Transcript Slide 1

Electricity
Field Lines/Pot Surf
TOC
Definition of a Field
Field Lines
Electric Field Lines
Definition of a Potential Surface
Motion of Particles in an Electric Field
Quiz
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Electricity
Field Lines/Pot Surf
What is a Field?
TOC
Fields are properties that 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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Electricity
Field Lines/Pot Surf
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
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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
Electricity
Field Lines/Pot Surf
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
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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
Field Lines/Pot Surf
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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Electricity
Field Lines/Pot Surf
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
Field Lines/Pot Surf
Look at the example below…
TOC
The first (on the left) set of field lines represents a uniform field that
is twice the magnitude of the second (on the right). Both fields
represent vectors that point to the right.
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Electricity
Field Lines/Pot Surf
TOC
Rules for Field Lines
All electric field lines
1. Point in the direction of the electric field vector at every point.
2. Start at positive charges or at infinity.
3. End at negative charges or at infinity.
4. Have a number entering or leaving a charge which is
proportional to the charge.
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Electricity
Field Lines/Pot Surf
Here is another example…
TOC
The first (on the left) set of field lines represents a radial field that is
twice the magnitude of the second (on the right). The first is
generated by a charge that is twice that of the second.
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Electricity
Field Lines/Pot Surf
TOC
Here is an example of how to find the direction of the electric field at a point
on the filed line…
Each point is tangent to the field line and points is the direction
indicated by the black arrow.
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Electricity
Field Lines/Pot Surf
TOC
Positive point charges have electric field lines that point outward.
Negative charges have electric field lines that point inward.
The number of field lines is proportional to the amount of charge.
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Electricity
Field Lines/Pot Surf
Definition of a Potential Surface
TOC
A surface is an equipotential surface if the electric potential at every
point on the surface is the same.
As charges move on an equipotential surface the electric force
does no work.
The electric field at a point is always perpendicular to the
equipotential surface on which the point lies.
The electric field always points in the direction of decreasing
potential.
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Electricity
Field Lines/Pot Surf
TOC
Rules for Potential Surfaces
All electric potential surfaces
1. Are perpendicular to the electric field.
2. Decrease in value as you move in the direction of the electric
field.
3. Are often evenly spaced in terms of potential so that the
distance between them is proportional to the magnitude of the
electric field.
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Electricity
Field Lines/Pot Surf
TOC
Rules for Motion
When subject to an electric force
positive charges
1. Move in the direction of the electric field.
2. Move from higher to lower potential.
negative charges
1. Move opposite the direction of the electric field.
2. Move from lower to higher potential.
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Electricity
Field Lines/Pot Surf
TOC
The electric field lines follow these five simple rules...
1. The number of field lines entering or leaving a charge is proportional
to the absolute value of that charge.
2. The field lines leave positive charges and enter negative charges.
3. The field lines never cross each other.
4. Field lines are closer to each other where the field has a larger
magnitude and farther from each other when the field has a smaller
magnitude.
5. Charges follow the field lines (positive charges in the same direction
as the field lines, negative charges opposite to them)
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Electricity
Field Lines/Pot Surf
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If I have two charges as shown and the value of charge A
is 2 μC, what is the value of charge B?
A
Answer: -3 μC
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B
Electricity
Field Lines/Pot Surf
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Which is not a correct way to draw field lines?
A.
B.
C.
D.
Answer: D
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Electricity
Field Lines/Pot Surf
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Where is the field the strongest?
C.
A.
D.
B.
Answer: C
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Electricity
Field Lines/Pot Surf
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Which way will the electron initially accelerate?
A.
B.
C.
D.
Up
Down
Left
Right
Answer: A
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Electricity
Field Lines/Pot Surf
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Gauss’s Law follows these three simple rules...
1. By definition, flux is given by the equation Φ = EA cos(φ).
2. It also follows Gauss’s equation Φ = 4π k Qinside.
3. The electric field inside the material of a conductor is zero.
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Electricity
Field Lines/Pot Surf
TOC
What is the flux through the surface shown assume that
the particles are electrons and protons?
Answer: -1 x 4πke
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Electricity
Field Lines/Pot Surf
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What is the flux through the surface shown assume that
the particles are electrons and protons?
Answer: 3.62 x 10-8 Nm2/C
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Electricity
Field Lines/Pot Surf
TOC
A charge of -2e is added to
the spherical shell.
Where does that charge go?
A.
B.
C.
D.
It evenly distributes in the shell.
It goes to the inside surface of the shell.
It goes to the outside surface of the shell.
Some will be on the outside surface and some on the inside surface
of the shell.
Answer: C
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Electricity
Field Lines/Pot Surf
TOC
A charge of -2e is added to
the spherical shell.
A charge of 16e is placed
inside the shell.
Where does the charge in the
shell go?
A.
B.
C.
D.
It evenly distributes in the shell.
It goes to the inside surface of the shell.
It goes to the outside surface of the shell.
Some will be on the outside surface and some on the inside surface
of the shell.
Answer: D
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Electricity
Field Lines/Pot Surf
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A charge of -2e is added to
the spherical shell.
A charge of 16e is placed
inside the shell.
How much charge is on the
inside surface of the shell?
Answer: -16 e
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Electricity
Field Lines/Pot Surf
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A charge of -2e is added to
the spherical shell.
A charge of 16e is placed
inside the shell.
How much charge is on the
outside surface of the shell?
Answer: 14 e
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