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1Norah Ali Al-moneefking Saud unversity
23.1 Properties of Electric harges23.2 harging !"#ects $y %nduction23.3 oulom"&s 'a(23.) *he Electric +ield
23., Electric +ield 'ines23. otion of harged Particles in a /niformElectric +ield
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Electric harge
*ypes Positive lass ru""ed (ith silk issing electrons
Negative
4u""er0Plastic ru""ed (ith fur E5tra electrons
Ar"itrary choice convention attri"uted to 6
/nits amount of charge is
measured in 7oulom"s8 Empirical !"servations
'ike charges repel /nlike charges attract
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harge in the Atom
Protons 9:; Electrons 9-;
%ons Polar olecules
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23.1 Properties of Electric harges onservationelectricity is the implication that electric charge is al(ays conserved.
< *hat is= (hen one o"#ect is ru""ed against another= charge is notcreated in the process. *he electri>ed state is due to a transfer ofcharge from one o"#ect to the other.
< !ne o"#ect gains some amount of negative charge (hile the othergains an e?ual amount of positive charge.
@uantiation*he smallest unit of charge is that on an electron or proton. 9e B
1., 5 1-1C;
%t is impossi"le to have less charge than this
%t is possi"le to have integer multiples of this charge
Q Ne= )Norah Ali Al-moneef
king Saud unversity10102,
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onductors and %nsulators
onductor transfers charge on contact %nsulator does not transfer charge on contact Semiconductor might transfer charge on
contact
DNorah Ali Al-moneefking Saud unversity
23.2 harging !"#ects $y %nd
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harge *ransfer Processes
onduction Polariation %nduction
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23-3 oulom"&s 'a( Empirical !"servations
+ormal Statement
1 2F q q2
1Fr
irection of the force is along the line #oining the t(o charges
1 2
12 21221
kq q
F rr=
r
Norah Ali Al-moneefking Saud unversity
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Norah Ali Al-moneefking Saud unversity
F
Consider two electric charges: q1and q2 The electric force F between these two
charges separated by a distance r is given by
Coulombs Law
The constant is called Coulombs constantand is given by
221
r
qkqF=
229/CNm109=k
The coulomb constant is also written as
!is the "electric permittivity of vacuum#
$ fundamental constant of nature
2
212
00 Nm
C1085.8where
4
1 ==
k
2
21
0
4
1
r
qqF
=
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Norah Ali Al-moneefking Saud unversity
C
ou"le one of the charges
force dou"les hange sign of one of the charges
force changes direction
hange sign of bothcharges force stays the same ou"le the distance "et(een
charges force four times (eaker
ou"le "oth charges force four times stronger
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Norah Ali Al-moneefking Saud unversity
1
%&le:
'hat is the force between two charges of 1 C separated by 1 meter(
Ans(er F.CC 51CN=
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oulom"&s 'a( E5ample
Ghat is the magnitude of the electricforce of attraction "et(een an ironnucleus 9?B:2,e; and its innermostelectron if the distance "et(een them is
1.D 5 1-12m
*he magnitude of the oulom" force is + B k@1@20r2 B 9C. 5 1CN H m202;92,;91., 5 1I1C;
91., 5 1I1C;091.D51I12m;2 B 2. 5 1I3N.
11Norah Ali Al-moneefking Saud unversity
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Norah Ali Al-moneefking Saud unversity
12
E5ample - *he JeliumNucleus
Part 1 *he nucleus of a helium atom has t(o protons and
t(o neutrons. Ghat is the magnitude of the electric force"et(een the t(o protons in the helium nucleus6
Ans(er DF N
Part 2: What if the distance is doubled; how will the forcechange?Ans(er 1).D N
)nverse square law: )f the distance is doubled then the force isreduced by a factor of *+
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13
onsider t(o charges located on the 5 a5is
*he charges are descri"ed "y ?1B .1D 5 B . m ?2B .3D 5 B .) m
Ghere do (e need to put a third
charge for that charge to "e at an e?uili"rium point6At the e?uili"rium point= the forces from the t(o charges (ill
cancel.
x1
x2
-Position
Norah Ali Al-moneefking Saud unversity
10102,
mx
x
qq
kx
qq
k
16.0
)4.0()( 232
2
31
=
=
Jere the forces from ?1and ?2can "alance.
q3
xx
x x4.0
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Zero Resultant Force, Example
The magnitudes of the individual forces will beequal
,irections will be opposite
'ill result in a quadratic Choose the root that gives the forces inopposite directions
Two fi&ed charges- 1mC and ./mC are separated by 1!cm as shown in
the figure 0a where may a third charge be located so that no force acts on
it(
cmx
xx
x
qqk
x
qqk
7.13
)10(
103
)(
101
)10()(
2
6
2
6
2
32
2
31
=
+
=
+
=
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1D
two charges are located on the positive x-axis of a coordinate system, as shown inthe figure. harge q!"#n is #cm from the origin, and charge q#"-$n is %cm
from the origin. &hat is the total force exerted 'y these two charges on a chargeq$"(n located at the origin)
*he total force on q$is the vector sum of the forces due to q!and q#individually.
*he total force is directed to the left, with magnitude !.%!x!+-%.
Example:
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1,
E5ample - harged Pendulums
onsider t(o identical charged "allshanging from the ceiling "y stringsof e?ual length 1.D m 9ine?uili"rium;. Each "all has a chargeof 2D . *he "alls hang at an angleB 2D(ith respect to the vertical.
Ghat is the mass of the "alls6
Step 1*hree forces act on each"all oulom" force= gravity and the
tension of the string.
mgTF
d
kqTF
y
x
=
=
cos
si
!"e#$o%&""
2
2
5
y
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Norah Ali Al-moneefking Saud unversity
1
-Pendulums 92;Step 2:The balls are in equilibrium
positions. That means the sum of all
forces acting on the ball is zero
$&
/
cos
si
2
2
22
d
kqmg
mg
dkq
T
T
=
=
Ans(er m B ., kg
A similar analysis applies to the "all on the right.
d=2 l sin
10102,
mgT
d
kqT
=
=
cos
si2
2
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Norah Ali Al-moneefking Saud unversity
1F
+orce
oulom"&s 'a( that descri"es the electric force and
Ne(ton&s gravitational la( have a similar functionalform
$oth forces vary as the inverse s?uare of the distance "et(een the o"#ects. ravitation is al(ays attractive. k and give the strength of the force.
Felectric = kq
1q2
r2
Felectric = kq
1q2
r2 Fgravity = G
m1m
2
r2
Fgravity = Gm
1m
2
r2
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Norah Ali Al-moneefking Saud unversity
1C
Example:
n electron is released a'ove the surface of the Earth. second electrondirectly 'elow it exerts an electrostatic forceon the first electron ust greatenough to cancel out the gravitational forceon it. /ow far 'elow the firstelectron is the second)
e
e
mg
Fe
r " )
==
==
=
)8.9)(1011.9(
)106.1()109(
31
2199
21
2
21
x
x
r
mg
qqkrmgr
qqk
mgFE
(.! m
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( )( )
N102.8
m103.5
C1060.1
C
N.m109.
4
1
8
211
219
2
29
2
2
0
=
==
r
eFe
ompare the electrostaticand gravitationalthe forces
( ) ( )
( )N106.3m103.5
k1067.1k1011.9
k
N.m107.6
47
211
2731
2
211
2'
=
==
gg
gr
mmGF
pe
Fe/Fg" # x !+$0*he force of gravity is much wea1er than the electrostatic force
*he electron and proton of a hydrogen atom are separated 2on the average3 'y a
distance of approximately (.$ x!+-!! m. Find the magnitudes of the electric force
and the gravitational force 'etween the two particles.
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Norah Ali Al-moneefking Saud unversity
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Electric +orces and KectorsElectric +ields and +orces are A'' vectors= thus
all rules applying to vectors must "e follo(ed.onsider three point charges, 4!" 5.++ x!+-0 2located at the origin3,4$"(.++x!+-0, and 4#" -#.++x!+-0, located at the corners of a R67/* triangle. 4#is located at y" $ m while 4$is located %m to the right of 4#. Find the resultantforce on 4$.
4!
4# 4$
$m
%m
(m
4$
&hich way does 4#push 4$)&hich way does 4!push 4$)
Fon $ due to #
Fon $ due to !
" $8
" tan-!2$9%3
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=
=
23
2
999
234
)102)(100.5()1099.8(
F
xxxF
=
=
13
2
99
913
5)105)(106()1099.8(
F
xxxF
===
=
+=
==
=
=
)($&
)()(F
1062.6)37si(
1018.3
)37cos(
1
22
res"$&$
9
13
9
2313
x
y
res
yx
y
x
x
F
FDirection
F
FF
NxFF
NxF
FFF
4!
4# 4$
$m
%m
(m
4$
Fon $ due to #
Fon $ due to !
" $8" tan-!2$9%3
5.6 x10-9N
1.1x10-8N
F$,!cos$8
F$,!sin$8
7.34x10-9N
2*+/ !above the 3&
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oulom"&s 'a( E5ample 4 5 2+! mC
L 5 !+1! m 'hat is the magnitude and
direction of the net force on one ofthe charges(
F1
+
F2
F3
Q
x
y
L
++
+
L
QQ
Q
2)Norah Ali Al-moneefking Saud unversity
&e find the magnitudes of the individual forces on the charge at the upperright corner:
F!" F#" kQQ9L#" kQ#9L#" 20 x!+0 ; m#9#325 x!+$3#92+.!++ m3# " $.#% x!+8 .F$" kQQ92L
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Norah Ali Al-moneefking Saud unversity
2D
along the diagonal, or away from the center of the s4uare.
From the symmetry, each of the other forces will have the samemagnitude and a direction away from the center: *he net force oneach charge is" 5.#+ =!+8 away from the center of the s4uare.
.
( ) ( )
45$&
102.6107385.4107385.42 2
10385.4101.1451024.3
10385.4101.1451024.3
101.145707.0101.62si
101.145707.0101.62cos
45so1
*
*$&
0
01
7
777
777
77
33+
77
33,
0
F
F
45so1*
*$&
==
=+=
=+=
=+=
====
====
===
===
F
F
F
F
F
F
x
y
y
x
NF
N
N
N
N
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Norah Ali Al-moneefking Saud unversity
2,
E5ample - +ourhargesonsider four charges placed at the
corners of a s?uare (ith sides of
length 1.2D m as sho(n on theright. Ghat is the magnitude of theelectric force on ?)resulting from
the electric force from the
remaining three charges6
Ans(er
+ 9on ?); B .C1, N
L and the direction6
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#$-8> *hree point charges are located at the corners of an e4uilateraltriangle. alculate the net electric force on the 8.++ u charge.
HOMEWORK :
#$-?: *wo small 'eads having positive charges $q and q are fixed at theopposite ends of a hori@ontal insulating rod extending from the origin to thepointx =d.a third small charged 'ead is free to slide on the rod. t whatposition is the third 'ead in e4uili'rium) an it 'e in sta'le e4uili'rium)
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#$-!#> n o'ect having a net charge of #%.+ is placed in a uniform electricfield of 5!+ 9 that is directed vertically. &hat is the mass of this o'ect if itAfloatsB in the field)
$-!?> *wo #.++u point charges are located on thex axis. Cne is atx =!.++m, and the other is atx =-!.++ m. 2a3 Determine the electric field on the yaxis at y =+.(++ m. 2'3 alculate the electric force on a - $.++u chargeplaced on the y axis at y =+.(++ m.
#$-%!> n electron and a proton are each placed at rest in an electric field of(#+ 9. alculate the speed of each particle %?.+ ns after 'eing released.
#$-%%> *he electrons in a particle 'eam each have a 1inetic energy of !.5+ x !+-!8. &hat are the magnitude and direction of the electric field that stops theseelectrons in a distance of !+.+ cm)
10102, 2FNorah Ali Al-moneefking Saud unversity