Exam 2 on November 16. 2007 - Physics106- R. Schad
YOUR NAME
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STUDENTNUMBER
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A proton(mass1-.7x 70-"'kg andcharge1.6x 10-'" C) travelsdown the z axis with
velocityv=-10okm/s.AtallnegativevaluesofzthereisamagneticfieldB=3jT.
The proton entersthe region of magneticfield and re-emergesgrdistanced"awayfrom
r *
/
its initial trajectory.What is d? [make a drawing first].
A)
B)
--) c)
D)
E)
4.
ft
oLr'
,i\
3 . 5 . 1 0 -m
3
3 . 5 . 1 0m
3
7 . 1 . 1 0 -m
3
1 . 1 . 1 0m
3
1.1. 10-1m
s
k _fr,,,,
cl.2 r
'(t
Tr
ri
A 6V batteryis connectedthrough a doublethrow switch to an inductanceof 6mH and
a resistanceof 3000 Q. Initially the switch is openand the currentis zero.
At time t=0 the switch is thrown to position A.
At time tr = lps the switchis thenthrown to positionB.
What currentis flowing in the inductanceat time t = 2ps?
n)
a)
b)
c)
d)
e)
l'l frr, "/,',*p b
4.8 . 10-4A
1 . 2 .1 o - 3 A
7.8. 10-4A
2.4.r0-4A
1 . 6 '1 0 - 3 4
7;,=
*'D-,-*uJ
:
*,.**.*""..-1''
*
I
1,,
Sr"
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ffi
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rtTt
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l
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t
r
Q
Ca{ *1 oloath
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e
,/ry
: i f i - e n * ) r - YE
{
? =-R
Two coils lie on the table. ff the current in the larger coil is clockwise and increasingat
a constantrate. then the induced cuffent in the smaller coil will be
5.
B
(a)
(b)
(c)
(d)
(e)
clockwise and constant
counterclockwiseand constant <clockwise and increasing
counterclockwiseand increasing
zero.
An electronmoving in the positive x directionexperiencesa magneticforce in the
positive z direction.If Bx = 0, what is the directionof the magneticfield?
6.
f t
n
I
b.
negative y direction
positive y direction
negativez direction
d.
positive z direction
e.
negativex direction
Fs
r
=r
^\
ri's
VXB
\
lJ
n{. rt're
7.
fr
An electronmoveshorizontallytoward a screen.You want the electronto travel in a
straightiine, but there is a magneticfield present(out of the page).What directiondoes
the electric field have to point in order to cancel the force due to the magnetic field?
e
O
sereem
O
E
<-.\
0
Fe
0
o
0
o
0
'r/4C
r:
t
t
s
.
a
\.J
r
,l
4
n(Lrlc,u<F
(
1
L :
_
F
I-
,A
I L-<-.
L^/
(y'toward top of page
]
*
l
>d
IT-
C
I
B) toward bottom of page
C) into page
D) out of page
E) none of the above
8.
R
2 parallel,long, str
what direction doest
wirgS have large
7llnetic
the pageas shown.ln
fieldpo
j
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ftnneaf til**e
9.
A wire and a 10 f) resistorareusedto form a circuit in the shapeof a square,20 cm by
2O cm. A uniform but time-varyingmagneticfield is directedinto the plane of the
circuit. The magnitudeof the magneticfield is decreasedfrom 0.9 T to 0.3 T in a time
period of 60 ms. The averageinducedcurent in this time interval is:
c,
f* em
&
j7-_
--A
AL/_J_ dA
R m
e a
a & f f i
-c1'#
ctul
=;
e f f i f f i
r)
tnr 4 D
/
K-
ttt
irL
tril'$]
a.
b.
-)c.
d.
e.
1 2mA
24 mA
40 mA €
60 mA
80 mA
A chargedparticle travelingin the planeof this screenentersthe region of a uniform
1 0 . ,magneticfield pointing into the screen,as shown.The subsequentpath of the particlein
the region of the magneticfield could be representedby which path?(Selectall that
apply.)
b. path 1
q
-$.
path2<-
i(
d. path 3
e. noneof thesepathswould be possible
curv( )
--//
.tfr
T H . K HN : d l: )i
'"s.":1"H .r, Ii 7 \:
,H'.,il- ,*uo
K s : s & " H !i
j{
.".f
.X
!:
}{ Kj}{ ,H}"H H " q
H H t "
$u'S"-f;l
i,{}
K.}H X F{ """''
s . xH
K
4,
/
fron
k;o^
\
n th I
d
A particle (q = 5.0nC, m = 3.0 trrg)moves in a region where the magneticfield
1 1 . has componentsBx = 2.0mT, By = 3.0mT, andBz = -4.0 mT.
At an instant when the speedof the particle is 5.0 k*/s and the dj.rectionof its
velocity is 120orelative to the magneticfield, what is the magnitude of the
\s
acceleration of the particle?
l
a.
33m/s2
b.
17 rnts2
c.
d.
39 m/s2 €25 mls2
e.
45 m/s2
I
A= 2rh
{
tr --
r\r
f XrB
7r 0 t r q q
r
E=
^-
*-
E^,
One long wire carriesa currentof 30 A along the entire x axis.
12. A secondlong wire carriesa cuffent of 40 A perpendicularto the xy plane and
passesthroughthe point (0, 4, 0) m.
What is the magnitudeof the resultingmagneticfield at the point y = 2.0 m on the y
axis? [bettermake a drawing]
Qr
B
-=--)
( ;q!I
4opr
b,
=Qo4 *u( o{ t/' ff"-
5.0prrs-
c.
3.0pT
d.
7.0trrT
e.
1 , 0p T
4
at
(4 Z, 0)
E,
C,st4t116^(
Lr. 4o,,
= l/ i
8z go;n6',g(( =//i
D:,
=Jo$
u1
-/7
i
/toL
'ha
=3rT
?fT
There is no current in the circuit shown in the figure below until the switch is closed.
1 3 . The curryr+Lthloughthe 20-f) resistorthe instant after the switch is closedis either [1]
D
1,5A or [2] 5.0$, and
the curreiffiug!.-th-tQ{2
eitherI3ls.0n ofu 15),)
Which combinatioiMe
resistorafter the switch has been closed a long time is
above choicesis correct?
, L A
j (&t'|
,r
=2*r
:
--1t
a.
b.
c.
d.
e.
[1] and [3]
[1] and [a]
[2] and [3]
[2] and [4] <None of these
- IL
:p
4 V
2o[L t*o,Q
WP
At'- I. = fr_"
' :r",{"Tf:{'
,t
E)/2 =
/,,
,ffi =lrn
Kinematics
V=Yo*8't
x=xo*vs't*Yz'a'tz
v2=vo?+ 2a.(x-xs)
Newton'sLaw
y =(v+vdl2
F=m.a
F-,,i^,= m.E
Conservationof Energy
= KEz * Uz
KEl + U1 * W1,y6uj
Energy
Kinetik (linear):
Potential(gravity):
s = 9.80rrlsz
KEln = lzmv'
Un=mgy
Work
W=F'd=FdcosO
Power
P=Wt=E/t
(electrical)
oulomb force
P=IAV=12R=(AV)2/R
^
F=hgrgz/r'r
lectric field
h=Il4neo
.
/lnn
E = F l q =k " | 3 ,
= - VV
,r rvoLume
E=h q) tf
Electricflux
OB=
forapointcharge
Iiai
surface
Law
Gauss
t
@ -e =
'
Jl E d
A = Q i n s i a e /=€4on k * ' Q i n s i d e
closetlsurface
Potentialenergy
B _
I '
A U = U n - U a = - qt l l E d S
- qAV
A
Potential
AV = AUI q= -
-B-*)
-+
(=
pointcharge)
ln a s lGqh
A
Capacitance
Charging/discharging
of Caoacitor
parallel plate C]
C = Q/AV
[ = eoA/d
=
C"q Cr + C2 + C: + ... [parallelcombination]
l/C"q- l/Cr + llC2 + llC3 + . .. fseriesconibination]
IJ = Q2/2C=V2Q LY = L/zC(492 [energysroredin C]
q(t)=Q.(1 -"'un')
I(t)=(AV/R).e-Ync
q(t) = Q' e-'ec
I(t) = -(AV/R)'e-^"
Ohm'sLaw
R = AV/I = o. l/A
[o = resistivitv= 1/ol
Resistivity/ Resistance
P = m" I (n q't) [t = scatteringtime]
p = po [1 + cr(T - T")] [temperaturedependence]
1/R*q= l/Rr + 1/R2+ 1/R3+ ... fparallel]
R.^ = R' + Rc * Ra* ...
lseriesl
Masnetic force
Fs=g.yXB
Fn = I. L x B
lFB -I. dsxB
Fs/L = (UIrIz) I (?na)
Cyclotron motion
: - (mv) / (qB)
fcircular motion of a chargein 3=(qB)/m
a masneticfieldl
Magnetic Field by a current
Ampere'sLaw
[force on straightconductor]
[forceonconductorsegment]
lforce between2 puallel wiresl
[radius]
[frequency]
' (I ds x r) / rz
1B - trto/4n
Law]
[Biot-Savarr
B = (p"I) /Zna)
straight
wire]
fiong
qBds = ltol
"lorrkoop
Maenetic Flux
os= [iai
surface
Faraday'sLaw of Induction
) m f= ( A V = ) - N . ( d O B / d 0
Lenz'Law
the polarity of the inducedemf is suchthat it wants to act
'against'
the cause.
Inductor
LR circuit
emf=(AV=)-L.dVdt
electronmass
f f i " = 9 x 1 0 - 3 k1 g
proton mass
frp=2 x 1o-27
kg
elementarycharge
e= L.6x 10'1e
C
Coulomb constant
k"=9xloeNm2/c2
Permittivity of free space
ro= 9 x 10'12C2lNm2
Permeabilityof free space
Vo= 4n ' 10'7Tm /A
Speedof lieht
c=3x108m/s
I = AV/R . (1 - e-'^)
[ = AV/R . e'ut
l=L/R
'switch
on'
'switch
off'
[electron:-e ;proton:+e]
lG= 1/(4ne")