Download FINAL EXAM PHYSICS 121 SPRING 2007 A

SAMPLE FINAL EXAM
e = 1.6x10-19 C
PHYSICS 121
me = 9.11x10-31kg
μ0 = 1.26x10-6 T∙m/A
k=
mp = 1.67x10-27 kg
1
4 0
Acir = πR2
Asphere = 4πR2
 

A  B = (AxBy – AyBx) k
 
A  B =AxBx + AyBy + AzBy
0 = 8.85x10-12 C2/ Nm2
k = 8.99x109 Nm2/C2
Acyl = 2πRL
q q
F=k 1 2
r2
point charge:
 
 
1 p
p = qd, τ= pxE
flux:    E  dA
Φ = E·Acosθ
  E A
3
2 0 z
Q
Q
Q


E sph 
E sph , in  (
)r
E con 
E plane 

3
2
0
2 0
V
4 o R
4 o r

2 0 r
potential: ΔU = q ΔV
C
Capacitance:
U
Q2
2C
i
Q
t
I2R
U
1
CV 2
2
J
Q = ne
V2
R
P=
 A
C 0
d
Q
V
f 
V    E  d s
i
L
C  2 0
ln(b / a)
in series : Ceqv (
i
A
J = (ne)vd
C  4 0
1
1
1 1

 ...
)
C1 C2
Cn
in series : Req = R1+R2+…+Rn
in parallel:
ab
ba
E=k
F = qE
F = ma
V= V0 - E∙x
E
C  4 0 R
R
L
A
Reqv = (
dipole:
r2
Q

L
q
  e ncl
0
kq
r
q
V
d
U
kq1q 2
r
C
C0
C

ρ – ρ0 =ρ0α(T – T0)
1
1
1 -1
)

 ... 
R1 R 2
Rn

Q
A
v = v0 + at
in parallel: C1+C2+…+Cn current: i 
E = ρJ
V = i·R
V
ΔU + ΔK = 0
F
qo
E
E=
E cyl 
4
πR3
3
Vsphere =
0 A
d
dQ
dt
P = I∙V
P=
RC circuit:
charging:
t
RC
Q = Qf ( 1  e
)

 
F  qvxB
t
RC
V=Vc( 1  e
)
FB = qvBsinθ
 
  xB
µ = NiA
F  o i 1i 2

L
2d
  Blv

Bwire =
v2
R
Oscillations:  
Barc =
 
  B A
N
L
i
1
AC circuit:
X  XC
  tan  1 ( L
)
R
0 
1
LC
Vrms=
 = 2f
2
transformers: V2 
 o i
4R
=
mv
qB
2
T
f

qB
2m
 i
Bloop = N o
induction:
RL circuit:
Utot =
Pavg=VrmsIrms cosΦ
1 pC = 10-12C

t
RC
 
F  iLxB
Li max2
2
Btor =
1 mH = 10-3 H
 o iN
2r
emf   N

t

)
i  i 0e

d
dt
Rt
L
Q = Qm cos(t)
R 2  ( X L  XC ) 2
Pavg = Irms2R
magnetic field:
FB =iLBsinθ
d
dt
i = if ( 1  e
Utot =
Z=
i  i 0e
emf  
L

R
q m ax2
2C
t
RC
Bsol = µo·i∙n
2R

i= m sin(ωt –Φ)
Z
I
Irms= m
2
N2
V1
N1
discharging: V  V0 e
R=
di
emf   L
dt
emf = Εmsinωt
Vm
t
RC
Φ = BAcosθ
LC
i = - im sin(t)

qE = qvB
oi
2 R
 
Flux:    B  dA
Εmax = NBAω
UB =½Li2
FB = m
i  ioe
XL =  L
Resonance :
XC =
 L=
1
C
1
C
1.
In the figure, if Q = 30 µC, q = 5.0 µC, and d = 30 cm, what is the magnitude of the electrostatic force on q?
a.
b.
c.
d.
e.
2.
15 N
23 N
zero
7.5 N
38 N
A particle (mass = 4.0 g, charge = 80 mC) moves in a region of space where the electric field is uniform and is
given by Ex = –2.5 N/C, Ey = Ez = 0. If the velocity of the particle at t = 0 is given by vx = 80 m/s, vy = vz = 0,
what is the speed of the particle at t = 2.0 s?
a.
b.
c.
d.
e.
3.
Two point charges are arranged as shown. In which
region could a third charge +1 C be placed so that the
net electrostatic force on it is zero?
a.
b.
c.
d.
e.
4.
I only
I and II only
III only
I and III only
II only
The total electric flux through a closed cylindrical (length = 1.2 m, diameter = 0.20 m) surface is equal to –5.0 N 
2
m /C. Determine the net charge within the cylinder.
a.
b.
c.
d.
e.
5.
40 m/s
20 m/s
60 m/s
80 m/s
180 m/s
–62 pC
–53 pC
–44 pC
–71 pC
–16 pC
2
Two infinite parallel surfaces carry uniform charge densities of 0.20 nC/m and -0.6nC/m2. What is the
magnitude of the electric field at a point between the two surfaces?
a.
b.
c.
d.
e.
34 N/C
23 N/C
45 N/C
17 N/C
90 N/C
2
6.
A charge of 8.0 pC is distributed uniformly on a spherical surface (radius = 2.0 cm), and a second charge of –3.0
pC is distributed uniformly on a concentric spherical surface (radius = 4.0 cm). Determine the magnitude of the
electric field 5.0 cm from the center of the two surfaces.
a.
b.
c.
d.
e.
7
An uncharged spherical conducting shell surrounds a charge –q at the center of the shell. The charges on the inner
and outer surfaces of the shell are respectively
a.
b.
c.
d.
e.
8.
q, q .
q, q.
q, q.
q, q.
 q,0 .
C
–31
–19
6
An electron (m = 9.1  10
kg, q = –1.6  10
C) starts from rest at point A and has a speed of 5.0  10 m/s at
point B. Only electric forces act on it during this motion. Determine the electric potential difference V A  V B .
a.
b.
c.
d.
e.
9.
14 N/C
11 N/C
22 N/C
18 N/C
40 N/C
–71 V
+71 V
–26 V
+26 V
–140 V
The electric potential inside a charged solid spherical conductor in equilibrium
a.
b.
c.
d.
e.
is always zero.
is constant and equal to its value at the surface.
decreases from its value at the surface to a value of zero at the center.
increases from its value at the surface to a value at the center that is a multiple of the potential at the surface.
is equal to the charge passing through the surface per unit time divided by the resistance.
3
10.
Determine the charge stored by C1 when C1 = 20 µF, C2 = 10 µF,C3 = 30 µF, and V0 = 18 V.
a.
b.
c.
d.
e.
11.
0.37 mC
0.24 mC
0.12 mC
0.40 mC
0.50 mC
A parallel plate capacitor of capacitance C0 has plates of area A with separation d between them. When it is
connected to a battery of voltage V0, it has charge of magnitude Q0 on its plates. It is then disconnected from the
battery and the space between the plates is filled with a material of dielectric constant 3. After the dielectric is
added, the magnitudes of the charge on the plates and the potential difference between them are
a.
b.
c.
d.
e.
12.
If a mile of 24-gauge copper wire has a resistance of 0.14 k Ω and the resistivity of copper is 1.7  10
is the diameter of the wire? (1 mile = 1.6 km)
a.
b.
c.
d.
e.
13.
1
1
Q 0, V0 .
3
3
1
Q 0 , V 0 . (B)
3
Q 0 ,V 0 .
Q 0 ,3V 0 .
3Q 0 ,3V 0 .
–8
Ω  m, what
0.40 mm
0.50 mm
0.63 mm
0.80 mm
0.25 mm
Determine Ε when I = 0.50 A and R = 12 Ω
a.
b.
c.
d.
e.
12 V
24 V
30 V
15 V
6.0 V
4
14.
The circuit below contains three 100 W light bulbs. The emf ε = 110 V. Which light bulb(s) is(are) brightest?
a.
b.
c.
d.
e.
A
B
C
B and C
All three are equally bright.
15.
When does a constant, uniform magnetic field increase the kinetic energy of a charged particle?
a.
b.
c.
d.
e.
always
if the particle is moving in a circle
if the particle is moving across field lines
if the particle is moving along field lines
never
16.
What is the radius of curvature of the path of a 3.0-keV proton in a perpendicular magnetic field of magnitude
0.80 T?
a.
b.
c.
d.
e.
9.9 mm
1.9 cm
2.4 cm
1.5 cm
4.6 mm
5
17.
A current loop is oriented in three different positions relative to a uniform magnetic field. In position 1 the plane
of the loop is perpendicular to the field lines. In position 2 and 3 the plane of the loop is parallel to the field as
shown. The torque on the loop is maximum in
a.
b.
c.
d.
e.
18.
If a = 1.0 cm, b = 3.0 cm, and I = 30 A, what is the magnitude of the magnetic field at point P?
a.
b.
c.
d.
e.
19.
position 1.
position 2.
position 3
positions 2 and 3.
all three positions.
0.62 mT
0.59 mT
0.35 mT
0.31 mT
0.10 mT
Equal currents of magnitude I travel into the page in wire M and out of the page in wire N. Eight directions are
indicated by letters A through H.
The direction of the magnetic field at point P is
a.
b.
c.
d.
e.
C.
E.
F.
G.
H.
6
20.
An ideal solenoid of radius a has n turns per unit unit length and current I. The magnetic flux B through any
circular area of radius a inside the solenoid, centered on and perpendicular to the solenoid axis is
a.
c.
d.
2 0 a2nI .
e.
0.
C
2
At what frequency should a 200-turn, flat coil of cross sectional area of 300 cm be rotated in a uniform 30-mT
magnetic field to have a maximum value of the induced emf equal to 8.0 V?
a.
b.
c.
d.
e.
22.
 a2
nI .
4
 a2
0
nI .
2
0 a2nI .
b.
21.
0
7.5 Hz
7.1 Hz
8.0 Hz
8.4 Hz
16 Hz
As shown below, a square loop of wire of side a moves through a uniform magnetic field of magnitude B
perpendicular to the page at constant velocity v directed to the right. Judd says that the emf induced in the loop
is zero. Roger claims that it has magnitude B v . Which one, if either, is correct, and why?
a.
b.
c.
d.
e.
 








 








 








 








 








v
Judd, because the magnetic flux through the loop is constant.
Roger, because the magnetic flux through the loop is constant.
Judd, because the magnetic flux through the loop is not constant if v  0 .
Roger, because the magnetic flux through the loop is not constant if v  0 .
Roger, because the magnetic flux through the loop is B  0 .
7
23.
2
The coil shown in the figure has 2 turns, a cross-sectional area of 0.20 m , and a field (parallel to the axis of the
coil) with a magnitude given by B = (4.0 + 3.0t) T, where t is in s. What is the potential difference, VA – VC, at t =
3.0 s?
a.
b.
c.
d.
e.
24.
1.2 V
2.4 V
4.8 V
6.4 V
12 V
The circuit shown is in an uniform magnetic field that is into the page and decreasing at
the rate 174 T/s. What is the net current in the circuit?
a. 0.35 A
b. 0.60 A
c. 0.85 A
d. 1.25 A
e. 1.40
25.
There is no current in the circuit shown in the figure below until the switch is closed. The current through the 20
Ω resistor the instant after the switch is closed is either [1] 15 A or [2] 5.0 A, and the current through the 20 Ω
resistor after the switch has been closed a long time is either [3] 5.0 A or [4] 15 A. Which combination of the above
choices is correct?
a.
b.
c.
d.
[1] and [3]
[1] and [4]
[2] and [3]
[2] and [4]
e.
None of these
8
26.
A series LC circuit contains a 100 mH inductor, a 36.0 mF capacitor and a 12 V battery. The frequency of the
electromagnetic oscillations in the circuit is
a.
b.
c.
d.
e.
–4
5.73  10 Hz.
9.55 mHz.
0.442 Hz.
2.66 Hz.
44.0 Hz.
27.
The figure shows an LR circuit with a switch and a 240-volt battery. At the instant the switch is closed the current
in the circuit and the potential difference between points a and b, Vab, are
a.
b.
c.
d.
e.
28.
29.
0 A, 0 V
0 A, –240 V
0 A, +240 V
0.024 A, 0 V
0.024 A, +240 V
An electric heater draws an average power of 1100 Watts when plugged into a 110 V-rms outlet. Calculate the
resistance of the heater and the rms current.
a.
b.
c.
11 Ω, 10 A (rms)
110 Ω, 10 A (rms)
10 Ω, 11 A (rms)
d.
e.
10 Ω, 110 A (rms)
0.09 Ω, 11 A (rms)
The inductance of a tuning circuit of an AM radio is 4 mH. Find the capacitance of the circuit required for
reception at 1200 kHz.
a.
b.
c.
d.
e.
2.1 pF
4.4 pF
21.2 pF
43.4 pF
27.6 pF
9
30.
Determine the rms current for the circuit.
a.
b.
c.
d.
e.
31.
55 mA
77 mA
99 mA
0.190 A
61 mA
A series RLC circuit has an impedance of 120 Ω and a resistance of 64 Ω. What average power is delivered to
this circuit when Vrms = 90 volts?
a.
b.
c.
d.
e.
36 W
100 W
192 W
360 W
12 W
10