TOC 1 Physics 212 Electric Fields Definition of a Field Field Lines Electric Fields Superposition...

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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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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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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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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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Change Temperature

Temperature is a scalar

Its magnitude is changed when it heat is added or taken away.

It has no direction.



Magnitude

Direction

Units

0

none

degrees F

Degrees C

Example of a Scalar

255075100

Real Life

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Example of a Vector Field


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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Example of a Scalar Field


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


N

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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

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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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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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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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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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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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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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

TOC 1 Physics 212 Electric Fields Definition of a Field Field Lines Electric Fields Superposition...

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