Final Exam Physics 196 Spring 2011
Name:
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.
Some Physics Constants:
electronic charge
e = 1.6×10-19 C
Coulomb constant
k = 9.0×109 Nm2/C2
Permittivity of free space
ε0 = 8.85×10-12 C2/Nm2
Permeability of free space
m0 = 4p ´10-7 F / m
Mass of electron
me = 9.11×10-31 kg
Mass of proton
mp = 1.67×10-27 kg
Acceleration due to gravity g = 9.8 m/s2
1. A negatively charged rod is brought near conducting spheres A and B in contact with each other, with A
connected to ground. Afterwards, the spheres are separated. The charge on B is now
(a)
(b)
(c)
(d)
zero
negative
positive
indeterminate
2. The electrostatic force between two identical point charges 𝑞 a distance 𝑑 apart is 𝐹. If both charges are
tripled, and the distance is doubled, the force is
(a)
(b)
(c)
(d)
3F
3F
9F
9F
2
4
2
4
3. The electric field in a certain geographical location is 150 V / m downward. A charged particle of mass
3.0g is found to suspend in air by the electric field. The charge it carries is
(a)
(b)
(c)
(d)
-0.2 mC
0.2 mC
-0.2C
0.2 C
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)
90kN / C up
120kN / C down
240kN / up
360kN / C down
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 2 𝑎⁄3 from its center.
(
)
(b) Q ( 9pe a )
2
(a) Q 6pe0 a
2
0
(c) Q ( 6pe0 a)
(d) Q 90 a 
6. On the x-y plane, the electric field is uniform and is given by E = 50iˆ(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) 200V
(b) -200V
(c) 150V
(d) -150V
2
7. The electric potential measured in volts in a region of space is given by V(x, y) = 2x 3 y - 5y2 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 = -16 Ey =10
(d) Ex =16 Ey = -10
8. The diagram shows point charges −3𝑞 and +5q at a distance 2a
apart. Find the minimum work required to bring a point charge
+4q from very far away to the point in the middle of the two point
charges.
(a)
(b)
(c)
(d)
8kq a
4kq a
8kq 2 a
4kq 2 a
9. A point charge q occupies the center of an isolated conducting spherical shell of inner radius a and
outer radius b . The shell carries a total charge  3q . Find the electric potential of the shell, taking the
potential to be zero at infinity.
(a)
(b)
(c)
(d)
kq a
2kq (a + b)
-2kq b
-3kq b
3
10. A bare nucleus of helium atom 2 He 4 at rest is placed at a distance 3.0×10-11m 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)
462 eV
576 eV
614 eV
736 eV
11. A piece of dielectric is inserted into a parallel plate capacitor after it has been charged up and then
disconnected from the 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. A light bulb with rated power 100W at 120V is connected to a 12V battery. What is the current through
the light bulb?
(a)
(b)
(c)
(d)
2.4A
1.7A
0.6A
0.08A
13. Find the equivalent electrical resistance between the
points A and B in the network shown where the
resistance of each resistor is 1.0Ω
(a)
(b)
(c)
(d)
5 2W
7 2W
7 5W
8 7W
4
14. The diagram shows four conducting rods of circular cross-section with varying lengths and diameters as
labeled. Select the one(s) with the same electrical resistance as one with length and diameter d .
15. The diagram shows a 12V battery connected to a 40W resistor and a
voltmeter. The reading on the voltmeter is 9.0V . What is the internal
resistance of the battery?
(a)
(b)
(c)
(d)
8.0W
13W
21W
32W
16. Determine the current 𝐼 indicated in the circuit:
(a)
(b)
(c)
(d)
4.0A
3.0A
2.0A
1.0A
5
17. In which of the following diagram(s) for the magnetic field, particle velocity, and magnetic force, does
the charged particle carry negative charge?
18. In a region where the magnetic field is 30𝜇𝑇 due north, a proton with kinetic energy 50MeV travels in
the direction 60 S of E. Find the magnitude of the force experienced by the proton.
(a) 1.6 ´10-16 N
(b) 2.4 ´10-16 N
(c) 3.5´10-16 N
(d) 4.1´10-16 N
19. A proton with velocity 8.0 ´10 7 m / s enters a region
where the magnetic field is 2.5T perpendicular to the
paper from the point a and exits at the point b as shown.
Find the straight line distance ab and the direction of
the magnetic field
(a)
(b)
(c)
(d)
44cm
44cm
67cm
67cm
into paper
out of paper
into paper
out of paper
6
20. 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)
4.4V
5.5V
6.6V
7.7V
21. The concept of the magnetic moment of a current loop is useful for
(a)
(b)
(c)
(d)
calculating the energy of the loop in a magnetic field
calculating the magnetic flux through the loop
understanding the magnetic field created by the loop
applying Faraday’s law to determine the induced emf in the loop
22. In a rectangular coordinate system ( x, y, z ) where coordinates are in meters, a wire extends from the
point (-1,1,0) to the point (2,0,3). A current of 5.0A runs from the first point to the second, and there is
a uniform magnetic field of 0.2 T in the positive z-direction. Find the magnetic force on the wire
(a) 3iˆ + ĵ ( N )
(b) -3iˆ + ĵ ( N )
(c) iˆ - 3 ĵ ( N )
(d) -iˆ - 3 ĵ ( N )
7
23. The diagram shows two very long wires parallel to each other
and at a distance of 8.0cm apart. With the currents indicated, the
magnetic field at a point P midway between the two wires is
(a)
(b)
(c)
(d)
25mT out of the paper
25mT intothe paper
5mT out of the paper
5mT out of the paper
24. A very long wire with circular cross-section of radius a carries a
current I uniformly distributed over its cross-sectional area. The
magnetic field at a distance 3a 4 from its axis is equal to
(a) m0 I (8p a)
(b) m0 I ( 4p a)
(c) 3m0 I (8p a)
(d) m0 I ( 2p a)
25. The diagram shows a square wire loop of side 30cm placed in a uniform
magnetic field whose component pointing out of the paper is given by
B = 4.0cos2p t in Tesla, with time t measured in seconds. Find the
magnitude and direction of the induced emf at t =1 12s
(a) 1.13V clockwise
(b) 1.13V counter - clockwise
(c) 2.52V clockwise
(d) 2.52V counter - clockwise
26. In the circuit shown, what is the current through the
4.0W resistor immediately after the switch is closed?
8
(a)
(b)
(c)
(d)
0
3.0 A
6.0 A
9.0 A
27. A 12m F capacitor is charged and then connected across a 3-μH inductor.
After how long is the stored energy completely in the inductor?
(a) 37.7m s
(b) 18.8ms
(c) 12.3m s
(d) 9.4ms
28. In the AC circuit shown, the emf measured in volt is ℇ = 10cos(5𝑡)
where 𝑡 is in seconds. The current is
(
)
(b) I = 2cos ( 5t - 53 )
(c) I = 5cos ( 5t + 27 )
(d) I = 5cos ( 5t - 27 )
(a) I = 2cos 5t + 53
29. In the AC circuit shown, where the frequency of the generator is
60Hz, the peak voltage of the inductor is 10.0V. What is the peak
emf of the generator?
9
(a) 12.7V
(b) 18.8V
(c) 22.5V
(d) 26.4V
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 impedance increases
the peak current increases
the peak voltage across the resistor decreases
the peak voltage across the capacitor 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

En 

0
C  C1  C 2
1
1
1


R R1 R2
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
Bapp
B  0 M
M  m
M
 
dm
d
m   Bn dA
  N m
  B
 E  d    dt
dt
1 2
dI
N2
1 B2
N m  LI
U  LI
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 
VC
tan  
I  I 0 cost   
2
P  I rms
R
XL  XC
R

I0 
Z
0 
1
LC
11
1
1
1


C C1 C 2
Q
0

XC 
1
C