01AP Physics C - Electric Fields and Forces
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Transcript of 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
$sin
r
b
%
21
2221
22
21
2222222
)(cos
)(sin
)()()(
b!
b
b!
!b!b!rb!r
+=
+=
++=+=
?hat is r the separation istance from the dqto point b
r
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E$tended ChargeDistri&utions
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$o+nt of
charge: "o find the
""* -fie)d for
each an eery )itt)edq #e #o+)d need
to///
INTEGRATE!
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E$tended ChargeDistri&utions
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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E$tended ChargeDistri&utions
rrq
rorrx
q
"
q
Micro
!
Q
"
QMacro
2
)(2
2
=
==
==
Assume that for an insulating is3 the
charge is istribute throughout its area. ?emust use the 'A,$ techni@ue to erive the
moments of inertia. $7cept instea of the
mass being istribute it is the CA%/$.
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E$tended ChargeDistri&utions
rbr
rbEE
br
bqE
br
b
br
qE
br
b
s
qEE
!
o
!
xx
o
x
o
x
o
x
+
=
+=
++=
+==
0 2
22
0
2
22
21
2222
21
222
)(4
2
))(4
(
))(
)()(4
1(
))(
)(4
1(cos
rrq
rorrx
q
"
qMicro
!
Q
"
QMacro
2
)(2
2
=
==
==
!
o
x
!
o
!
xx
brb
bE
r
br
rbEE
02
122
0
2
22
0
))(
11(
2
)(4
2
+=
+
=
?e still nee to apply the limitsI
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E$tended ChargeDistri&utions
))(
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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.our turn /let"s ta0e it step&* step1
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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.our turn /let"s ta0e it step&* step1
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: