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Physics 212Electric Fields
Definition of a Field
Field Lines
Electric Fields
Superposition
Relationship to Electric Force
Field as a Physical Property
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Physics 212Electric Fields
Field
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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Physics 212Electric Fields
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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Physics 212Electric Fields
N
Example of a VectorChange Wind
Speed
Change WindDirection
Wind Velocity is a vector
Its magnitude is changed when it increases and decreases its speed.
Its direction is changed when it changes the compass angle toward which it blows.
Real Life
GraphicalRepresentation
MathematicalRepresentation
Magnitude
Direction
Units
24
Northwest
mph
61218
NortheastSoutheastSouthwest
e
s
w
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Physics 212Electric Fields
Change Temperature
Temperature is a scalar
Its magnitude is changed when it heat is added or taken away.
It has no direction.
GraphicalRepresentation
MathematicalRepresentation
Magnitude
Direction
Units
0
none
degrees F
Degrees C
Example of a Scalar
255075100
Real Life
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Physics 212Electric Fields
GraphicalRepresentation
Example of a Vector Field
MathematicalRepresentation
Magnitude
Direction*
Units mph
N
Latitude 40°
118°Longitude
Position
Wind Velocity is a function of position.
This position is given by the latitude and longitude of the vector’s tail.
38°32°47°41°29°47°30°40°28°
123°106°100°91°95°73°83°86°81°
1012112051454116
85°2°85°2°0°45°225°315°44°43°N
W
* Angles for direction are taken counterclockwise from East.
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Physics 212Electric Fields
Example of a Scalar Field
MathematicalRepresentation
Magnitude
Direction
Units degrees F
Latitude 40°
118°Longitude
Position
38°32°47°41°29°47°30°40°28°
123°106°100°91°95°73°83°86°81°
657482586275485182N
W
Temperature is a function of position.
This position is given by the latitude and longitude of the point where the temperature is taken.
none
87
GraphicalRepresentation
N
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Physics 212Electric Fields
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 212Electric Fields
The wind velocity can also be represented by lines.
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 212Electric Fields
Electric Fields
Consider two positive charges, q0 and q1.The force from q1 on q0 is given by Coulomb’s Law.
This last equation is true regardless of the value of q0.
q1
1 0 11,0 02 2
1,0 1,0
Fq q q
k q kr r
q0
0,1F
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Physics 212Electric Fields
Electric Fields
We could now divide by q0 and this is what we call the electric field at the point where q0 used to be.
Notice that it no longer depends on the value of q0. It depends only on a position.
q1
11,0 2
1,0
Eq
kr
0,1E
1 0 11,0 02 2
1,0 1,0
Fq q q
k q kr r
q0
1,0F
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Physics 212Electric Fields
Electric Fields
For a point charge, the electric field changes only with its distance from the charge.
It gets smaller as you move away from the charge.
q1
11,0 2
1,0
Eq
kr
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Physics 212Electric Fields
Electric Fields
If we draw the filed lines, we can see that they get less dense with distance
The number of lines is proportional to the amount of charge.
11,0 2
1,0
Eq
kr
q1
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Physics 212Electric Fields
Electric Fields are fields which add as vectors
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
where 0 tells us the position at which the measurement is being taken.
20,1
10,1
r
qkE
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Physics 212Electric Fields
Finding Electric Force
To find the force exerted by q1 on another charge q0, use the equation
where E1,0 is the electric field at the point where the charge is found.
0,100,1 EF
q
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Physics 212Electric Fields
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 212Electric Fields
Definition of a Field
Field Lines
Electric Fields
Superposition
Relationship to Electric Force
Field as a Physical Property