.'. A balloon, initially neutral, is rubbed with fur. until it
acquires a net charge of -0.60 nCo (a) Assurrung that
only electrons are transferred, were electrons removed
from the balloon or added to it? (b) How many electronS
were transferred?
b)
(")0:
O. ~'l(\~-~C­
0
-
\. '-0
'f, \C)_\~c.
l.~. A +2.0-nC point charge is 3.0 cm away from a -~.O-nC
point charge. (a) What are the magnitude and direction
of the electric force acting on the +2.0-nC charge?
(b) What are the magnitude and direction of the electric
force acting on the -3.0-nC charge?
_(%1'1 ~\O 'I ~l.) (:I XIO'" Co) l3" ,~"\::.)
--­
r£­
(0.
03 rn,)"Z­
\F' - ~)( 10-0; N
~ ~t)~
Col-
~~ wo... ~
6')
1:>"",,
-+"--
-t l.t
~~
~ fQ)~
- ~, U.n.
oc. -\\.....
~ 'fY"\o..j~\~
-th..
<-\-l... ~ L.O
CI-. s
~',
0'"
-\i-.
,e-J-i.;).l'\
c...
ti>I~
e..- \..o..r~
t
t..."'.0...,
V­
0",
-t L.,O V" ~
-Y 4:o",,~JJ
15. In the figure, a third point charge -q is placed at point P.
What is the electric force on -q due to the other two
point charges?
I-d-l- 2d---l
r
to"
1.=
-\-~
-
'3,0 n<:' t\.Q.r~ ;j
c.. "'-e- 'f-..
'0 vJ- .+ "j I "­
-\-4. 2.,0 V'\ c... L~)SL-'
----......,.-------------------­
--
'18. Three point charges are fixed in place in a right triangle.
What is the electric force on the -o.60-J.lC charge due to
the other two charges?
+0.80 JlC
I,
I ,
+
I
' ,10.Oem
I
,
8.0 em)
,
I
f~
-,;;)- -0.60 I1C
+, =
'
""7"\\
--
"-~
+ 1.0 I1 C
+- O. ?>J-AL
~z. -= -
e:t- ;3
0.1.0 JAC
-I- 1,0}-'- C--.
-
F~ L.:: \1. \~ ~\))~ ~ :( 8.'\ 'I tlQ "I~",- (0, ~ A10-b e)( (;h(.X \(;,'" e-)
d /2.2­
( 0,08' rt"\ ;1..
::O.6'lN_~
1="'-3
:=-
":.. \
~ .. ~'\-"!>~
d'l. ~
:=-
(~ ,<1 '" x\ 0'" tl.t) ( fa ,lo ItlO-1o '--\
)l \ C-10
)"Z. ----- -.---------­
((),C~ ~
I. S N -t~~~-.C.'5 '-"~
-
( \
'F\2.l. 40 ~Z7
'S\(\C-t
\F l~ SFll.'- -t 1=1-~ ~ ~(u.\,1)~d',S)'e::.. t 0.",-' l~ t"-,,,-I ( O,c.1-)
\
1=1. ~ )
=
1
(1'\
1...-10
L
().DO\)
e...
;0
\
+ >'.
\
0'-\
\,5
L
D....
r~LTl
= \-V-IN
c...')
22. Two Styrofoam balls with the same mass
m = 9.0 X 10-8 kg and the same positive
charge Q are suspended from the same
point by insulating threads of length
L =0.98 m. The separation of the balls is
d =0.020 m. What is the charge Q?
;
_ (D,OZO\
2 (O/1i"/
-
~
"Q
D.O\
S'l,,-1 (0,0 \ )
::.
. -:. _O,~'6°
t.{)v,-"
h.,
le)?) ..
rE =
k <i'Z.
':
f~
~ L f) bu"",S/1..
o:; ci.
\)~n
::
l\}.(} 1. 0);;'1. t 8 .~L ){ 10-? N)
c-~
__ .•.---..... ... \
____- - -
-to-V) e /L..­
~,q ~ X, 0 9 ~ 1.
- ~. 0 X\ 0 -41 C.
....
0 .. 0\
/
~
-
c.
F" I r~
c)l-
Q:::
lO' ~~ )
C.
i
I
-6J.~t9rSg
'::'J
What are the magnitude and direction of the electric
field midway between two point charges, -1511C and
+1211C, that are 8.0 cm apart?
~.,\<1.)( \o'1..~N'\2/(}·
f ,-=
\o..0 4 ~) "L.
:: to •., X'1G t N!L.
E 1. ~ e.g, '1 9 x\ o~ }\hn1./"1.)( \ 5 V'ObC\
lo, O~ ~)"Z..-- 3.L\ 'f..llJ 1- NIt.- -T~ ~ r.)'-' ~
~ \ V" ~ \001;\'~
E =
=­
-
~, ~
[ , . \- t:
7­
--
\.~~\OiN/c.
t,~ fO\~~
~,7XI()1tJJc
to +k I;' hT-
1-
\A
~, lot X \01-
~L,
S~ cl\r~
~/(..
Ccr -ty.
Or
dll"~D.i'\)
-t ow""" &.0 - I';~C. (.,~P-
Sketch the electric field lines in the Q
-2Q
Q
plane of the page due to the charges~')
shown in the diagram.
l)~ fi)'I0-\-\ o..~
t r 0 rw-.. +- .... -c/
--\ 0 IN o.r J !>
Th. ';) O,rt~
M~,..1..
e.A.,..",...l--o
..+k e-k ov yv.:'
i.o1
/1')'
Problems 39-42. Two tiny objects with equal charges of
7.00 lie are placed at the two lower corners of a square with
sides of 0.300 ro, as shown.
;-39. Find the electric field at point B,
A
B
midway between the upper left and
right corners.
40. Find the electric field at point C,
the center of the square.
[Jc
-+ 1. Find the electric field at point A,
the upper left corner.
Problems 39-42
t \ ~ -\ ~-z.-?XO
-
e
:: (,
- 2, S- 4
/'
-
E :: \
I
J r t1.Y
')(\0 5
~f '5 ~ \ 0 5 NIL
EX'"l..
-+ £y1­
~ :' t~"_r (~)
\ ~:' f15~ Q\'~v<?-
~
=
h~-'
~to '5 NIL
JJ
Ie..) ~ l.-.S~
X!t)
'>JJ/c
I
I
50. A horizontal beam of electrons initially moving at
4.0 x 107 m/s is deflected vertically by the vertical elec­
tric field between oppositely charged parallel plates. The
magnitude of the field is 2.00 x 104 N/C. (a) What isthe
direction of the field between the plates? (b) What is the
charge per unit area on the plates? (c) What is the verti­
cal deflection d of the electrons as they leave the plates?
\} l.
-= Y,0 )( \
t -
1-- W\) C;
C)
"2 ,QO 1- \0'4.}J I C-
~ k ~~ rQ"'"
o...)
~~ I
'F=
~C
~ 1':
S \ '" t..L
J..t. c..~~
~or~ \" ~ C",\?
'S
~
~~..s
1:: W'I'-' \-
t\
~ S~ ~ vet
~ ~.\'" t- ol(,,)w~
I
----l._----=-=~
Vi
=4.0 x 107 mls
I
~L .. O
\0)
'E.
'::
~--2.0cm---
G - E Co
-60Q A
= l7-,CO X \()~ ~/c.)(~.~SX)O-\7. s::
}.]'tVI~
A
G
= I. 'I ~
..­
X 10-
~
c... /vn 7..
A
c)
F; "J
r.=:
(..L'-
~c..h u-
1-1:: :: Ct, 6x \ 0\<1 C) ( 7.00 )110'1 JJIc.)
~ I:: =- ""' 0...
~
3, S'
CXd-~
F:',J -l \ ~
\:>t.~ -
~
p\~
7J t
-1
y1-
o
+
'1LtA.
1t
\J 'f...:' 'I-­
t
Xl
I~ 9,\( ~\O-3\~
0:> n,/s'Z-
t :'
-
"I­
~)' ~ )\) \ 5' 'f\') I)7.- ') l 5' )1\ \)- 'I) 5)Z-.
q. l..\ )( 10 -1../
VY'"\
1
\
'I-
Vi-
_
"2,..)1 62 ",",
4.0)(lu1
1r}/J
)
------=--"L
1­
856. A conducting sphere that carnes a total charge of -6 ~C
is placed at the center of a conducting spherical shell
that carries a total charge of + 1 /-le. The conductors are
in electrostatic equilibrium. Determine the charge on
the outer surface of the shell. [Hint: Sketch a field line
diagram.]
7
n-..- ,h.\\ b
~ 'ho..ry1h.L
c..
l
­
N-\­
0'- "" \,M L
\ '" 1"\ i f S W ~ u.
S~ ~
_
~~~
-\- ~ Y r- -+
0
Q
~~\I
- 7'
t 4l..­
L
c...,,",ar~
fA
oC
bc;..\",",~c> -tkQ,. ~6,J'- ~ s f ~ ~ \ 1'\,,) \ L
-
+-l}A-C
857. A conducting sphere that carries a total charge of +6 ~C
is placed at the center of a conducting spherical shell
that also carries a total charge of +6 /-le. The conductors
are in electrostatic equilibrium. (a) Determine the
charge on the inner surface of the shell. (b) Determine
the total charge on the outer surface of the shell.
/
: !--=~+,c J
/
\
J
~