SP212-3321/5521
April 5, 2016
Exam IV
A resistor network is shown below.
AW
2.012
3.0r2^
6.0Q
2.oa
-wv
Question 1; What is the equivalent resistance of this network?
(A) 13.0 n
(B) 0.67 12
0.90 n
Question 2: An 18.0 V potential difference is applied across the terminals of this
network. How much current is flowing through the 3.0 Q resistor?
(A) 2.3 A
JRl 1-0 A
(C) 2.0 ^
JTJTTTA
(E) 6.0 A
Ja " ^
:iM.^:iJL
^e^" 3-/L
;h ier.'Cf
C
•• ^
Ip.O fi
•^3) 6.0^ ^Jkf
^
/J"V
V' t ^
llookej U IZM i^H-y
^
.
- 3.0^
j j ,
,
ToT^^I Chtrts'f'
0.0>4) fi?.0 Jl) - (i.o v <icr«j ffiic'i 3-flrOisivf i*> ier!cj.
3.iZ. ^ 4 -fi.
^
V
'' R
1-1
.
3.0Jt ' •^•<'
li- lo A
1
SP212-3321/5521
April 5, 2016
Exam IV
Question 3: In the circuit shown below, the current through the 9.00 n resistor is
1.18 A directed from left to right. What is the current passing through the 3,00 0
resistor? (Both batteries are ideal, and the ^of the top battery is unknown.)
3.oon
VAr9.00 a
A/W
JA) 0.450^
i=1.18 A
T^TA
(C) 1.63 A
(D) 0.730 A
(E) 3.54 A
G.oon
15.0 V
Question 4: The capacitor in the circuit below is initially uncharged when the switch
is closed at time /-=U. How much current is running through the circuit at time
i=0.75 s?
250.0 Q
AAV
\
(A) 2.80x10-2 A
(B) 3.60x10-2 A
^D) 8.03x10-^ JT)
(E) 2.1^x10-2 A
2.00 raF
9.00 V
413^
3o9oi^
\
(5 V- 6a
L
- (LIZA) (1.0Jl)'O
ISV- lo.U^y
^ O.730 A
(ff.0 .JL
6,
= lit A
c,^o.H5c> A
^C- KC' (QSoJi) (4.0^16^ F)^ 0.50s
6-
lev ,
p
3-50A ^
£
-Vr,
K^
^ I^
O.Soj
=' (o.o%A)e
-3
c - ^.oZ^io' A
I.S
3
' ^'OZ<ic>' A
SP212-3321/5521
April 5, 2016
Exam IV
Question 5: A point charge with q=~3.bfiC is moving with u={440 m/s)i in a region
with a uniform magnetic field S=5.0 T oriented as shown in the figure. What is the
magnetic force acting on this particle? Answer both magnitude and direction.
8=0.0 T
y
,150^
-> v=4A0 m/s
-> X
+2 is out of the page
Direction (30%)
(A) +x direction
(B) -\-y direction
(C) —y direction
Magnitude
(XA) 0.00385"^
(C) 0.00770 N
(D) O.OO550 N
(D), +z direction
(E) 0.00538 X
—2 direction
Question 6: A particle with charge g=+250 mC travels at a constant velocity of
i;=(55.0 m/s)z through a region with a uniform ma.gnetic field given by B-{0.150 T)k
as well as a uniform electrjc field. What is the electric field? Answer both magnitude
and direction.
p
' ©B=(0.150 T)A:
i;=(55.0 m/s)i
-+ X
+ 2 is out
)f the page
Direction (30%)
Magnitude
(A) 0.00273 A'/C
'Hi 2.00 y_/c
(rrnixi] N/c
(E) 13.75 N/C
&
(A) +x direction
^B) +y directiojj)
(C) —y direction
(D) +z direction
(E) —z direction
fi-
i:-,0 •- (i.S'io''c)Ctio-ys) (B.ol) s;, Iso'
= O.Oo3^>S/V
r«'^l4 ktha rule 1
o'^'^ o'f'-fU
(yg)
k'f 2.
Fg =-o.oo^^SAiK
S(,^
CeV'K'v"/" V
l'>»«4K5
^
50 vS-5
E-CSS'V,)C.I5oT)= 8^.55 ^
Fjj >> ;s -y cl;rfcT."T)-»
5® FE "i5 is
ol>rfe.r»0'
^ >
^os; live. ^ 5o £ ;5 «il5e ;>,
E-- ?.3S^ J
li^u r<t/e
♦
v cj;roc>>»n
SP212-3321/5521
April 5, 2016
Exam IV
Question 7: A positively charged particle moves at constant speed vq in a straight
line through a region with a uniform electric field g^nting up and a uniform mag
netic field that points out of the page.
C
lllB' klvB
E-V5
(a) An identical (positively charged) particle is theiPsent along the same pathway,
but this second particle is faster than the first (?; > fo). In what direction does this
second particle bend?
(AIUd
'f ^ ^
1) Dowi^
Jutm the page
f
§
(D) Into the page
(E) It also travels in astraight line
I
^
^ ~^^1S ^
C
V
r.
Win5
'
(b) Another particle is then sent along the same pathway at the same speed as the
first particle (a = vq), but this third particle is negatively charged. In what direetion
does this third particle bend?
(A) Up
(B) Down
(C) Out of the page
'Di Into the nage
(E) It also travels in astraight lin^
l>o"hi
Thy siill iJd -Ic
^
a
F »9V
0
c
ol.'cec-htw-)
O
^
SP212-3321/5521
April 5, 2016
Exam IV
Question 8; A point particle with mass 2.0 x 10"'-^ kg and charge +3.0 x 10" C is
travelling at a constant speed of 2500 m/s in a circle of radius 6.5 m, moving clockwise
when viewed from above. What is the magnetic field in this r(^gion? Answer both
magnitude and direction.
n
/,p
2500 m/s
X
6.5 m
+z is out of the page\
Direction (30%)
(A) +x direction
Magnitude
(A) 1.60 T
-1
(B) 5.78 T
Co 2.bQT>
(D) 6.41 T
(E) 1.08 T
—X direction
(C) +z direc^oi
xlO
•=rrTJTfection
(E) +'£/ direction
Question 9; A rectangular wire loop of dimensions 0.600 m by 0.400 m lies in the
xy plane. A current of 1.80 A moves counter-clockwise around the loop when
viewed from above. The magnetic held in this region is uniform and is given by
S=(0.350?+0.650^) T. What is the magnitude of the torque acting on the wire loop
at this moment?
y
2=1.80 A
<
(A) n.9.K1 N-m
0.400 m
(fB) 0.151
(^) 0.319 N-rn
(D) 0.378 N-m
(E) 0.468 N-m
0.600 m
lliy/S>'-'^^
c.
^
<v^
^p
s>= ,§r
- nos/ T
Cs*/o-^c) a.s^) ^ O. i?56,T
^0* \ •
—i.
&
Q
r*
Ik
Vicft
^V
V
^
^ * oltrcc'f'r'">
^
ol,V^c/•^»-i
ty
g-- 3M'I6''t ^
*7'
A-A/t/4Ck)' 1 Cl.^oA)(.i^* ,i^) k
- O.U3 y^-rv,^ /T
t ^(.''3^^m k) ^ 63se •^.6s J)T
CCw ^roclkci $clecL
c«^Ur
•C= f.lsa/4 «M6ss T)' o.is; /v.».
"t-- O.isl a/'m]
SP212-3321/5521
April 5, 2016
Exam IV
Question 10: Two very long wires, separated by 0.50 rn, are perpendicular to the
page, i[ carries 3,0 A out. of the page, while 12 carries 5.0 A into the page. What is
the magnetic field at poiiit/f marked below?
0
j;2=5.o a
Direction (20%)
(A) +.T direction
(B) —X direction
Magnitude
(A) 2,75 T
(B) 4.00 T
(C) 3.73 T
D) 4.40 T
^C) +v direction
xlO
(D) —y (iirectio_r^
E) 1.07^
+2 clirectKm
Question 11: A current of 3.5 A moves around a loop as shown below. The circular
regions of the loop have radii of 0.40 m and 0.95 rn, and subtend 120° of angle. What
is the magnetic field at point P, the center of curvature for the two arcs?
-i-3.5 A
0.95 m
-> X
+z is out of the page
P
0.40 m
(A) 1.33 T
Direction (20%)
(A) +.T direction
(B) 2.60 T
(g 6.Q7T
f g 4-2 direction
Magnitude
1.06 Ip
(E) 1.49 T
(B) —.7; direction
xlO
^(D) —z directio^
(E)
direction
JU,,^
6--
6,^
3lXtr
(In'10^
-- 3.1'16''7
ar Co.asm)
6,
Coki^rC "cJoclCtJtjc.
Af />o:,+
- (ZHk10'''T)j
?^
n , (tTr*lo^'^)(SA)
.
r:—7-T-— : l.sy^lo T
air
I> c}oc.ki^stj li P
P
v-Li)
D,
15-
M,c <i>
ilaiJ!:
+-n.J3*/o"^T)3
Lo^^io^'r ^
d!>
'r
i /^O'* iIL£2f!Z2i!£
,' ^3
3^po
.
—.
otiter rsd^kj'. co(it»"f*r "C./«tlciji'jc ctjf/>frk")- SO &
iMHer r^ijt!t*i\ c/ocfctvJje Ct^rrt^i- so
«»/
i"
•^2"
^ . (%«/0 y)C3.5A)(f)^ (1ll'l6*'^)(l.SA)(f]
"'^
fir Co. ISO
*
•hr(o.lo^) ''(4)
• (?.7I(.<I0*T *) *(~l.n3fl6'Ti)
-- l.oi,'l6''J I
SP212-3321/5521
April 5, 2016
Exam IV
Question 12; Two very long, straight wires run parallel to each other and separated
by 0.75 m. The wire on the left carries 2.5 A in the -\-y direction, while the wire on
the right carries 5.0 A in the -y direction. What is the force acting on a 1.5 m long
section of the wire on the right? Give both the magnitude and direction,
12=5.0 A ^
m,
X
0.75 m
..
11=2.5 A
Direction (30%)
Magnitude
(A^ i.noxin-^
N
A) -\-x directioip
({B) 5.00x10"^
—X direction
(Gj i.uuxiO"-'N
(D) 1.25x10-*^ N
(C) +y direction
(D) —y direction
(E) +z direction
(E) 0 N
Question 13: A toroid is wrapped with 1200 turns of wire. The inner radius of the
toroid is 0.100 m while the outer radius is 0.150 in. The wire carries a current of
3.25 A. What is the magnitude of the largest magnetic field inside the toroid?
(A) 6.24x10"^ T
4.90x10-^ T
(C) 7.80x10-^ T
3.4^xlU ^
(E) 5.20x10-^ T
#12) r .
^
aF ^V5»h)
/<vr*,/fe/ c^f«n")> •%'Hr<tJ^ Ai^.'-parJlef cc,f/>^eHt fe^el
Hoc
( 4- X cl:reeh»^ )
F-+5.00^/0^/7 6 i
4f/3) C-
^
anr
Ltkr^e^'f B
r*
tile
T'i . loo Kn
C/ir^/o^^ ^)(S.^SA)(IStoo)
Sir ('()
6-- 7.ro>/o'T/
SP212-3321/5521
April 5; 2016
Exam IV
Question 14: A long straight wire has a radius of 1.80 mm (0.00180 m) and carries
a current of 12.0 A in the +k direction (out of the page). The current is evenly
distributed with a constant current density. What is the magnetic field at point P
shown below? Give both the magnitude and direction. Point P is 0.00120 m from
the center of the wire, in the +j direction from the center.
X
+z is out of the page
Direction (30%)
(A) +.T direction
Magnitude
f(A} 8.89x10-^' ID
B) ^93x10"'' T
(C) 2.00x10"^ T
(D) 1.33x10"^ T
-X directiorQ
(C) +y direction
(D) —y direction
(E) +2 direction
(E) 0.370 T
Question 15: The current flowing through the 2.50 mH inductor shown below is given
by i{t) = 1.5P + 2.0/., where i has units of amperes when I has units of seconds and
a positive current indicates current flowing to the right. What is the induced emf
across this inductor at time /=0.75 s?
I
2.50 mH
Magnitude
(A) 1.93x10-3 V
(B) 6.56x10-3 Y
(C) 5.86x10-3 V
7E) 0.0106 V
pirection (30%)
fXA) Induced £f^ points left (against current
\Bj Inclucea
points rigtit (.witn current)
o
f=
M
'O
c*
t^-
«r^
X
o
-el's
ri
fl
n
U
c
fi
c
Off
OQ
o
VA
r
=€
cl
1.5
c-n
CO
cO
X
to
o
CK
rt
-'c.
t=
O
r
a>
'o
0
.n
u
0
1
"o
c
%
I
f I
or
+
CO
n
•K
Of
«y
'nj
•-0
f'
ni
•iU\
r^
vS
cO
l»
LA
r»rt
o'
SJ
^f:
>
o
o
0
1
or
•<{^
r
cA
X
Q
iy\
Of
ft
KJ
SP212-3321/5521
April 5, 2016
Exam IV
Question 16: A circular loop of radius /?i=0.150 rn is placed in a uniform magnetic
field S=0.450 T directed into the page. The circle then shrinks to a final radius of
Hf=O.ObO m over a period of 6,00 s. What is the average induced cmf in the loop
while it is shrinking? Answer for both the magnitude and direction of the induced
emf.
/?,=0.15 m
05=0.450 T
Magnitude
Direction (30%)
(A) 2.36x10"^ V
fAi Copnter-Qockwise
Clockwi^
(B) 0.838 V
(C) 5.06x10^ V
'^E) 4.71x10-3^
Question 17: A square loop of wire, 0.25 in on each side, lies in the plane of the page.
A uniform magnetic field points out of the page, and is increasing in magnitude at
the rate of ^=0.15 T/s. What is the induced emf in the loop? Answer for both the
magnitude and direction of the induced emf.
®
0.25 m
®
Magnitude
GA) 9.38x10"';^^
(B) i75xi()-^ V
(C) 8.95x10^ V
(D) 0.600 V
(E) 2.95X10-W
®
®
®
®
®
®
®5 is increasing
Direction (30%)
tAi Connter-Clockwise
(^B) Clockv^d^
4l(A
§a'-
c
D clA
E=-S^:ii
A
oU.• Af j—tj
Af-A."
'if
ir'-=T5fS7^''--°='«s'
£- -.(-o.Hsor)(-o.oio1^^
£ - -H.T-l'^id^^
o|.'rccT;»«\ ! cleclCulJC
tX-f-crnnl
ItioliiCajf & •'5
jS
pkte J
'i clockk>>SC,
m) £-A(-^ A(-i .J
(5 =-Co.is''>i)fo.jsi>,f = -
£ =-7.J« '/0"^V
J.'rec-^^n'. c^loclCulse.
"Tlfe
IS iS »ncrc<s/^ j ^6 "Me t'xJttCffJ S <^.'11
oppoific e>i.4«rH*( R
I^Jucecl Brs Jh-L Ue
St l^JucoJ ccrre^f .<3 docku,:s^
SP212-3321/5521
April 5, 2016
Exam IV
Question 18; A circuit is shown below. The emf of the ideal battery is £^=16.0 V,
each of the two identical resistors is of resistance /?=4.0
and L=1.0 H for the
inductor.
R
+
R
L
(a) How much current is output by battery immediately after the switch is closed?
cic4> ni
(A) 8.0 A
(B) 16.0 A
tro k<n
no
4.0 a;)
JouK
.'s-frr/tfr
D) 1.0 A
(E) 2.0 A
Hsi
^ Iky
<•• 'iSL ""
I,
(b) How much current is output by battery a very long time after the switch is closed?
(A) 8.0 A
"(B) Id.O A
(C) 4.0 A
(D) 1.0 A
{£) 2.0 A
i6V —
'fJl
L
mA
Jl 6
I
_L
"iSL
/4 V
c --fL
^ ^.oA
A
SP212-3321/5521
Exam IV
April 5, 2016
A solenoid wrapped with A^=350 turns is 0,250 m long and has a cross-sectional
area of 0.00150 m'^.
Question 19: If a current of 4.5 A runs through the solenoid wires, what is the mag
nitude of the magnetic field inside it?
(A) 1.98 T
(B) 1.19 T
(C) 2.36 T
-3
xlO
).54 T
[E) 7792 T"
Question 20: What is the inductance of this solenoid?
(A) 6.50 H
(B) 2.31 H
(C) 5.77 H
(D) 7.91 H
(fe) 9.24^
-1
XlO
&-JUt I n
N
ZSO iuii*s
It,
n- 7 -- —TP— " IHoo
j,
6' f1i7«/cr'^)Cf,5/11(;Yoo-^g-«)' o.oojiiT
6- ?.?2«/o-^T
Al
L'-ClTr*ld'
^)Vo.C)o/so,n')
/L' taf'io''jO