Fundamentals of Physics
Chapter 22 Electric Fields
1.
2.
3.
4.
5.
6.
7.
8.
Charges & Forces
The Electric Field
Electric Field Lines
Electric Field due to a Point Charge
Electric Field due to a Electric Dipole
Electric Field due to a Charged Disk
A Point Charge in an Electric Field
Measuring the Elementary Charge
Ink-Jet Printing
Volcanic Lightning
A Dipole in an Electric Field
Potential Energy of an Electric Dipole
Review & Summary
Questions
Exercises & Problems
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Physics 2112
Fundamentals of Physics
Chapter 22
1
The Electric Field
Action at a Distance
Gravitational Field
Electric Field
The electric field determines the
direction & magnitude of the force on a
charge.
Scalar fields
Vector fields
Changes in an electric field are
propagated at the speed of light.
electromagnetic waves
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Fundamentals of Physics
Chapter 22
2
The Electric Field
The presence of an electric field is detected by observing a
force on a small positive test charge.
Measure the force on the test charge.
vector - magnitude and direction
The electric field is obtained by dividing the measured
force force by the magnitude of the test charge:
E
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F
q0
(newton / coulomb)
Physics 2112
Fundamentals of Physics
Chapter 22
3
Electric Field Lines
E
vector field
E
F
q0
Visualization of a vector field:
Space around a charged body is filled by lines of force.
The direction of E is the tangent to the field line.
The magnitude of E is given by the number of lines-of-force per unit area.
Electric field lines originate at + charge
terminate at - charge.
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Fundamentals of Physics
Chapter 22
4
Electric Fields and a Sheet of Charge
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Physics 2112
Fundamentals of Physics
Chapter 22
5
Electric Field Lines
+ and - charges
E
F
q0
attraction
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2 + charges
repulsion
Physics 2112
Fundamentals of Physics
Chapter 22
6
Electric Field due to a Point Charge
Coulomb s Law
F1, 2
E1
4
F1, 2
q2
q1 q2
1
0
q1
1
4
r2
0
r2
Principle of Superposition
E1
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E1, 2
E1,3
E1, 4
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E1,n
Fundamentals of Physics
Chapter 22
7
Checkpoint 1
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Chapter 22
8
Example 2
q1 = +2Q
q2 = -2Q
q3 = -4Q
E at the Origin
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Fundamentals of Physics
Chapter 22
9
Checkpoint 2
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Chapter 22
10
Electric Field due to an Electric Dipole
Electric Dipole - equal & opposite point charges separated by d.
1
E
4
q
z
0
1
1
2
d
2
4
q
0
z
1
2
d
2
It is easy to show that:
E
1
2
0
qd
z3
for z
d
Electric Dipole Moment = q d
A vector pointing from
E
2006
to + charge.
1
2
0
p
z3
Physics 2112
Fundamentals of Physics
Chapter 22
11
Electric Field due to a Line of Charge
A Ring of Uniform + Charge:
= linear Charge Density (coulomb / meter)
E
r
dE cos
2
z
dq
2
R
4
0
dq
r2
qz
E
4
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2
1
ds
z
r
cos
E
dE
0
z
2
q
4
0
z
2
R
z
2
3
2
R
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Fundamentals of Physics
Chapter 22
12
Example 3
Uniform charge distribution Q
1200 circular arc or radius R
in terms Q, R what is E at P?
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Fundamentals of Physics
Chapter 22
13
Problem Solving Tactics
1.
2.
3.
4.
Choose element of charge, ds or dx
Relate charge dq of element to its length, dq= ds or dx
Express field dE produced at P by dq, direction depends on charge
Look for and use axis of symmetry to cancel opposing components. Add
adding components via integration.
5. Simplify integral where possible
6. Use integration order that gives positive results
7. replace with Q/L if answer is to be stated in terms of Q
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Physics 2112
Fundamentals of Physics
Chapter 22
14
Checkpoint 3
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Chapter 22
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Electric Field due to a Charged Disk
Plastic Disk of + Surface Charge:
= charge density (coulomb / meter2)
z dq
dE
4
dq
E
E
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z
0
2
r
dA
2
0
2
2 r dr
R
0
1
0
3
2 r dr
z
4
2
z
2
r
2
3
2
z
z2
R2
Physics 2112
Fundamentals of Physics
Chapter 22
16
Electric Field due to an Infinite Plane of Charge
Consider a very large disk:
E
2
R
z
1
z2
0
R2
z
Electric Field of an Infinite Plane of Charge
E
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2
0
Physics 2112
Fundamentals of Physics
Chapter 22
17
A Point Charge in an Electric Field
F = qE
The Electrostatic Force F acting on a charged particle located
in an external electric field E has the direction of E if the charge
q of the particle is positive and the opposite direction if q is
negative
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Physics 2112
Fundamentals of Physics
Chapter 22
18
A Point Charge in an Electric Field
F = qE
Ink Jet Printing:
Each ink drop is given a charge in C, deflected by the electric field, and hits
the paper in the desired location!
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Physics 2112
Fundamentals of Physics
Chapter 22
19
Example 4
m = 1.3 x 10-10 kg
Q = 1.5 x 10-13 C
vx = 18 m/s
L=1.6 cm
E is downward, uniform, =1.4 x 106 N/C
What is the vertical deflection at the edge of
plates?
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Fundamentals of Physics
Chapter 22
20
An Electric Dipole in an Electric Field
Water H2O
= F x sin + F (d
= ( q E ) d sin
p
x) sin
E
(right hand rule)
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Physics 2112
Fundamentals of Physics
Chapter 22
21
An Electric Dipole in an Electric Field
= pxE
(right hand rule)
Potential Energy:
U
W
U
p E cos
90 0
d
90 0
p E sin
d
p E
The frequency of the electromagnetic field in microwave ovens is tuned to the natural
frequency of oscillation of the H2O dipole moment.
flipping H2O molecules
friction
heat
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Physics 2112
Fundamentals of Physics
Chapter 22
22
Checkpoint 5
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Physics 2112
Fundamentals of Physics
Chapter 22
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Problem
q1 = +1.0 x 10-6 C
q2 = +3.0 x 10-6 C
d = 10 cm
E(x) ?
Ei
E
4
Physics 2112
Fundamentals of Physics
r2
0
E1
E x
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qi
1
E2
1
4
q1 x
0
x
3
q2 x d
x d
3
Chapter 22
24
Problem
Where is there no force on a 3rd charge?
q1
5q
q2
2q
Enet
0?
Sketch the electric field lines.
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Fundamentals of Physics
Chapter 22
25
Problem
2q
5q
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Physics 2112
Fundamentals of Physics
Chapter 22
26
Problem
Consider a charged rod:
What is the linear charge density of the charged rod?
charge
Length
q
L
What is the electric field at point P due to the charged rod?
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Fundamentals of Physics
Chapter 22
27
Problem
a
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Fundamentals of Physics
L:
Chapter 22
28
Problem
Equation for E along a perpendicular
bisector of the rod?
dE
1
4
0
r
dq
r2
sin
x
q
L
dq
r2
sin
2006
dx
x2
y2
y
r
Physics 2112
Fundamentals of Physics
Chapter 22
29
Problem
Semi-infinite rod, show the angle of E
at point P is 450 independent of R
dq
r
r2
dEP
1
4
0
x2 R2
dq
r2
x
Physics 2112
Fundamentals of Physics
R
cos
R tan
R
cos 2
dx
Ex
Ey
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dx
1
d
450 !
Chapter 22
30
Problem
a = 1.80 x 109 m/s2 eastward due to E
magnitude and direction of E?
E
F
e
F
qE
F
eE
ma
a
E
E
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ma
e
1.02 10
Physics 2112
9.11 10
31
kg 1.80 109 m s 2
1.60 10
2 N
19
C
C
Fundamentals of Physics
Chapter 22
31
Problem
Two large parallel copper plates are
5.0 cm apart, uniform E.
p and e released at same time,
where will they pass each other?
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Physics 2112
Fundamentals of Physics
Chapter 22
32
Problem
p and e form two corners of an equilateral triangle
d = 2.0 x 10-6 m
E at 3rd corner
Enet
Ee
d
Enet
Ex
2 Ee cos
1
4
0
e
d2
3.6 10 2 N C
d
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Physics 2112
Fundamentals of Physics
Chapter 22
33
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