01AP Physics C - Electric Fields and Forces

7/25/2019 01AP Physics C - Electric Fields and Forces

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Electric Fields andForces

AP Physics C


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Electric Charge

Charge is a property of subatomic particles.Facts about charge:

There are basically 2 types: positive (protons)

an negative (electrons) !"#$ charges %$P$! an &PP&'"T$

charges ATT%ACT

Charges are symbolic of fluis in that they

can be in 2 states 'TAT"C or *+A,"C.


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Electric Charge The

specifcs'ome importantconstants:

-The symbol for CA%/$ is q

-The unit is the C&0!&,1(C)name after Charles Coulomb-"f e are tal3ing about a '"+/!$

charge particle such as 4 electron

or 4 proton e are referring to an

$!$,$+TA%* charge an often

use e to symboli5e this.

Particle Charge ,ass

Proton 4.674894C 4.6; 74892;3g

$lectron 4.674894C .44 7489


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Charge is CONSERVED

Charge cannot becreate or estroyeonly transferre from

one ob=ect to another.$ven though these 2charges attract initiallythey repel after

touching. +otice the+$T charge stays thesame.


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Conductors and Insulators

The movement of charge is limite by the substance

the charge is trying to pass through. There are

generally 2 types of substances.

Conuctors:Allo charge to move reaily though it.

"nsulators:%estrict the movement of the charge

Conuctor > Copper ?ire

"nsulator > Plastic sheath


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Charging and Discharging

There are basically 2 ays

you can charge

something.

1. Charge by friction

2. "nuction

1"&+"Cis the first9ever ionic formula

mascara. The primary ingreient in1"&+"C is a chain molecule ith a

positive charge. The friction cause by

seeping the mascara brush across

lashes causes a negative charge. 'ince

opposites attract the positively charge

formula aheres to the negativelycharge lashes for a ramatic effect that

lasts all ay.
http://www.smashbox.com/index.cfm/fuseaction/products.detail/categoryID/9ec2c870-e97d-4276-8d49-1e9378210522/productID/08278600-dd84-4fd1-b7c6-4ef8abe40ae1http://www.smashbox.com/index.cfm/fuseaction/products.detail/categoryID/9ec2c870-e97d-4276-8d49-1e9378210522/productID/08278600-dd84-4fd1-b7c6-4ef8abe40ae1


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Induction and roundingThe secon ay to charge something is via

"+0CT"&+ hich re@uires +& P*'"CA!C&+TACT.

?e bring a negatively charge ro near a neutral sphere. The protons in the sphere

locali5e near the ro hile the electrons are repelle to the other sie of the sphere. A

ire can then be brought in contact ith the negative sie an alloe to touch the

/%&0+. The electrons ill alays move toars a more massive ob=ects to increase

separation from other electrons leaving a +$T positive sphere behin.


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Electric ForceThe electric force beteen 2 ob=ects is symbolic of the gravitational force beteen 2

ob=ects. %$CA!!:

MmFg2

1

rFg

LawsCoulombr

qqk

r

qqF

C

Nmx.k

mFx

r

qqF

rFqqF

o

E

o

o

o

EEE

'4

1

10998constantCoulomb4

1

1085.8spacefreeoftypermittivi

alityproportionofconstant41

1

2

21

2

21

2

2

9

12

2

21

221

==

===

==

=


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Electric Forces and Ne!ton"s#a!s$lectric orces an iels obey +etonBs !as.

$7ample:An electron is release above the

surface of the $arth. A secon electron

irectly belo it e7erts an electrostatic

forceon the first electron =ust great enough

to cancel out the gravitational forceon it.

o far belo the first electron is the

secon

e

e

mg

e

r > =

==

=

)8.9)(1011.9(

)106.1()1099.8(

1

2199

21

2

21

x

xx

mg

qqkrmg

r

qqk

mgFE

D.4 m


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Electric Forces and Vectors$lectric iels an orces are A!! vectors thus

all rules applying to vectors must be folloe.

Consier three point charges @4> 6.88 7489C (locate at the origin)@

D.887489C an @2> 92.887489C locate at the corners of a %"/T triangle. @2

is locate at y> < m hile @


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E$a%ple Cont"

=

=

2!

2

999

2!4

)102)(100.5()1099.8(

F

xxxF

=

=

1!

2

99

91!

5)105)(106()1099.8(

F

xxxF

@4

@2 @.44 7 489 4.6; 74892;3g

@both>4.6 74894C

vo> 8 mFs

$ > D28 +FC

t > EK 7 489 s

=

==

E

EE

F

x

F

q

FE

19106.1520

==

====

axamF

axamF

FFmaF

pE

eE

NetENet

)106#.1(

)1011.9(

2#

1

==

==+=

)1048(

)1048(

9

9

xav

xav

atvv

pp

ee

o

8.3& x10-17N

9.13x1013$ss

4.98 x1010$ss

4.38 x106$s

&.39 x103$s


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(n Electric ,oint ChargeAs e have iscusse all charges e7ert forces on other charges ue to a fiel aroun

them. 'uppose e ant to 3no ho strong the fiel is at a specific point in spacenear this charge the calculate the effects this charge ill have on other chargesshoul they be place at that point. !i3eise for avery smallamount of charge.

2c%ar&epoint

2

2

r

kQ

E

r

QqkEq

EqF

q

FE

r

QqkF E

EE

=

=

===

P&"+T CA%/$

T$'T CA%/$

2244 r

qE

r

QE

oo ==


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E$a%ple -4x10-1&C charge is ()aced at the origin. ,hat is the

$agnit+de and direction of the e)ectric fie)d (rod+cedby if a test charge #ere ()aced at x % -0.& $ /

=

=

==

ir

mag

E

E

xxr

kQE 2

129

2 2.

)104(1099.8

0.899 NC

"o#ards to the right

%emember our e@uations ill only give us ,A/+"T0$. An the electric

fiel !$AJ$' P&'"T"J$ an $+T$%' +$/AT"J$.

-

0.& $


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Electric Field o- a ConductorA fe more things about electric fiels suppose you bring a conuctor

+$A% a charge ob=ect. The sie closest to hich ever charge ill be"+0C$ the opposite charge. oever the charge ill &+!* e7iston the surface. There ill never be an electric fiel insie a conuctor."nsulators hoever can store the charge insie.

There must be a

positive charge on

this sie

There must be a

negative charge on

this sie &% this

sie as inuce

positive ue to theother sie being

negative.


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E$tended ChargeDistri&utionsAll e have one so far has been ealing ith specific P&"+T' in

space. ?hat if e are ealing ith an &1L$CT that has acontinuous amount of charge over its surface

Consider a hoo( of radi+s #ith a

tota) charge of distrib+ted

+nifor$)y on its s+rface. *ets

derie an ex(ression for the e)ectricfie)d at distance b +nits do#n the

!x axis.

?e begin by efining a ifferential charge dq atsome arbitrary position on the loop. This ifferential

amount of charge ill prouce a ifferential

electric fiel dE at 7>b


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E$tended ChargeDistri&utions?e begin by efining a ifferential charge dq atsome arbitrary position on the loop. This ifferential

amount of charge ill prouce a ifferential

electric fiel dE at 7>b

$

$cos

$sin

?hat is r the separation istance from the dqto point b

r


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E$tended ChargeDistri&utions

$

$cos

$sin

r

b

%

21

2221

22

21

2222222

)(cos

)(sin

)()()(

b!

b

b!

!b!b!rb!r

+=

+=

++=+=

?hat is r the separation istance from the dqto point b

r


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21

2221

22

21

2222222

)(cos

)(sin

)()()(

b!b

b!!

b!b!rb!r

+=

+=

++=+=

$

$cos

$sin

r

))(4

(

))(

)()(4

1(

))(

)(4

1(cos

2

22

21

2222

21

222

b!

bqE

b!

b

b!

qE

b!

b

r

qEE

o

x

o

x

o

x

+=

++=

+==

"hat is for N ery

s$a)) a$o+nt of

charge: "o find the

""* -fie)d for

each an eery )itt)edq #e #o+)d need

to///

INTEGRATE!


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2

22

2

22

222

21

2222

21

222

)(4

))(4

()(

))(4(

))(

)()(4

1(

)

)(

)(

4

1(cos

b!QbE

qb!

bEE

b!

bq

E

b!

b

b!

qE

b!

b

r

qEE

o

x

o

xx

o

x

o

x

o

x

+=

+=

+=

++=

+

==

o o e 3no e i it

right

!etBs ma3e b >>>> R then R

oul be so tiny that from

that istance the hoop oul

loo3 li3e a point.

'o if Rent to M$%& then

the e7pression oul loo3

li3e:

2 4)(4 bQ

bQbE

oo

x

=

"t is the 'A,$ e@uation as that of a point chargeI


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rrq

rorrx

q

"

q

Micro

!

Q

"

QMacro

2

)(2

2

=

==

==

Assume that for an insulating is3 the

charge is istribute throughout its area. ?emust use the 'A,$ techni@ue to erive the

moments of inertia. $7cept instea of the

mass being istribute it is the CA%/$.


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rbr

rbEE

br

bqE

br

b

br

qE

br

b

s

qEE

!

o

!

xx

o

x

o

x

o

x

+

=

+=

++=

+==

0 2

22

0

2

22

21

2222

21

222

)(4

2

))(4

(

))(

)()(4

1(

))(

)(4

1(cos

rrq

rorrx

q

"

qMicro

!

Q

"

QMacro

2

)(2

2

=

==

==

!

o

x

!

o

!

xx

brb

bE

r

br

rbEE

02

122

0

2

22

0

))(

11(

2

)(4

2

+=

+

=

?e still nee to apply the limitsI


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))(

11(

2

)0())(

11(2

))(

11(

2

)(4

2

21

22

21

22

02

122

0 222

0

b!b

bE

b!bbE

brb

bE

rbr

rbEE

o

x

o

x

!

o

x

!

o

!

xx

+=

+

=

+=

+=

oo

x

o

x

bbE

!b

bE

22

01

)!)0(

11(

2 221

22

==

+

=

!etBs ma3e % NNNNN b in other

ors e are loo3ing at the is3

0P C!&'$.

Thus b approaches M$%& an

% oul go to infinity. ?hathappens

?hat oes this mean

The electric fiel hen istribute over an area is "+$P$+$+T of separation

istance. This means that the fiel is C&+'TA+T at all points aay from the

area.


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.our turn /let"s ta0e it step&* step1

!

!

!

!

!

!!

!

!

!

!

!

?hat is the electric fiel E as a function of r. for an

"+"+"T$ !"+$ of charge (a.3.a a very long ro). 1eginith the hori5ontalI

y

7

r

ylq

l

qMicro

L

QMacro

==

==

==

?hat is dqe@ual to


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ylq ==

))(4

())(4

(

))(

)()(4

1(

))(

)(4

1(cos

2

222

22

21

2222

21

222

yx

yx

yx

xqE

yx

x

yx

qE

yx

x

r

qEE

oo

x

o

x

o

x

+

+=

++=

+==

!

!

!

!

!

!!

!

!

!

!

!

?hat is the electric fiel E as a function of r. for a !"+$

of charge (a.3.a a ro). 1egin ith the hori5ontalI

y

7

r?hat is dExe@ual to


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ylq

l

qMicro

L

QMacro

==

==

==

!

!

!

!

!

!!

!

!

!

!

!

?hat is the electric fiel E as a function of r. for a !"+$

of charge (a.3.a a ro). 1egin ith the hori5ontalI

y

7

r?hat is Exe@ual to

rE

rxi#xx

xE

y

xy

xEE

ox

oo

x

o

xx

2

!2

)2

(4

)(

1

4

2

2

22

=

==

+

=

1y ma3ing 7 > r e are

saying this is the electric

fiel along a line parallel

to the ro a istancex

or rin this case aay.


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2hat a&out the *direction3

=

+=

y

o

yy

E

yxyyEE

2

22 )(4

M$%&I

The y components CA+C$! out above an belo the ro. The

ones belo the origin e7ten upar an the ones above the ro

e7ten onars. The symmetry CA0'$' the components to

cancel out.

The e@uation is ientical e7cept for &? you solve the integration. "n the

hori5ontal e coul bring the 7 out because it as constant. "n this case the

y CA++&T be brought out as the dqvaries in height above an belo the

origin. 'o the y is a CA+/"+/ variable.


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In su%%ar*All of the electric charge istributions ere erive from that of a

point charge.22 44 r

qEr

QEoo

==istributions can prouce ifferent

functions epening on hether the charge

is istribute over a !$+/T A%$A or

J&!0,$.

;+nction ?o)+$e@

Ais' or =heet>@

*ine rod orcy)inder

>*BN@

$@uation24 r

QEo

=r

Eo

2

=o

E2

=

"hese eq+ations are i$(ortant for )ater so 'ee( these in $ind:

01AP Physics C - Electric Fields and Forces

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Transcript of 01AP Physics C - Electric Fields and Forces