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Physics IClass 19

The Electric Field

Rev. 13-Mar-04 GB

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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:

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Temperature Map(Temperature Field)

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Coulomb’s Law ofElectrostatic Force (Review)

)r̂(rqq

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, squared.r̂: Unit vector from charge 1 to charge 2.

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Superposition ofElectrostatic Forces (Review)

)r̂(r

qq4

1F

N

2ii2

i

i1

01on

(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

1q)r̂(

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

1q)r̂(

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 !

1

1onN

2ii2

i

i

0 q

F)r̂(

r

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 #19Take-Away Concepts

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

)r̂(r

q4

1E i2

i

i

0

2 . F orce 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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Class #19Problems of the Day

___1. An electron is placed in a region of space where themagnitude of the electric field is 100 N/C and the direction ofthe electric field is north. The direction of the electric force onthe electron is:

A. North.B. South.C. East.D. West.E. Undefined unless we know the locations and values of the

charges that create the electric field.

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Class #19Problems of the Day

2. An electron begins the problem traveling north at 5 x 106 m/s ina region of space where the electric field is 100 N/C in the northdirection. How far will the electron travel before it comes to a stopmomentarily? Or will the electron not come to a momentary stop?

Some useful constants:

e = 1.6 x 10-19 Cme = 9.1 x 10-31 kg

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Activity #19Electric 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.