19
In Fig. 24-33,
wharis rhenerelecrric
potentialar poinr
P due to the four particlesif
fl
r
e
'
V : A at infinity,q : 5.00fC,
3
\
ul/-,
andrl = 4.00cm ? $sftn
"
-0.'
\
-q
--tl--
'o t {v
\\ ,
tI
S = V+
r V.*V3+V.
3 & l .+tg.
d
J
= 1 td
* (s- f -ol s + $r. lO
\
^-lS
o.0cf
-A
,.6I xlO
V.
\.
't
-.,il
L
. -fS
r 5x l0 r,
It-
sxld
a,
-
)
l'5 cm apart and
are
plates
metal
parallel
Two large
Gd
\-/
but oppositesignson their
of equalmagnitu{es
lr*u" charges
Take the potentialof the negativeplate to
facingsurfaces.
be zero.If the potentialhalfwaybetweenthe platesis then
+5.0 V' what is the electricfield in the regionbetweenthe
plates?
]fl"
r
i
V=? 0
< - d >
-t
E . d- =-Ed
'|df
s
J'F'
l a v l =Ecf
AV=
-'
0 .o 0 ? 5
E
x
E
*
d
=
=
s
5
a
+ E = 66+\A
t
\
The electricpotentialat pointsin an,ryplaneis givenLry
(2.0Vim?)x? (3.0 V/m?)y?.In unit-vectorncration,
V
_
wtratis the electricfield at the point (3.0m, 2.0 m)?
l /
I
V --V(*,?)
E*3 -
*t^r o dirn cnJfons .
2vr-
-
-
4 3
7*
FJc
z"l
d Ct, a) :>
rl
-
6a
12
F*s-
Ei"s l z
-l
E a . - f a -i
* r ai
$/-
lPl . lrrlf Vc,
0 s - t 5o
How much work is re-
At
quired to set up the arrangement *f Fig. 24-46 if q - zJlA
pc, ft
ticles are initially infinitely far
apart and at rest? ssrurtrw
-q
+q
l?.-'=?
l
&
f
l
,
l
-L.-*|,
tffuflfrt
-q
+q
fig, a4-q6 Problem
37.
Th. p"h.h*l .h.?Y + +ti ?.)tle'"r
,t Po"hJari s
U = U , . + U r g+ U r + + U e 3 + U z r +
+ Ur+ ,
u3*1'(-*-+
=14, (
a-
r
\vi
-
#
+
*.
*.- #-il
q
x
l x Q * t O €.*ro')1r.r
o.6rf
- ) =
= - - 1 . 1x l 6 ' t s
Th. c.*0,^niof nlotk' .lone is W= AU
_13
W - - U = - 1 . { xl o s
U4-
,('
S]$, In the rectangleof Fig.
21-49,rhe sideshave lengths
ob-
-1-
ri
b
5.0 cm and 15 crTl,r11_ -5.0
'With
PC, and.Qz: +2,A p,C.
U = 0 at infinity, what is the
---o{,
electricpotenrialat (a) corner Fig, z4-4g probrem
41.
A and (b) corner B? (c) How
muchwork is requiredto movea charge :
Qs +3.0 pC from
of therecangre?
j:.4 along4 diagonar
itl oo*s rhiswork
IIncrease
or decrease
the electricpotentialenergyof thethree_
chargesystem?rs more. less,or the same
work requiredif
q3 is movedalonga parh rhatis (e) inside
the rectanglb
but
not on a diagonarand (f outsidethe rectansre?
)
ss'
'') VA= e(*
+
ff)=
Vo= ( 1 i . $ \ =
4
6 xl 0 v
a 7,8x t
0v
4rl
-\
C,l
-l
\r
.
f
vV=
al
\
{
V.) =
=
CVnlrAV 1,
3 * l 6 n ( 6 *l d * ? . g x
tf) = e,sJ
V\J) o : +
lnCl^ea Sa i n
P,E, o+
++.f sh'n [ w = a a >oJ
e)a"d I) Elsstric fo.,. is conscr ,,.li vg
=> n/o"h is **e sarnc- (\ fcrrrernlacr
?\ttoD
,o----l
'or
an electron
particle(.either
a proton)is movingrightward
betweentwo paratlelitrarged
l,l'*
l.l
il
|
til
i2
46'
Fig.z4-5o Problem
Vr = -70't) V anrl l': =
are
potentials
plate
The
mm.
=
qtl't)
d 3.00
of
speed
initial
an
from
is'slowing
*50"0V. The particle
(a) Is the particlean elecrronor a proprate.
reft
the
ar
n*1,
* " r ( b ) W h a t i s i t s s p e e c l j u s t a s . i t r e a c h e sI p l a t e 2r-', }
L
plates separatedby distance
t-.
fr
, Thc' farhde'
rr
-l-'l^
NhlleAtcclcration
t.
If
lO+
lL
+offi. nbl'tb
flrou;n1
- ?oV
:) ,b ir e, proton(1>o)
b) Gnrcnrut,r + ensraY
AK + AU = o
l<+-k3 ,- Aq 3 - lAV
k 1B K c - 1 a V
I
jr
AV
*
C
l
5
- v
^ rg. t ,e- L
2A
Av
nt'^/il
5 - I '
A4= 6.5rl0{ m/s
- 5oV
QSf) What is the excesscharge on a conductingsphere of
frd-iurr : 0.15m if the potentialof the sphereis 1500V and
V - 0 at infinitv? ssm
V..*u B
+ q + 1= Y+g 2.5.r6t
lL
R
--{
A hollowmetalspherehasa potentialof +400V with
@
*
Hlect to ground(definedto be at V 0) and a chargeof
5.0 x 10*qC. Find the electricpotentialat the centerof the
sphere"
V"; n cpnter tr tf,'e Sarrrgqr V
on n swrfi.e
Vr*.f.,.s + 4oov=Vcr.rtr
it\sidt
e$althrrt
U
:,
Hr, sph€re..
QSf) What is the excesscharge on a conductingsphere of
frd-iurr : 0.15m if the potentialof the sphereis 1500V and
V - 0 at infinitv? ssm
V..*u B
+ q + 1= Y+g 2.5.r6t
lL
R
--{
A hollowmetalspherehasa potentialof +400V with
@
*
Hlect to ground(definedto be at V 0) and a chargeof
5.0 x 10*qC. Find the electricpotentialat the centerof the
sphere"
V"; n cpnter tr tf,'e Sarrrgqr V
on n swrfi.e
Vr*.f.,.s + 4oov=Vcr.rtr
it\sidt
e$althrrt
U
:,
Hr, sph€re..
F b s p h e r e l w i t h r a d tro*
i u s Rspheie
l h a s pI oand
s i tinitially
i v e c huncharged'
argeq.Sphere2
far
is
2.00Rr
radius
ffih
with a wire thin
connected
are
spheres
After the separated
V1of
(1),t-
charg*'
,o ,.ilin ""rv negligible
enough
ryi::j,tal
spherelgreaterthan,lessthanlorequaltopotentialVsof
s p h e r e ? ? W h a t f r a c t i o n o f q e n d sof
u pthe
o nsurface
( b ) s p hcharge
erel.and(c)
iatioo'to'
,irr*r* zr ll[l'l*";-
urt
densitiesof the sPheres?
.A
&td
4) hJlra"ttt. fi^ro .f hens are 6nn ctFcol tfi'*7
Uitl haw ftc' Sarrtr- pt
PoF"tfi^l '
u
q
't)
vf:
Ll,
Vr B {]*
lR,
R,
b * V ,= V r + g . =2 1 ,
1t
fg
t
-
6tb
41rR,r
o,.d ol.+1z=1
=+(*f *"a=
^/.."\,
sphericalshells
conducting
1.r58) Two isolated,concentric,
}ilt radii Rr * 0.500m and Rz : 1.00m, uniformcharges
thicknesses.
Qr: +2.00;rC andQz: + 1.00pC, andnegligible
Whatis the magnitudeof the electricfieldE at radialdistance
(a) r : 4.00m, (b) r : 0.700m,,and (c) r : A.2A0m? With
V: {) at infinity,whatis Iz at (d) r: 4.00m, (e) r - 1.09m,
m,and(i) ' :
(t) =9JS:1' (e)ggloo,m' (h)r - 0'200
0? (j) SketchE(r) and lz(r).
R ,= 0 . S r n
R.= ( t'\
^
O
t
)
lru
\3
6lL -- I f, C\l t T
I
qJr
-
v
:
I-: I 'ra
v-- +9:11't
- 6.+*tJV
r
It
I': trn
3 R,l
l^l 0.?.n
l'I
0"5rn
?, R,
f :
0.1rn
V B
V=,
r+ fur
&-g
r
3 . 5 x 1 0V
Ra
*, qo,= 4 . 5 x roqy
? + q-
V =q ' +
cl
4p1B 4 . 5 x t D ?
(:
r*\
I
q
charges
fgq
$C
89 )] Two charses
Q : *2.0 pC
Yn."J;il;". ert-2.0cm
t - a
\-/n
\
)
r
l'
t
/rn
1
---
tUsart
*.yart (Fig. 24-69). (a) With
l,/ : 0 at infinity, what is the
electricpotentialat point C?
{,
/r.
^
f*
d/,2
I
rt/Z--*I*-rl/2*9
q
(b) You bring a third charge q
q = +2,ApC from infinity to
Fig.z4-69 Problem89.
C. How muchwork mustyou
do? (c) What is the potentialenergyU of.the three-charge
whenthe third chargeis in place?
configuration
Solv.d+ J"u.tq )
- - )
(
\
I