Download Exam 5 (Fall 2010)

Final Exam Physics 196 Fall 2010
Name:
Write name in upper right corner of this page.
Time allowed is 2 hours
Answer all questions on the question sheets and turn in the sheets.
Total number of points is 15. Each question is worth 0.5 points.
Communications with classmate result in no credit given for the exam.
1. Find the force acting on the charge q due to the charges 2Q and Q in the figure shown (k=Coulomb’s
law constant)
Qq
2r 2
3Qq
b. k 2
2r
5Qq
c. k 2
2r
7Qq
d. k 2
2r
a. k
2. Find the magnitude of the electric field at the point P due to the charges 6nC and –6nC in the figure
shown (Take Coulomb’s law constant k=9×109 N-m2/C2)
a.
b.
c.
d.
1.3 N/C
2.1 N/C
3.6 N/C
4.8 N/C
3. It is desired to put a charge of +8.0nC on an isolated metallic sphere of radius 4.0cm by connecting it to
a battery. What should be the voltage of the battery? (Take Coulomb’s law constant k=9×109 N-m2/C2)
a.
b.
c.
d.
600 V
1200 V
1800 V
2400 V
1
4. The potential difference between two plates of a parallel plate capacitor is 200 V. A helium ion with
twice the charge of a proton and four times the mass of a proton is released at rest on the plate at lower
potential. What is its velocity when it reaches the other plate? (mass of proton = 1.67×10-27 kg, charge of
proton = 1.6×10-19 C)
a.
b.
c.
d.
4.24×105 m/s
3.06×105 m/s
2.22×105 m/s
1.38×105 m/s
5. A solid sphere of radius a carries a total charge q uniformly distributed throughout its volume. Using
Gauss’s law, the electric field at a distance r from the center is
qr
20 a 3
1 q
b.
40 a 2
1 qr
c.
40 a 3
1 q
d.
20 a 2
a.
1
6. The electric potential in a region of space is given by
and V is in volts. Find the electric field at x=1.0m.
a.
b.
c.
d.
V x   10  8x  6 x 2
where x is in meter
8 V/m
4 V/m
–8 V/m
–4 V/m
7. A metallic sphere of radius R carrying charge Q is connected by a conducting wire to a distant metallic
sphere of radius R/3 initially carrying no charge. Find the charge on the large sphere after the
connection.
Q
4
3Q
b.
4
Q
c.
2
2Q
d.
3
a.
2
8. Point charges Q and  Q occupy adjacent corners of a square of side a . How much work must be done
to move a point charge q from the unoccupied corner closer to the charge  Q to the other unoccupied
corner?
kQq
a
kQq
b. 0.59
a
kQq
c.  1.47
a
kQq
d.  0.59
a
a. 1.47
9. The diagram shows a region where a uniform electric field of 60V/m exists and point to the right. The
points A,B, and C form a right angled triangle with sides indicated. The line BC is perpendicular to the
electric field lines. The potential difference VA  VB is
a.
b.
c.
d.
300 V
-300 V
240 V
-240 V
10. In a DC circuit where a 5-V battery with internal resistance 2Ω is connected to a 8.0Ω resistor, the
potential difference between the terminals of the battery is
a.
b.
c.
d.
3V
4V
5V
6V
3
11. A potential difference of 12.0V is applied to the combination of resistors as shown. The potential
difference across the 3.0 Ω resistor is
a.
b.
c.
d.
2V
3V
4V
5V
12. Find the current I indicated in the circuit as shown:
a.
b.
c.
d.
1.0 A
2.0 A
3.0 A
4.0 A
13. The emf of a battery is
a.
b.
c.
d.
the potential difference between the positive and negative terminals of the battery
the energy delivered by the battery in unit time
the energy delivered by the battery for every unit of charge flowing through it
the ratio of the current over resistance
14. A 20-μF capacitor is initially charged to 50V. It is then discharged through a resistance 200Ω. After
what time is the charge on it equal to 0.29 mC?
a.
b.
c.
d.
2.0 ms
7.0 ms
3.0 ms
5.0 ms
4
15. You charge up a 4μF parallel plate capacitor to 8μC by a battery. With the battery disconnected, you
move the plates apart so that the distance between them is doubled. The work you do is
a.
b.
c.
d.
4μJ
-4μJ
8μJ
-8μJ
16. The period of the orbit of a 10 keV proton moving perpendicular to a magnetic field of 0.02T is (mass of
proton=1.67×10-27kg, charge of proton=1.60×10-19C)
a.
b.
c.
d.
1.1 μs
2.2 μs
3.3 μs
4.4 μs
17. The diagram shows the circular orbits in a magnetic field of four particles with the same kinetic energy
which carry charge of the same magnitude but different masses. Two of the charges are negative. The
magnetic field points into the paper. Which orbit corresponds to the heaviest particle with a positive
charge?
a.
b.
c.
d.
1
2
3
4
18. The diagram shows two infinitely long wires carrying 5.0A currents in opposite directions. With
distances as indicated, the magnetic field at the point P is
a.
b.
c.
d.
0.15 mT
0.25 mT
0.35 mT
0.45 mT
5
19. A very long wire of radius a carries a current I uniformly distributed over its cross-sectional area. The
magnetic field at a distance a / 3 from its axis is equal to
a.
0 I
4a
 I
b. 0
6a
 I
c. 0
4a
 I
d. 0
6a
20. A horizontal circular loop of radius 10 cm carries a current of 10A running counter clockwise when
viewed from the top. An electron happens to be at the center travelling with velocity 8.0×106 m/s due
east. The magnitude and direction of the force on the electron are
a.
b.
c.
d.
8.0×10-17 N due north
8.0×10-17 N due south
6.0×10-17 N due north
6.0×10-17 N due south
21. A current element has length 3.0mm and carries a 8.0A current in the y-direction of a rectangular coordinate system. The magnetic field it creates at the point (1,2,-3) is (coordinates are measured in
meters)
a. (1.37iˆ  0.46 ˆj )  10 10 T
b. (0.46iˆ  1.37 ˆj )  10 10 T
c. (0.46iˆ  1.37kˆ)  10 10 T
d. (1.37iˆ  0.46kˆ)  10 10 T
22. The diagram shows the orientations of four current carrying rings in a region of uniform magnetic field.
The ring that will return to its original position when disturbed is
a.
b.
c.
d.
1
2
3
4
6
23. A metal ring 1.0cm in radius and with 2.0Ω electrical resistance lies flat on a table in a region where
there is a uniform magnetic field of 2.5T upward. The magnetic field reverses direction in 5.0ms. The
magnitude and direction of the electric current induced in the ring are
a.
b.
c.
d.
0.16A clockwise
0.16A counter-clockwise
0.25A clockwise
0.25A counter-clockwise
24. The thick arrow indicates the direction of the magnetic moment created when an external field Bapp is
applied to a material specimen. Which of the following statements is correct?
Bapp
a.
b.
c.
d.
the material is paramagnetic and the magnetic field inside the specimen is less than Bapp
the material is paramagnetic and the magnetic field inside the specimen is greater than Bapp
the material is diamagnetic and the magnetic field inside the specimen is less than Bapp
the material is diamagnetic and the magnetic field inside the specimen is greater than Bapp
25. You connect a dc battery to a resistor and a switch. When the switch is closed, you find that it takes a
little while before the current reaches its final value. You can conclude that
a.
b.
c.
d.
The switch is not perfect
The battery has internal resistance
The circuit has inductance
The circuit has capacitance
26. A 4-μF capacitor is charged and then connected across a 25-μH inductor. The frequency of oscillations
of the current is
a.
b.
c.
d.
20 kHz
16 kHz
12 kHz
8 kHz
7
27. An LR circuit has a resistance R=4.0Ω, an inductance L=2.0 H, and a battery of emf=12 V. How much
energy is stored in the inductance of this circuit when a steady current is achieved?
a.
b.
c.
d.
0J
3J
6J
9J
28. A series RLC circuit is driven by a 2.0-kHz oscillator. The circuit parameters are Vrms=30 V for the
oscillator, L=1.0mH, C=12.0μF, and R=10 Ω. Under steady-state conditions, the rms current in the
circuit will be
a.
b.
c.
d.
1.5 A
2.6 A
3.7 A
4.8 A
29. For the same circuit as question 28, if the voltage from the oscillator has the temporal dependence
cos t , the current along the resistor has the behavior
a.
b.
c.
d.
cost  90
cost  90
cost  31
cost  31
30. A circuit consists of a 600Ω resistor in series with a 5.0μF capacitor and an AC signal generator of
frequency 60Hz. The rms voltage across the resistor is found to be 3.0V. The rms voltage of the AC
generator is
a.
b.
c.
d.
5.0 V
4.0 V
3.0 V
2.0 V
8
Formula Sheet (PHYS 196)
F
1 q1q2
4 0 r 2


F  qE
k

E
1
4 0
1
q
rˆ
40 r 2
 
V2  V1    E  d 
2
Ex  
1
1 Q2
U
2 C
L
R
A
Q
C
V
V  IR
q
 E dA  
n
V
x
C  0
 9.0  109 Nm 2 / C 2
U  qV
A
d
P  IV
0
V 
1
2
  0E2
P  I
1
q
40 r
E
E0

R  R1  R2
  RC 

 



  
F  q  B
F  IL  B
  IAn
  B

  0 Id   rˆ
 
dB 
 0  4  10 7 T  m / A
B  d  0 I
2

4 r
0 I
 I
B
B 0
B   0 nI
2r
2R
B  0 M
M  m
En 

0
C  C1  C 2
1
1
1


R R1 R2
Bapp
M
 
dm
d
m   Bn dA
  N m
  B
 E  d    dt
dt
1
dI
N2
1 B2
N m  LI
U  LI 2
V   L
L  0
A
B 
2
dt
L
2 0
L
 
R
1
Arms 
A0
  2f
VR  IR
VL  IX L
VC  IX C
X L  L
2
VL
I
I
VC
Z  R 2  X L  X C 
tan  
2
I  I 0 cost   
   0 cos t
P  I rms  rms cos 
0 
1
LC
Q
1
1
1


C C1 C 2
XL  XC
R

I0 
Z
2
P  I rms
R
0

9
XC 
1
C