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Physics 212
Electric Fields
TOC
Definition of a Field
Field Lines
Electric Fields
Superposition
Relationship to Electric Force
Field as a Physical Property
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Physics 212
Electric Fields
Field
TOC
The influence of some agent, as electricity or gravitation,
considered as existing at all points in space and defined by
the force it would exert on an object placed at any point in
space.
http://www.infoplease.com/dictionary/field
Fields are things which change their value depending on what
point in space or time you are measuring them.
They may depend on direction (vector fields) or they may not
(scalar fields).
Examples of Fields:
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Temperature Profile (scalar)
Wind Velocity Profile (vector)
Physics 212
Electric Fields
Definitions
TOC
Magnitude: The amount of a quantity represented by a vector or scalar.
Direction: The angle of a vector measured from the positive x-axis
going counterclockwise.
Scalar: A physical quantity that has no dependence on direction.
Vector: A physical quantity that depends on direction.
Field: A set of an infinite number of related vectors or scalars found at
every point in space and time.
Units: A standard quantity used to determine the magnitude of a vector
or value of a scalar.
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Physics 212
Electric Fields
Example of a Vector
Change Wind
Speed
TOC
Wind Velocity is a vector
Its magnitude is changed when it
increases and decreases its
speed.
Change Wind
Direction
Its direction is changed when it
changes the compass angle
toward which it blows.
Graphical
Representation
N
Real Life
Mathematical
Representation
Magnitude
24
18
12
6
w
e
Southeast
Northwest
Northeast
Direction Southwest
4
Units
mph
s
Physics 212
Electric Fields
Example of a Scalar
TOC
Temperature is a scalar
Its magnitude is changed when it
heat is added or taken away.
Change
Temperature
It has no direction.
Real Life
Graphical
Representation
Degrees C
Mathematical
Representation
5
Magnitude
100
75
50
25
0
Direction
none
Units
degrees F
Physics 212
Electric Fields
Example of a Vector Field
TOC
Wind Velocity is a function
of position.
This position is given by
the latitude and longitude
of the vector’s tail.
Graphical
Representation
N
Mathematical
Representation
Position
6
Magnitude
Latitude
28°
40°
41°
32°
30°
29°
47°
38°
N
Longitude
100°
106°
123°
118°
81°
86°
83°
73°
95°
91°
W
14
12
10
20
11
5
4
6
Direction*
315°
225°
85°
45°
43°
44°
0°
2°
Units
mph
* Angles for direction are taken counterclockwise from East.
Physics 212
Electric Fields
Example of a Scalar Field
TOC
Temperature is a function
of position.
This position is given by
the latitude and longitude
of the point where the
temperature is taken.
Graphical
Representation
N
Mathematical
Representation
Position
7
Magnitude
Latitude
28°
40°
41°
32°
30°
29°
47°
38°
N
Longitude
100°
106°
123°
118°
81°
86°
83°
73°
95°
91°
W
Direction
Units
51
48
75
62
58
82
74
65
87
none
degrees F
Physics 212
Electric Fields
TOC
Wind velocity can be represented by placing arrows
at many locations.
Each arrow represents the value of the velocity at the
location of the tail of the arrow.
The direction of the arrow gives the direction of the
wind velocity.
The length of the arrow gives the magnitude of the
wind velocity.
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Physics 212
Electric Fields
The wind velocity can also be represented by lines.
TOC
The lines do NOT connect the arrows!
The lines are closer together where the magnitude of
the wind velocity is greater.
The direction of the wind velocity at a point on any
line is tangent to the line.
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Physics 212
Electric Fields
Electric Fields
TOC
Consider two positive charges, q0 and q1.
The force from q1 on q0 is given by Coulomb’s Law.
F1,0  k
q1 q0
r1,0
2
 q1 
 q0  k 2 
 r 
 1,0 
This last equation is true regardless of the value of q0.
q1
10
q0

F1, 0
Physics 212
Electric Fields
Electric Fields
TOC
We could now divide by q0 and this is what we call the electric
field at the point where q0 used to be.
q1
q
q
1 k
0
E
F1,0  k 1,0 2 r 2q0
r1,0 1,0
 q1 
 k 2 
 r1,0 
Notice that it no longer depends on the value of q0. It depends
only on a position.
q1
11
q0

EF1,0
1, 0
Physics 212
Electric Fields
Electric Fields
TOC
For a point charge, the electric field changes only with its
distance from the charge.
E1,0
q1
k 2
r1,0
It gets smaller as you move away from the charge.
q1
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Physics 212
Electric Fields
Electric Fields
TOC
If we draw the filed lines, we can see that they get less dense
with distance
E1,0
q1
k 2
r1,0
The number of lines is proportional to the amount of charge.
q1
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Physics 212
Electric Fields
Electric Fields are fields which add as vectors
TOC
Electric fields add the same way electric forces do, as vectors.
The electric field is different at different locations.
The magnitude of the electric field for a point charge is
E1, 0
q1
k 2
r1,0
where 0 tells us the position at which the measurement is being
taken.
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Physics 212
Electric Fields
TOC
Finding Electric Force
To find the force exerted by q1 on another charge q0, use the
equation


F1,0  q0 E1,0
where E1,0 is the electric field at the point where the charge is
found.
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Physics 212
Electric Fields
TOC
Electric Field is a physical property of a particle with
charge
Electric field is something we can measure independent of
other charges.
For a given particle, the electric field around it never changes
unless we physically change the particle.
Electric fields have their own energy and momentum.
We can talk about the electric field even when the charge that
causes the field is unknown.
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Physics 212
Electric Fields
TOC
Definition of a Field
Field Lines
Electric Fields
Superposition
Relationship to Electric Force
Field as a Physical Property
17