Physics210
SectionL
Oct.24,200,8
Time: 50 minutes
V 1p.l'I
Name N l- /
Instructor:Julie Alexander
Total marks=40
Pleaseshowall of your work in ttrresppeprovided. Part markswill be awardedfor work shown.
Calculatorsareallowed.k=9Xl O\.ImzlCt %=8.85X10-12C?/Nm2
1) A charge+q is at theorigin.A charge-3q is at x = 4.00m on thex axis.For whatfinite value(s)of x is
(a) the electricfield zero? (3 marks)
l-)
Id-l
r
ler I
9= *trt
(x++1T,
7+4 = U3
)L
0.ns'. x; - 5,*6 n
ft= (J-u-r) r
fi-r
(b) the elechic potentialzerc? (3 marks)
'=V,
a=ry
t
Qns',
t
B
$= I
= +\vn
cA_3
V =V,
I
9
z
q-fts
+-.{
+"5=3W
=gj
z++
z++--vz
z-_7
Physics21O
A^^+:^1
Section
L
z
2) A solid, insulatingsphereof radius,a, hasa uniform chargedensityanda total charge2Q. Concenhic
with this sphereis an uncharged,conductinghollow spherewhoseinner andouterradii areb andc, as ,
shownbelow.
(a) Find the magnitudeof the elecfricfield in the regionr < a, (3 marks)
E/)
l-
EQ
Yrn,
+ TI-a3
a3 rrr
3
z
3
ftt.
4T(z
€o
(b) Find themagnitudeof theelecnicfield in theregiona < r < b. (2 marks)
E-- 2 zo
*
I
(r{ r
a
7rft, c_
&
3
Ov
Physics210
SectionI
(c) Find the magnitude of the elechic field in the region b < r < c. ( I mark)
E*o
(d) Find themagnitudeof theelectricfield in theregionr > c. (2 marks)
E-: aKo
t,r^ 7
I
(e) Determine the induced chargeper unit areaon the inner and outer surfacesof the hollow sphere.
(2 marks)
d
v lrtn({
4$b>
to*T<,{
2A
4rrc'
(f) Sketchtheelectricfield asa functionof r. Labela,bandc on yourdiagram.(3 marks)
V
Physics210
SectionI
4
3) A line of.chargestartsat x = +2mand extends
to.x1+5m.The linear chargedensityis L = b/x
whereb
constant20pc'
Determinatuetagnituae
anaairectioiofthJelecric
retJatLe origin.
,o'lir?Sittttve
?c
dd ==K JE (-i)
0
7'5
b
rs
Kt ()'dt. = -Lt
\-
fr,
-LrV
=t'l'
b (&
r"l
J 7-'
z
)T'
z
-z
L
qxtJ t_.2o*("uf
,__ :,1 =
A'
4)g:T:^:,i*,1"ilr":::o*:'-h,
+-2y73what
is*,,1r",**
*
theelecticfieldatthepointp thathas
*?*trri-toi=
i!, ?\'v
coordinales
ri, o,-ij-rr i+ martg
E
EJ=
I
E=
2
oy= _f
Dz
rl
trl=
\
*8
=
-l*Lz\
+
63*J
t4'
J=
(-..
-7
. SectionI
Physics210
5
5) A long cylinder (Jadius= 4.0 cm) is filled with a nonconductingmaterialwhich carriesa uniform charge
densityof 1.5nC/m3.Determinethe electic flux througha sphericalsurface(radius= 2.0 cm) which hasa
point on the axisof thecylinderasits center.(3 marks)
+=st-"
=
NT
[-/
--
t zo
d=
\,5nc/,;
\x- ( ,ozq)
4{-- D
5bfxro-'tt /rn>
C
6) A particle(m = 2.0 pg, q =:5.0 nC) hasa speedof 40 m/sat point A andmoves(with only electric
forcesactingon it) to point B whereits speedis 90 m/s.Determinethe electricpotentialdifference
VA -VB.(3marks)
=
*f
(vn-vr)
B
KEo {e
I
-)
E
L
2
-f (Vo-vu)
-'ry)
(rx ro
(+f- qo-)
+ fxro-1c
=
l,3o ylo3v
Phvsics210
Section1
7) A +4.0-pCchargeis placedon thex axisat x = +3.0m, anda--2.0-1tC
chargeis locatedon they axisat
y = -1.0m. PointA is on the y axisat y = a{.Qm. Determinetheelectic potentialat point A-(relativeto
zeroat theorigin).(3marks)
A
A
-2/c
8) Chargeof uniformdensity60 nC/# is disnibutedthroughouttheinsideof a longnonconducting
cylindricalrod (radius= 7.0 cm).Determinethemagnitudeof thepotentialdifferenceof point A (3.0cm
from the axisof therod) andpointB (5.0cm from theaxis).(4marks)
Z=
AV=
AV= -
-hO
??"
(-L
\-!
z
e,1tv