Download Exam 5 (Spring 2011)

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
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 ´107 F / m
me = 9.11×10-31 kg
mp = 1.67×10-27 kg
1. Two electrically neutral objects A and B are rubbed against each other. Afterwards, the charge on A is
found to be +480nC . Assuming that the charging is due to transfer of electrons, how many have been
transferred and from which object?
(a)
(b)
(c)
(d)
3 × 1012 𝑓𝑟𝑜𝑚 𝐵
3 × 1012 𝑓𝑟𝑜𝑚 𝐴
6 × 1012 𝑓𝑟𝑜𝑚 𝐵
6 × 1012 𝑓𝑟𝑜𝑚 𝐴
2. The electrostatic force between two identical point charges 𝑞 a distance 𝑑 apart is 𝐹. If the charges are
doubled, and the distance is tripled, the force is
(a)
(b)
(c)
(d)
2𝐹 ⁄3
2𝐹 ⁄9
4𝐹 ⁄9
4𝐹 ⁄27
3. If it is desired to push a point charge of  8nC toward the SW direction with a force of 320µN from an
electric field, the magnitude and direction of the electric field should be
(a)
(b)
(c)
(d)
40𝑘𝑉/𝑚, NE
40𝑘𝑉/𝑚, SW
30𝑘𝑉/𝑚, NE
30𝑘𝑉/𝑚, 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)
31 𝑉 ⁄𝑚, left
31 𝑉 ⁄𝑚, right
23 𝑉 ⁄𝑚, left
23 𝑉 ⁄𝑚, right
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 𝑎⁄3 from its center.
(a)
(b)
(c)
(d)
𝑄 ⁄(3𝜋𝜀0 𝑎2 )
3𝑄 ⁄(4𝜋𝜀0 𝑎2 )
3𝑄 ⁄(8𝜋𝜀0 𝑎2 )
𝑄 ⁄(12𝜋𝜀0 𝑎2 )
2

6. On the x-y plane, the electric field is uniform and is given by E  300iˆ( N / C ) . Find the potential
difference VB -VA between the point A , which has coordinates ( 2,-1) and B , which has coordinates
 5,4 where coordinates are measured in meters
(a)
(b)
(c)
(d)
1900𝑉
−1900𝑉
2100𝑉
−2100𝑉
7. The electric potential measured in volts in a region of space is given by V ( x)  4  7 x 2  x 4 where x is in
meters. The electric field at the point x  2 is
(a)
(b)
(c)
(d)
2 𝑉 ⁄𝑚
−4 𝑉 ⁄𝑚
6 𝑉 ⁄𝑚
−8 𝑉 ⁄𝑚
8. The diagram shows two identical point charges 𝑞 at adjacent corners of a square of side 𝑎. How much
work is required to move another point charge 𝑞 from A to B where A and B are the unoccupied corners
as shown.
(a)
(b)
(c)
(d)
−0.59 𝑘𝑞 2 ⁄𝑎
+0.59 𝑘𝑞 2 ⁄𝑎
−0.26 𝑘𝑞 2 ⁄𝑎
+0.26 𝑘𝑞 2 ⁄𝑎
3
9. A metallic spherical shell of radius 3.0𝑐𝑚 is charged by connecting it to a power supply so that its
electric potential is 60𝑘𝑉 assuming the potential is zero at infinity. Given that the breakdown electric
field in air is 3.0𝑀𝑉/𝑚, will the charge stay on the sphere? Give reason for your answer.
(a) Yes
(b) No
(c) Not enough information
10. Which of the following statement(s) regarding the capacitance of a capacitor are correct?
(a)
(b)
(c)
(d)
It increases with the charge on the capacitor
It increases when the potential difference is reduced
It decreases when dielectric is introduced
None of the above is correct.
11. A bare nucleus of helium atom 2 He 4 at rest is placed at a distance 5.0×10-10m from a carbon nucleus
that contains 12 protons. Pushed away from the carbon nucleus by electrostatic repulsion, what is the
highest kinetic energy of the helium nucleus?
(a)
(b)
(c)
(d)
310𝑒𝑉
240𝑒𝑉
138𝑒𝑉
69𝑒𝑉
4
12. When a parallel plate capacitor is charged to the voltage 20𝑉 and then discharged through a resistor, it
takes 30ms for the voltage to fall to 12𝑉. If the distance between the plates is doubled and the resistance
is also doubled, the time for the same change of voltage is
(a)
(b)
(c)
(d)
7.5𝑚𝑠
15𝑚𝑠
30𝑚𝑠
120𝑚𝑠
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)
4.5Ω
3.0Ω
2.75Ω
1.25Ω
14. When a load of resistance 20W is connected with a battery, the observed current is 2.0A . When the
load is replaced by one with resistance 15W , the current is 3.0A. Find the emf of the battery.
(a)
(b)
(c)
(d)
20𝑉
30𝑉
40𝑉
50𝑉
5
15. Determine the current 𝐼1 indicated in the circuit:
(a)
(b)
(c)
(d)
1.0𝐴
2.0𝐴
3.0𝐴
4.0𝐴
16. Which of the following statements concerning the emf of a battery is correct?
(a) It is the force that pushes electric charge inside the battery.
(b) It has the unit of work per unit charge
(c) It is a quantity occurring in Ohm’s law.
(d) It is equal to the terminal voltage of the battery in an open circuit.
17. In which of the following diagram(s) for the magnetic field, particle velocity, and magnetic force, does
the charged particle carry negative charge?
6
18. In a region where the magnetic field is 25𝜇𝑇 due north, a proton with kinetic energy 200MeV travels in
the direction 60 S of W. Find the magnitude of the acceleration experienced by the proton.
(a)
(b)
(c)
(d)
4.17 × 1012 𝑚⁄𝑠 2
3.46 × 1012 𝑚⁄𝑠 2
2.35 × 1011 𝑚⁄𝑠 2
1.29 × 1011 𝑚⁄𝑠 2
19. A proton with velocity 6 ´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 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
20. A very long solenoid is formed by winding tightly a wire of diameter 0.15𝑚𝑚. Find the magnetic field
inside when a 5.0A current runs through the wire.
(a)
(b)
(c)
(d)
0.027𝑇
0.042𝑇
0.066𝑇
0.075𝑇
7
21. The diagram shows two very long wires parallel to each other
and at a distance of 2.4m apart. They carry anti-parallel currents
of 18.0A each. The magnetic field at a point P midway between
the two wires is
(a)
(b)
(c)
(d)
0.0𝜇𝑇
2.0𝜇𝑇
3.0𝜇𝑇
6.0𝜇𝑇
22. A very long wire of radius a carries a current I uniformly distributed over its cross-sectional area. The
magnetic field at a distance 2a / 3 from its axis is equal to
(a)
(b)
(c)
(d)
𝜇0 𝐼 ⁄(2𝜋𝑎)
3 𝜇0 𝐼 ⁄(2𝜋𝑎)
2𝜇0 𝐼 ⁄(3𝜋𝑎)
𝜇0 𝐼 ⁄(3𝜋𝑎)
23. Faraday’s law can explain the operation of (more than one answer is possible)
(a) A transformer
(b) A mass spectrometer
(c) A cyclotron
(d) An AC generator
24. The diagram shows a planar wire loop of electrical resistance 40W. The area
inside the loop is 0.03m2 . A uniform magnetic field exists in pointing into the
paper. It is observed that a clockwise current of 15m A runs in the wire while the
magnetic field is changing. The magnetic field is
(a)
(b)
(c)
(d)
increasing at 0.02 𝑇/𝑠
decreasing at 0.02 𝑇/𝑠
increasing at 0.04 𝑇/𝑠
decreasing at 0.04 𝑇/𝑠
8
25. In the circuit shown, what is the energy stored in the inductor a long time after the switch is closed?
(a)
(b)
(c)
(d)
12𝑚𝐽
24𝑚𝐽
36𝑚𝐽
48𝑚𝐽
26. A capacitor is charged and then connected across a 25-μH inductor. The frequency of oscillations of the
current is found to be 12kHz. Find the capacitance.
(a)
(b)
(c)
(d)
6.0𝜇𝐹
7.0𝜇𝐹
8.0𝜇𝐹
9.0𝜇𝐹
27. In the AC circuit shown, the emf measured in volt is ℇ = 150𝑐𝑜𝑠300𝜋𝑡 where 𝑡 is in seconds. The
current is
(a)
(b)
(c)
(d)
𝐼
𝐼
𝐼
𝐼
= 30𝑐𝑜𝑠(300𝜋𝑡 − 0.64)
= 30𝑐𝑜𝑠(300𝜋𝑡 + 0.64)
= 60𝑐𝑜𝑠(300𝜋𝑡 − 0.32)
= 60𝑐𝑜𝑠(300𝜋𝑡 + 0.32)
9
28. In a series RLC circuit with an AC power source of frequency 𝑓, denoting by 𝛿 the phase difference
between the emf and the current, maximum power will be delivered to the resistor if (multiple answer
possible)
(a)
(b)
(c)
(d)
𝑅=0
𝛿=0
4𝜋 2 𝑓 2 𝐿𝐶 = 1
𝑓 = 1⁄√𝐿𝐶
29. In the AC circuit shown, where the frequency of the generator is 60Hz, the peak voltage of the capacitor
is 10.0V. What is the peak emf of the generator?
(a)
(b)
(c)
(d)
13.5𝑉
12.9𝑉
11.7𝑉
10.3𝑉
30. Which of the following circuits can be used as a high-pass filter? (multiple answer possible)
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
1 Q2
2 C
L
R
A
Q
C
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
 
dB 
 0  4  10 7 T  m / A
B  d  0 I
2

4 r
 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 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 
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