Download Exam 5 (Fall 2012)

Final Exam Physics 196 Fall 2012
Name:
Time allowed is 2 hours
Some Physics Constants:
electronic charge
Coulomb constant
Permittivity of free space
Permeability of free space
Mass of electron
Mass of proton
e = 1.6×10-19 C
k = 9.0×109 Nm2/C2
ε0 = 8.85×10-12 C2/Nm2
m0 = 4p ´10-7 F / m
me = 9.11×10-31 kg
mp = 1.67×10-27 kg
1. A negatively charged rod was brought near an uncharged sphere permanently connected to ground with
a metal wire. The rod was never in contact with the sphere, and it was then withdrawn. Afterwards, the
charge on the sphere was
(a)
(b)
(c)
(d)
positive
negative
zero
indeterminate
2. A point charge A of 5nC near a positive point charge B is moved away from B so that their distance
apart becomes twice as much as before. If the charge on A can change, what should it become so that the
force becomes attractive and has the same magnitude as before?
(a)
(b)
(c)
(d)
 20nC
 20nC
-10nC
+10nC
3. If it is desired to push a point charge of -6nC toward the SW direction with a force of 150µN using an
electric field, the magnitude and direction of the electric field should be
(a) 5.0 ´10 4 N / C pointing NE
(b) 5.0 ´10 4 V / m pointing SW
(c) 2.5´10 4 N / C pointing NE
(d) 2.5´10 4 V / m pointing SW
1
4. Find the magnitude and direction of the electric field produced by the
two point charges at the point P as shown:
(a)
(b)
(c)
(d)
11 𝑉 ⁄𝑚, to the right
11 𝑉 ⁄𝑚, to the left
3 𝑉 ⁄𝑚, to the right
3 𝑉 ⁄𝑚, to the left
5. A solid sphere of radius 𝑎 is uniformly filled with electric charge throughout its volume. The total
charge is 𝑄. Find the electric field at a point in its interior that is at a distance of 3 𝑎⁄4 from its center.
(
)
(b) Q (3pe a )
(c) 3Q (8pe a )
(d) 3Q (16pe a )
(a) Q 6pe0 a 2
2
0
2
0
2
0
6. On the x-y plane, the electric field is uniform and is given by E = 80 ĵ(N / C) . Find the potential
difference VB -VA between the point A , which has coordinates (-2,3) and B , which has coordinates
(1, -1) where coordinates are measured in meters
(a)
(b)
(c)
(d)
240V
-240V
320V
-320V
2
7. The electric potential measured in volts in a region of space is given by V(x, y) = 2x 3 y2 - y3 where the
coordinates x and y are in meters. The components of the electric field at the point (x, y) = (1,-2) in
V/m are
(a) Ex = -12 Ey = 22
(b) Ex =12 Ey = -22
(c) Ex = +24 Ey = -20
(d) Ex = -24 Ey = +20
8. Point charges -3q and +4q occupy the vertices A and B of a right-angled
triangle ABC as shown. The sides AC and BC have lengths 3a and 4a
respectively. The point D is the midpoint of AB. The work required to move
another point charge q0 from C to D is
(a)
(b)
(c)
(d)
-2kq0 q 5a
2kq0 q 5a
3kq0 q 4a
-3kq0 q 4a
9. Draw the electric field vector at the center of the square where there are four point charges at the
corners as shown.
3
10. A bare nucleus of helium atom 2 He 4 at rest is placed at a distance 2.5×10-10 m from a carbon nucleus
that contains 6 protons. Pushed away from the carbon nucleus by electrostatic repulsion, what is the
highest kinetic energy of the helium nucleus?
a.
b.
c.
d.
14 eV
57 eV
69 eV
81 eV
11. A piece of dielectric is inserted into a parallel plate capacitor connected to a fixed voltage source. Select
the correct statement(s) from the following
(a)
(b)
(c)
(d)
the capacitance increases
the voltage of the capacitor increases
the charge on the capacitor decreases
the energy of the capacitor decreases
12. Three identical capacitors with a capacitance of 6pF each are connected as
shown. Find the equivalent capacitance.
(a)
(b)
(c)
(d)
12pF
9pF
6pF
3pF
13. Which of the following statement(s) concerning the emf of a battery is correct?
(a) It is the force on one Coulomb of charge inside the battery
(b) It is the work done by the battery when one Coulomb of charge flows through the battery
(c) It is equal to the energy delivered when one Ampere of current flows through the battery
(d) It can be measured directly with a voltmeter
4
14. Point charges -2q and +q both lie on the x-axis. Sketch the electric potential function V ( x ) for points on
the x-axis.
15. The correct answer(s) for the total energy delivered by a 12V- battery of life-time 150 A-hr is (are)
(a)
(b)
(c)
(d)
6.48MJ
6.48kJ
3.24kWh
1.80kWh
16. The diagram shows a 12V battery with internal resistance 20W connected to a 40W load resistor and a
voltmeter. What is the reading on the voltmeter?
(a)
(b)
(c)
(d)
2.0V
4.0V
6.0V
8.0V
5
17. Find the current I indicated in the circuit as
shown:
(a)
(b)
(c)
(d)
4.0A
3.0A
2.0A
1.0A
18. In which of the following diagram(s) for the magnetic field, particle velocity, and magnetic force, does
the charged particle carry positive charge?
6
19. In a region where the magnetic field is 15𝜇𝑇 due north, a proton with kinetic energy 60MeV travels in
the direction 60 S of E. Find the magnitude of the force experienced by the proton.
(a)
(b)
(c)
(d)
2.2 ´10-16 N
1.3´10-16 N
4.1´10-16 N
3.5´10-16 N
20. A proton with velocity 1.2 ´108 m / s enters a region where the magnetic field is 5.0 T perpendicular to
the paper from the point A and exits at the point B as shown. Find the distance AB and the direction of
the magnetic field.
(a)
(b)
(c)
(d)
0.25𝑚
0.25𝑚
0.50𝑚
0.50𝑚
𝑜𝑢𝑡 𝑜𝑓 𝑡ℎ𝑒 𝑝𝑎𝑝𝑒𝑟
𝑖𝑛𝑡𝑜 𝑡ℎ𝑒 𝑝𝑎𝑝𝑒𝑟
𝑜𝑢𝑡 𝑜𝑓 𝑡ℎ𝑒 𝑝𝑎𝑝𝑒𝑟
𝑖𝑛𝑡𝑜 𝑡ℎ𝑒 𝑝𝑎𝑝𝑒𝑟
21. In the circuit shown, after connecting to the point A for a
long time, the switch is reconnected to the point B. Find the
potential difference of the capacitor at 50m s after the
reconnection.
(a)
(b)
(c)
(d)
3.6V
4.4V
6.7V
7.5V
7
22. Refer to the diagram showing a triangular wire frame abc carrying a clockwise current in a uniform
magnetic field pointing up. Draw in the torque vector and indicate the direction of motion of the point a
as a result of the torque, assuming the frame starts at rest.
23. The diagram shows two very long wires parallel to each other and at a distance of
1.2 m apart. They carry anti-parallel currents of 9.0A each. The magnitude and
direction of the magnetic field at a point P midway between the two wires is
(a)
(b)
(c)
(d)
3.0𝜇𝑇 𝑖𝑛𝑡𝑜 𝑡ℎ𝑒 𝑝𝑎𝑝𝑒𝑟
3.0𝜇𝑇 𝑜𝑢𝑡 𝑜𝑓 𝑡ℎ𝑒 𝑝𝑎𝑝𝑒𝑟
6.0𝜇𝑇 𝑖𝑛𝑡𝑜 𝑜𝑓 𝑡ℎ𝑒 𝑝𝑎𝑝𝑒𝑟
6.0𝜇𝑇 𝑜𝑢𝑡 𝑜𝑓 𝑡ℎ𝑒 𝑝𝑎𝑝𝑒𝑟
24. The diagram shows a magnet approaching a circular wire loop. When
viewed in the position shown, the direction of the induced current in the
loop is
(a) clockwise
(b) counter clockwise
8
25. A circular wire loop of radius 0.20m and electrical resistance 5.0W is placed in a region where there is a
uniform magnetic field of 3.0T perpendicular to the plane of the loop. The loop is flipped though 180
in 4.0s. The average induced current in the loop is
(a)
(b)
(c)
(d)
38𝑚𝐴
25𝑚𝐴
17𝑚𝐴
0.6𝑚𝐴
26. In the circuit shown, what is the current through the 2.0W
resistor immediately after the switch is closed?
(a)
(b)
(c)
(d)
0
1.5A
2.0A
6.0A
27. A 12m F capacitor is charged and then connected across a 3-μH inductor. In
which of the following time(s) is the energy completely in the inductor?
(a)
(b)
(c)
(d)
3p ms
6p m s
9p m s
12p ms
9
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. An AC generator is connected to a capacitor with capacitance of 0.25F . The emf of the generator
measured in volt is given by ℇ = 3.0𝑐𝑜𝑠(8𝑡 − 1.2) where the argument of cosine is in radians. The
current (in A) through the inductance is
(a)
(b)
(c)
(d)
𝐼
𝐼
𝐼
𝐼
= 1.5𝑐𝑜𝑠(8𝑡 + 1.57)
= 1.5𝑐𝑜𝑠(8𝑡 + 2.14)
= 6𝑐𝑜𝑠(8𝑡 + 0.37)
= 6𝑐𝑜𝑠(8𝑡 + 1.57)
30. Referring to the AC circuit as shown, select the correct statement(s) when the
frequency of the AC voltage source increases:
(a)
(b)
(c)
(d)
the peak current increases
the peak current decreases
the potential difference of the inductance increases
the potential difference of the inductance decreases
10
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
C
1 Q2
2 C
L
R
A
Q
V
V  IR
q
 E dA  
n
V
x
C  0
U
 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
 
7
dB 


4


10
T

m
/
A
B
0
  d  0 I
4 r 2
 I
 I
B 0
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
Z  R 2  X L  X C 
2
   0 cos t
P  I rms  rms cos 
1
1
1


C C1 C 2
VC
tan  
I  I 0 cost   
2
P  I rms
R
XL  XC
R

I0 
Z
0 
1
LC
11
Q
0

XC 
1
C