
dqkE
E
rdds
x
x
x
y
Why?
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CA
dq
Detemine the electric field generated at point P
by a uniformly charged ring of radius and total charge .
Point P lies on the normal to the ring plane that passes through
the ring cente
E
R q
Example :
2 2
r C, at a distance . Consider the charge element
of length and charge shown in the firgure. The distance
between the element and point P is
The charge generates at P an electric fiel
z
dS dq
r z R
dq
2
3/ 23 2 2
d of magnitude
and which points outwards along the line AP.
The z-component of is given by: 4
cos From triangle PACwe have: cos /
4 4
o
z
z zo o
dE
dqdE dE
r
dE dE z r
zdq zdqdE E
r z R
3/ 2 3/ 22 2 2 2
4 4
z
z
o o
dE
z zqE dq
z R z R
(22-9)
dq
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The Geometry (the disk)
Define surface charge density=charge/unit-area
dq=dA
dA=2rdr
(z2+r2)1/2
dq= dA = 2rdr
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(z2+r2)1/2
R
z
z
rz
rdrzkE
rz
z
rz
drrk
rz
dqkdE
02/322
2/1222222
2
2)cos(
![Page 23: Electric field Chapter 22 Week-2 Electric Fields In this chapter we will introduce the concept of an electric field. As long as charges are stationary.](https://reader036.fdocuments.us/reader036/viewer/2022062408/56649f145503460f94c28662/html5/thumbnails/23.jpg)
(z2+r2)1/2
Final Result
0z
220
2E
,R
12
When
Rz
zEz
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q
q
negative ch
3. Electric field lines extend away from (where they originate)
and towards (where they terminate)
Example 1 : Electric field lines of a nega
a
t
rg
iv
positive
e point c
c
h
harge
arg
e
s
s
e - q
2
1
4 o
qE
r
-The electric field lines point towards the point charge
-The direction of the lines gives the direction of
-The density of the lines/unit area increases as the
distance from decreases.
E
qN
In the case of a positive point charge
the electric field lines have the same
form but they point
outw
ote :
ards
(22-11)
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Electric field lines generated by
an electric dipole (a positive
and a negative point charge of
the same size but of opposite
sign)
Example 3.
Electric field lines generated by
two equal positive point charges
Example 4.
(22-13)
![Page 26: Electric field Chapter 22 Week-2 Electric Fields In this chapter we will introduce the concept of an electric field. As long as charges are stationary.](https://reader036.fdocuments.us/reader036/viewer/2022062408/56649f145503460f94c28662/html5/thumbnails/26.jpg)
Look at the “Field Lines”
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F+
F-
x-axis
Consider the electric dipole shown in the figure in
the presence of a uniform (constant magnitude and
direction) electric field
Forces and torques exerted on electric dipoles
by a uniform electric field
along the -axis
The electric field exerts a force on the
positive charge and a force on the
negatice charge. The net force on the dipole
0net
E x
F qE
F qE
F qE qE
The net torque generated by and about the dipole center is:
sin sin sin sin2 2
In vector form:
The electric dipole in a uniform electric field does not move
bu
F F
d dF F qEd pE
p E
t can rotate about its center p E
0netF
(22-14)
![Page 28: Electric field Chapter 22 Week-2 Electric Fields In this chapter we will introduce the concept of an electric field. As long as charges are stationary.](https://reader036.fdocuments.us/reader036/viewer/2022062408/56649f145503460f94c28662/html5/thumbnails/28.jpg)
A
B
U
180˚
90 90
90
sin
sin cos
U d pE d
U pE d pE p E
Potential energy of an electric dipole
in a uniform electric field
p E
E
p
min
At point ( 0) has a minimum
value
It is a position of equilibriums
A
table
U
U pE
max
At point ( 180 ) has a maximum
value
It is a position of equilibriumunst le
B
ab
U
U pE
U p E
cosU pE
(22-15)
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p
Ef
Fig.b
p
Ei
Fig.a Consider the electric dipole in Fig.a. It has an electric
dipole moment and is positioned so that is at an p p
Work done by an external agent to rotate an electric
dipole in a uniform electric field
i
f
angle
with respect to a uniform electric field
An external agent rotates the electric dipole and brings
it in its final position shown in Fig.b. In this position
is at an angle with respect to
E
p
The work W done by the external agent on the dipole
is equal to the difference between the initial and
final potential energy of the dipole
cos cos
cos cos
f i f i
i f
E
W U U pE pE
W pE
(22-16)
![Page 30: Electric field Chapter 22 Week-2 Electric Fields In this chapter we will introduce the concept of an electric field. As long as charges are stationary.](https://reader036.fdocuments.us/reader036/viewer/2022062408/56649f145503460f94c28662/html5/thumbnails/30.jpg)
What did we learn in this chapter??
We introduced the concept of the Electric FIELDFIELD. We may not know what causes the field. (The
evil Emperor Ming) If we know where all the charges are we can
CALCULATE E. E is a VECTOR. The equation for E is the same as for the force
on a charge from Coulomb’s Law but divided by the “q of the test charge”.
![Page 31: Electric field Chapter 22 Week-2 Electric Fields In this chapter we will introduce the concept of an electric field. As long as charges are stationary.](https://reader036.fdocuments.us/reader036/viewer/2022062408/56649f145503460f94c28662/html5/thumbnails/31.jpg)
What else did we learn in this chapter? We introduced continuous distributions of
charge rather than individual discrete charges.
Instead of adding the individual charges we must INTEGRATE the (dq)s.
There are three kinds of continuously distributed charges.
![Page 32: Electric field Chapter 22 Week-2 Electric Fields In this chapter we will introduce the concept of an electric field. As long as charges are stationary.](https://reader036.fdocuments.us/reader036/viewer/2022062408/56649f145503460f94c28662/html5/thumbnails/32.jpg)
Kinds of continuously distributed charges
Line of charge = the charge per unit length. dq=ds (ds= differential of length along the line)
Area = charge per unit area dq=dA dA = dxdy (rectangular coordinates) dA= 2rdr for elemental ring of charge
Volume =charge per unit volume dq=dV dV=dxdydz or 4r2dr or some other expressions we will
look at later.
![Page 33: Electric field Chapter 22 Week-2 Electric Fields In this chapter we will introduce the concept of an electric field. As long as charges are stationary.](https://reader036.fdocuments.us/reader036/viewer/2022062408/56649f145503460f94c28662/html5/thumbnails/33.jpg)
Summary
222
,2
2
2
)()()(
r
rdsk
r
rdAk
r
rdVk
r
Qk
q
General
r
Qk
q
r
qQk
unitjj
jjj
unit
unit
E
rF
EE
rF
E
rF
(Note: I left off the unit vectors in the lastequation set, but be aware that they should
be there.)
![Page 34: Electric field Chapter 22 Week-2 Electric Fields In this chapter we will introduce the concept of an electric field. As long as charges are stationary.](https://reader036.fdocuments.us/reader036/viewer/2022062408/56649f145503460f94c28662/html5/thumbnails/34.jpg)
To be remembered …
If the ELECTRIC FIELD at a point is E, then E=F/q (This is the definition!)
Using some advanced mathematics we can derive from this equation, the fact that:
EF q