Midterm 2 Solutions Nov. 10, 2010

Physics210 Midterm #2
N o v .1 0 , 2 0 1 0
lnstructor:
Dr. JulieAlexander
Time= SOminutes
TotalMarks= 30
1
IGY
Name
Cafculate
theenergyreguired itoI a sSlS E M ble
the arrayof chargesshownbefow,
wherea = 0.300m.
mar
rks
s)
'(i
b - 0.400m, andg = O.Od1.rC.
q
-t,l
,+
.
l
lI '
I
I
t l
"JI
Ll
/( J(:l)
/.,,="j
I
I
J
I
t-
l_ .+
-I
.. l._,
,
r
Y-f,
Y) . C(
i
+rt)(7)
-.tJI
:-1.(
|
-r- Cr z)
)(
+ (-z{z)
r C2XZ)
"J
T,t=4,
r5
+ t3[z )
-+
L
2[
+4
L
,3
1)l
!-++
,! G
=
vfi'(
il
r:
\J.
,r3,
l113:f
V',€-,-
2'
over a ceftaint9gi9nof space,
the electricpotentialis v = 5x magnitudeof the electricfield
3f y + 4yz2v.what is the
at inu ptirt p thatnas cooroinates
(t, o, l'z) ^z(4 marks)
\ -T
-
€
?
a-j=
6x"1 i _ ), 45
J -l
a;
L5
..-u:
>v
'- -Tttrnrl?1
2^.2
qJ (= _f'*r+
\
d.\
.J
=
L
[BJ.]:o
Irl: -t3
L-
\€l
2
-\tt 3+5
V
"
lt
2.-'
-''
I
'r ci)^,
N
= t|l'it = t11,"[
f-:-
\--
3'
The temperature
of a sampleof tungsteninitiallyat 20.Oocis
raisedwhilea sampleof copperis
maintainedat 20'0'c' At what temperature
will tfrergsistivityof the tungstenbe four times
that of the
copper?Ptunssten=S.6X10-BQm,
ot-r
otungsten=4.SX1g-i
oC_1
anOp."*',er-=1.TX10-oOm,
o.opp"r=3.gX10-3
(4 marks)
(-
a\
\1! = Itn,,(bTl
=-
l'-t'
o
\
\ -,'
\rd,
L*
\L
r)
= 4= (".(\t
\\.L
/\
'
_p ,/
e,br)
5 .uxrc (' * Lt Sxlcry
/
i-r-X
\/r,-
l, 1x1C
)c
4
etz
: |-r;{Ar
AT= ,7tb:
-T; :=T,
T
+S,ooL
14?= Lt'e
4'
A conductorof radiusr, length J and resistivity
p has resistanceR. what is the new resistance
this pieceof materialis stretchedto + times
if
its originitiength.E*prus you answeras
a murtipre
(4 marks)
of R
/t
u
Xc
f{-+!,"
R,=p Q-
+?J
E:
R.
r
Y-v
ft"t"= AE
T(.'1, =1t ('z'rt
/ f \z
F)
lr"\l =
('+Iq=L
7.(.'/
R*,= (aR
-=t \
n
li
Ao
f\
t/
b
T
+
I
a
J
Chargeof uniformdensity(4.5nC/m)is distributed
alongthe circulararc shownbelow.Determine
5.
to zeroat infinity)
the electricpotential(relative
at pointP.(4marks)
,U
Ad]=)\L&(al
\-; tJ t?=
,Ir=(.Inp .i.,,,0
KJo
i )
-,'
R
\(-.V
(^
(
\
\r
\ O\q
t
i
: i
i : '
r
.
rl
lr'
I\
(.J
qxr
T,
*
o?u
^ZL
+Sr(c-''r^^x
t3
V' 2K !.=
:
/+ 2-t*
I\
lU'rY\
=(
A 4.0-mFcapacitorinitiallychargedto 50 V and a 6.0-mFcapacitor
chargedto 30 V are
6.
connectedto each otherwith the positiveplateof each connectedto the negativeplateof the other.
(4 marks)
What is the finalchargeon the 6.0-mFcapacitor?
Aftr
E.Lt-t'-,"-
a =ev
Q.
Ir
I
+
\4trrP
+-\t+
f sov
tr
\
AD,O*.CW,
r i' =
".o\at
lb''rtF
4nff
t?o(
V
+- t \+-+-
r
t
\(onC
TCC'^C
- lQ'CtnC
7O w'C
a_1
4
60 r'4Qq
b(2)-a3) = 4Qo
|> C
LtLxq = Q Q+'
-*Lo
-,F
4
7'
A parallelplatecapacitorof capacitanceCohas platesof areaA with
separationd betweenthem.
When it is connectedto a batteryof voltageVe,it has chargeof magnitude
eo on its plates.lt is then
disconnected
from the batteryand the plalesare pulleduplrt to a separation2d without
discharging
thgm' Afterthe platesare2d apart,findthe magnitude
of ihe chargeon the plates,the potential
difference
betweenthe plates,and the potential
energyof the systemin termsof eo,v6,dhd p.E.o
respectively.
(3 marks)
/
rA
W
a\
F\-k+,4(
e-:'
-------.-J____-- ?, A/.\
-
I
-
|
i
r)
Y -'-.
i
v.,
CrUa" '=:
L
I
t--
v=
\-1
(
\_7/
^z-)
7
i
\-Y :
/-ll
lV'
'a
;:
*t(r ^
i
II
\
I
?\ ,
?s =iQu=
I
8.
A parallelplatecapacitorof capacitanceCehas platesof areaA with separation
Jout*"en them,.
When it is connectedto a batteryof voltageVq,it has chargeof magnitude
eo on its plates.Whileit is
connectedto the battery,the spacebetweenthe platesis titteowith a material
of dielectricconstant5.
Afterthedieloctric
is added,findthe magnitud"oitn" chargeon the plates,the potential
difference
betweenthe plates,and the potentialenergyof the systemin termsof
eo,Ve,ofld p.E.orespectively
(3 marks)
--r
/
l
(/ ) = , }-t"\-:-=n,
( (i , t / r _
-*-
m
l\
, \/
I V
/
-/
/
\/
V , '\)
^
f
/'
),.-_.,
"*
i
I
]
t)
Y
p)
\
rl
L
-7
i -_.
l'-
;
I
i
-fr
L)< v
r"
/
/1
\
|
_\ sQ_,\tr
2u
/-.--
5T€
/t l
| ,
\t
v.):
eo(rf.)
olI
A0+'
,/
z-
z_\_,o
1
I
<
E lt-'.
-r\

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