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Electricity
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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Electricity
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:
Temperature Profile (scalar)
Wind Velocity Profile (vector)
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Electric Fields
TOC
Definitions
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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Electric Fields
TOC
Example of a Vector
Change Wind
Speed
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
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TOC
Example of a Scalar
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
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Magnitude
100
75
50
25
0
Direction
none
Units
degrees F
Electricity
Electric Fields
TOC
Example of a Vector Field
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
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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.
Electricity
Electric Fields
TOC
Example of a Scalar Field
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
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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
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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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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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Electricity
Electric Fields
Electric Fields
TOC
Consider two positive charges, q0 and q1.
The force from q1 on q0 is given by Coulomb’s Law.
q1 q0
 q1 
Fk
 q0  k 2 
2
r
 r 
This last equation is true regardless of the value of q0.
q1
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q0
F
Electricity
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 q0 q1  q1 
F  k E 2 k 2 q0  k 2 
r r
 r 
Notice that it no longer depends on the value of q0. It depends only on a
position.
q1
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q0
E
F
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Electric Fields
Electric Fields
TOC
For a point charge, the electric field changes only with its distance from the
charge.
q1
Ek 2
r
It gets smaller as you move away from the charge.
q1
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Electric Fields
TOC
If we draw the filed lines, we can see that they get less dense with distance
q1
Ek 2
r
The number of lines is proportional to the amount of charge.
q1
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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
q1
Ek 2
r
where 0 tells us the position at which the measurement is being taken.
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Electric Fields
TOC
Finding Electric Force
To find the force exerted by q1 on another charge q0, use the equation
F  q0 E
where E is the electric field at the point where the charge is found.
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Electricity
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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