1. Definition of a Field
Field Lines
Electric Fields
Superposition
Relationship to Electric Force
Field as a Physical Property

2. Field Examples of Fields:
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.
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)

3. 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.

4. Example of a Vector Change Wind Speed 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.
Change Wind
Direction
Graphical
Representation N
Real Life
Mathematical
Representation
Magnitude 6 18 12 24 w e
Direction
Southwest
Southeast
Northeast
Northwest
Units
mph s

5. Example of a Scalar Temperature is a scalar
Its magnitude is changed when it heat is added or taken away.
It has no direction.
Change
Temperature
Real Life
Graphical
Representation
Degrees C
Mathematical
Representation
Magnitude 50 25 75
100
Direction
none
Units
degrees F

6. 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
Magnitude 11 10 20 12 14 4 11 5 5 6
Latitude
40°
28°
30°
41°
38°
47°
32°
47°
40°
29° N
Direction*
44°
43° 2°
45°
225°
315° 0° 2°
85°
85°
Longitude
95°
81°
123°
118°
100°
106°
91°
83°
86°
73° W
Units
mph
* Angles for direction are taken counterclockwise from East.

7. Example of a Scalar Field65 74 82
Example of a Scalar Field 58 62
Temperature is a function of position.
This position is given by the latitude and longitude of the point where the temperature is taken. 75 48 51 82 87
Graphical
Representation N
Mathematical
Representation
Position
Magnitude 74 65 82 87 62 82 51 48 75 58
Latitude
47°
30°
29°
41°
47°
32°
40°
28°
38°
40° N
Direction
none
Longitude
86°
106°
123°
118°
100°
91°
81°
73°
83°
95° W
Units
degrees F

8. 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.

9. 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.

10. Electric Fields q1 q0 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 q0

11. 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 q0

12. 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

13. 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. q1

14. 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.

15. 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.

16. 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.

17. Definition of a Field
Field Lines
Electric Fields
Superposition
Relationship to Electric Force
Field as a Physical Property