20-1

Physics IClass 20

The Electric Field

20-2

What Is a Field?

A field is nothing more than a function of location, either f(X,Y)or f(X,Y,Z). There is a uniquely defined value of a certainquantity at each point. Example – a temperature map:

20-3

Temperature Map(Temperature Field)

20-4

Coulomb’s Law ofElectrostatic Force (Review)

r̂rqq

41

F 221

0

(Prof. B’s version.)

The meaning of each term:

F: Electrostatic force on charge 1 from charge 2.

041:Electrostatic force constant = 8.98755 × 10+9 N m2/C2

1q: Value of charge 1, positive or negative.

2q: Value of charge 2, positive or negative.2r: Center distance from point charge 1 to point charge 2.r̂: Unit vector from charge 1 to charge 2.

20-5

Superposition ofElectrostatic Forces (Review)

N

2ii2

i

i1

01on r̂

r

qq41

F

(find and add X and Y components)

resultant

+1.0 C+5.0 C

resultant -3.0 C

+5.0 C

X

Y

1

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The Idea of Electric Field(Step 1)

W h e n f i n d i n g t h e f o r c e o n c h a r g e # 1 , w e n o t i c e t h a t q 1 a p p e a r si n e a c h t e r m i n t h e s u m , s o w e c a n f a c t o r i t o u t o f t h e s u m :

N

2ii2

i

i

01

N

2ii2

i

i1

01on r̂

r

q4

1qr̂

r

qq4

1F

N o t e t h a t t h e q u a n t i t y i n ( ) a b o v e i s a v e c t o r .

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The Idea of Electric Field(Step 2)

A f t e r d o i n g t h e f i r s t p r o b l e m , s u p p o s e w e w e r e a s k e d t o s o l v e as e c o n d p r o b l e m w i t h a d i f f e r e n t c h a r g e a t p o s i t i o n # 1 , c a l l i t q 1 ´ .

I f w e w e r e s m a r t e n o u g h t o h a v e s a v e d t h e v e c t o r p a r t f r o m t h ef i r s t p r o b l e m , w e c o u l d f i n d t h e n e w f o r c e j u s t b y m u l t i p l y i n g b yq 1 ´ i n s t e a d o f q 1 :

N

2ii2

i

i

01

N

2ii2

i

i1

01on r̂

r

q4

1qr̂

r

qq4

1F

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The Idea of Electric Field(Step 3)

T h e v e c t o r q u a n t i t y w e h a v e c a l c u l a t e d d e p e n d s o n t h e l o c a t i o n o f t h e p o i n t ( # 1 ) . d e p e n d s o n t h e u n i t v e c t o r s t o t h e o t h e r c h a r g e s . d e p e n d s o n t h e d i s t a n c e s t o t h e o t h e r c h a r g e s . d e p e n d s o n t h e v a l u e s o f t h e o t h e r c h a r g e s .

I t d o e s n o t d e p e n d o n t h e v a l u e o f t h e c h a r g e a t t h e p o i n t .I n f a c t , i t c a n b e c a l c u l a t e d e v e n w h e n t h e r e i s n o c h a r g e t h e r e !

N

2ii2

i

i

0

r̂r

q4

1)1#point(E

)1#point(EqF 11on

Electric Field

Force / Field Relationship

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-+

The Electric Field of a Point Charge (as a Source)

The electric field is a vector field, meaning at each point inspace the electric field has a magnitude and a direction. Weshow that by drawing arrows at representative points in thecorrect directions with lengths proportional to the magnitudes.

Away from positiveToward negative

Just because we don’t draw an electric field vector ata point doesn’t mean there is no electric field there.

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Example Problem

A sphere with mass m and charge+q is suspended in a horizontalelectric field, E, by a string.What is the angle that the stringmakes with the vertical direction?

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Example ProblemThe Six-Step Method

1. Identify ForcesTension from string.Gravity.Electrostatic.

2. Coordinate System:X right, Y up

3. Free-Body Diagram

4. Resolve Off-Axis Forces

5. Newton’s 2nd Law

6. Solve

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Example ProblemSolution

X : 0am)sin(TEq x

Y : 0amgm)cos(T y

gm)cos(T Eq)sin(T

gmEq

)tan()cos(T)sin(T

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Class #20Take-Away Concepts

1 . E lec tric fie ld fro m p o in t charge sources:(T o ta l fie ld is the superpositio n o f po in t source fie ld s.)

i2

i

i

0

r̂r

q4

1E

2 . F o rce on a charge in an e lec tric fie ld :

EqF

3 . E lec tric fie ld po in ts aw ay from + source charges.4 . E lec tric fie ld po in ts to w ard – source charges.

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Activity #20Electric Fields

(Computer Simulation Activity)Objective of the Activity:

1. Think about electric fields.2. Use the simulation program to draw electric field

vectors and field lines.3. Use what you learned to find “hidden” charges

from the electric field they make.