Download Exam 2

Name:_______________________ ___
PHY2061
11-8-05
Exam 2
Closed book exam. A calculator is allowed, as is one 8.511” sheet of paper with your own
written notes. Please show all work leading to your answer to receive full credit. Numerical
answers should be calculated to 2 significant digits. Exam is worth 100 points, 25% of your
total grade.
UF Honor Code: “On my honor, I have neither given nor received unauthorized aid in doing
this exam.”
Sphere: S  4 r 2
4
V   r3
  3.1415927
3
1 F  106 F 1 pF  1012 F
e  16022
.
 1019 C
g  9.8 m/s 2
1 eV  1.6 1019 J
1 C  106 C
1
 0  8.8542 1012 C2 / N m 2
K
 9  109 N m 2 / C 2
c  3.0  108 m/s
4 0
K 
1
0  4 k  1.257 106 T  m /A
k  2  0  107 T  m / A
 0 0  2
c
4
c
q
qq
F

F  K 1 2 2 rˆ12
E
 E   Ε  dΑ  enc
E 
S
r
q0
0
0
U
V
W  U   F  ds
V   E  ds
E  V
C
C
q0
1
Q2
2
U  C  V  
2
2C
dq
i
 RC  RC
dt
Q  C V
R
L
A
 
Reff  R1  R2
V2
P  Vi  i R 
R
V  iR
1
1
1
 
Ceff C1 C2
1
1
1
 
Reff R1 R2
Ceff  C1  C2
2
1
1 v / c
2
ux  v
vu
1  2x
c
2
t   t0
L
L0

x    x  vt 
t     t  vx / c
2

y  y
z  z
uy
E  mc2
EK   1 mc2
 vu 
 1  2x 
c 

2 4
p  mu
F  q(E  v  B)
m c  E 2  p2 c2
F  dp / dt
F  i L×B
i
i ds × r
2ki
dB  k
B wire  0 rˆ 
rˆ
B  ds  0 ienc
3

C
r
2 r
r
dB
Fz   z z
μ  iA
τ  μ×B
U  μ  B
τ  r ×F
dz
dB
  N
B   B  dΑ
S
dt
a  b  axbx  a y by  az bz
a  b   a y bz  by az  x   ax bz  bx az  y   ax by  bx a y  z
u x 
u y 
Page 1 of 12
PHY2061
11-8-05
Name:_______________________ ___
1. An RC circuit is discharged by closing a switch at time t = 0. The initial potential
difference across the capacitor is 5 V. The potential difference across the capacitor drops to
half of its value in 35 ms.
(a) [6 points] What is the time constant of the circuit?
(b) [4 points] If the total resistance in the circuit is 10 k, what is the capacitance?
Page 2 of 12
PHY2061
11-8-05
Name:_______________________ ___
2. [8 points] In the circuit shown, the resistances are R1  6 , R2  12 , and R3  24 . The
battery voltages are 1  18 V and  2  6 V . What is the current (in amps) flowing through
the battery with potential difference 1 ?
Page 3 of 12
PHY2061
11-8-05
Name:_______________________ ___
3. [6 points] Two identical amounts (volumes) of copper are formed into two cylindrical
rods, the first of length L and the second of length L/2. If the resistances of the two volumes
(measured between the two ends) are R1 and R2 respectively, what is R2 / R1 ?
4. [6 points] A large flat non-conducting sheet has an electric charge density of
  5.0C / m2 , where 1C  106 C , as measured in the rest frame of the sheet. What is the
charge density “seen” by an electron traveling at a velocity of v  2.9 108 m/s parallel to the
surface of the sheet?
Page 4 of 12
PHY2061
11-8-05
Name:_______________________ ___
5. [6 points] Galaxy A is reported to be receding from us at a speed of 0.41c. Galaxy B,
located in precisely the opposite direction, is found to be receding from us at the same speed.
What recessional speed would an observer on Galaxy A find for Galaxy B?
6. [6 points] An electron is accelerated from rest by a potential difference of 10,000 V. It
then enters a uniform magnetic field of magnitude 0.05 T with its velocity perpendicular to
the direction of the field. Calculate the radius in meters of its path in the magnetic field. The
mass of the electron is 9.111031 kg .
Page 5 of 12
PHY2061
11-8-05
Name:_______________________ ___
7. The rectangular-shaped loop shown in the figure is carrying a current i = 2A in the
clockwise direction shown. The length of the vertical sides is 7cm and the length of the
horizontal sides is 3.5 cm. A uniform magnitude field B = 0.05T makes an angle =30 with
respect to the plane of the loop.
(a) [6 points] What is the magnitude of the torque acting on the loop
if the left side is connected to a hinge?
(b) [6 points] If the loop is free to rotate about its hinge due to the torque, by how much will
the potential energy of the loop change when the torque becomes zero?
Page 6 of 12
PHY2061
11-8-05
Name:_______________________ ___
8. [8 points] A long straight wire carries a current i1  80A in the horizontal direction shown.
Below it is a square loop of side length b  50 cm carrying a current i2  40A in the
clockwise direction shown. The distance between the top of loop to the long straight wire is
distance a, which you can take to be much smaller than b ( a b ). If the mass of the loop is
m  10 g, what is the maximum distance a such that the loop is attracted to the wire with
current i1 with a force that overcomes the force of gravity? (the acceleration due to gravity
points in the yˆ direction).
b
b
Page 7 of 12
PHY2061
11-8-05
Name:_______________________ ___
9. [6 points] A horizontal power line carries a current of 3000A from south to north. Earth's
magnetic field, with a magnitude of 60T, is directed toward the north with a dip angle 60°
downward into the Earth relative to the horizontal. Find the magnitude and direction (use
compass directions) of the magnetic force acting on a 100 m length of power line.
Page 8 of 12
PHY2061
11-8-05
Name:_______________________ ___
10. [8 points] An infinitely long insulated wire carrying a current I = 100 A is bent into the
shape shown (straight line plus circle of radius R=3 cm with the currents in the direction
shown). Find the magnitude of the field B at the center of the circle.
Page 9 of 12
PHY2061
11-8-05
Name:_______________________ ___
11. [6 points] A conductor has a cylindrical cross section with a radius a = 2 mm.
Inside, a cylindrical cut-out hole (non-conducting) is made as shown, where the radius of
the cut-out is b = 0.5 mm and the distance between the center of the main conductor and
the center of the cut-out is d = 1 mm. The magnitude of the current density in the
conductor is j  105 A/m2 . What is the magnitude of the magnetic field at a radius of
r  0.5 mm from the center of the conductor along a line connecting to the center of the
cut-out? [Hint: try using the superposition principle.]
Page 10 of 12
PHY2061
11-8-05
Name:_______________________ ___
12. A rectangular loop of wire of sides L  2 L is moving with constant speed v into a region
of uniform magnetic field of magnitude B directed out of the paper as shown in the figure
(the long side is along the direction of motion).
(a) [6 points] What is the magnitude of the induced EMF in the
wire and the direction of the induced current just
after the loop enters the region of magnetic field?
L
(b) [6 points] If the total resistance of the wire is R, what is the power dissipated by the
loop?
Page 11 of 12
PHY2061
11-8-05
Name:_______________________ ___
13. [6 points] A circular loop of wire of radius 30 cm sits in the x-y plane in a region where
there is a uniform magnetic field of B  B0 zˆ , where B0 = 0.5 T. The magnetic field is now
increased at a constant rate such that it reaches three times its original strength in 20 s. What
is the magnitude of the induced EMF in the wire loop during this time?
Page 12 of 12