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

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**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)

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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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**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

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**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

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**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.

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**Example of a Scalar Field**

65 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

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**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.**

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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**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

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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

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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

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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

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**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.

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**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.

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

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