Download Final Exam

Name:_______________________ ___
PHY2061
12-10-04
Final Exam
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. 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.”
4
V   r2
  3.1415927
e  16022
.
 1019 C
3
a  b  axbx  a y by  az bz
a  b   a y bz  by az  x   axbz  bx az  y   axby  bx a y  z
Sphere: S  4 r 2
K
1
 9 109 N m 2 / C 2  0  8.8542 1012 C2 / N m 2 0  4 k  1.257 106 T  m /A
4 0
K 
k  2  0  107 T  m / A c  3.0  108 m/s
c
4
q
 E   Ε  dΑ  enc
 B   B  dΑ  0
0
S
FK
E 
S
dB
dt
q1q2
rˆ12
r2
E

0
F
q0
 B  0
d
B
B  dA
×E  

S
dt
t
d
d
E
C B  ds  0ienc  0 0 dt E  0 S j  dA  0 0 dt S E  dA  × B  0 0 t  0 j
U
V
W  U   F  ds
V   E  ds
E  V
C
C
q0
F F F



  xˆ  yˆ  zˆ
  F  div  F   x  y  z
x
y
z
x
y
z
  N
  F dV  
V

S
C
E  ds  
  ×F   dA  
F  dΑ
S
Q  C V
1
Q2
2
U  C  V  
2
2C
V  iR
P  Vi  i 2 R 
R
L
A
i
τ  r ×F
μ  iA
VL  L
dq
dt
di
dt
 RC  RC
L
 LR
NB
i
L

R
V2
R
C
F  ds
Ceff  C1  C2
1
1
1
 
Ceff C1 C2
1
1
1
 
Reff R1 R2
i ds × r
dB  k
F  q(E  v  B)
F  i L×B
r3
dB
Fz   z z
τ  μ×B
U  μ  B
dz
2
2
 E
1
U
B
U  Li 2
u 
 0
2
V 2 0
2
N
1
VS  S VP
LC 
NP
LC
Reff  R1  R2
Page 1 of 12
Name:_______________________ ___
PHY2061
12-10-04
1 eV  16022
.
 1019 J
c  3.0  108 m/s
 
u x 
1
1 v / c
2
t   t0
2
ux  v
vu
1  2x
c
p  mu
u y 
F  dp / dt
n1 sin 1  n2 sin 2
  2 f
k
S
2

L
L0
x    x  vt 
t     t  vx / c

uy
E  mc2
vu


 1  2x 
c 

2 4
m c  E 2  p2 c2
1
0
EB
f v
P
 Sav
A
c
vn 
n
2

K   1 mc2
I
Page 2 of 12
sin  

d
y  y
z  z
PHY2061
12-10-04
Name:_______________________ ___
1. The electric field component of a traveling electromagnetic wave is described by
E  E0 zˆ sin  kx  t  , where E0 is a positive constant.
(a) [6 points] What is the magnetic field component, both magnitude and
direction?
(b) [6 points] What is the average intensity of the wave per unit area
perpendicular to the direction of the travel?
(c) [6 points] What is the wavelength of the traveling wave if the angular
frequency   1014 Hz ?
Page 3 of 12
Name:_______________________ ___
PHY2061
12-10-04
2. [8 points] A light wave traveling horizontally strikes a glass prism with an index of
refraction of n=1.5 as shown. The prism has a triangular cross section, with each
interior angle measuring 60°. Calculate the angle relative to horizontal by which the
light wave deflects after traversing both faces of the prism.
60°
Page 4 of 12
PHY2061
12-10-04
Name:_______________________ ___
3. (a) [6 points] How much work is needed to accelerate a proton from a speed of
98.5% of the speed of light to 98.6% of the speed of light? The proton mass is
1.67 1027 kg , and its charge is q  e  1.6 1019 C .
(b) [6 points] If the proton travels enters a region where there is a constant magnetic
field of 0.5 T perpendicular to direction of motion at its final velocity of 0.986c, what
is the magnitude of the centripetal acceleration?
Page 5 of 12
PHY2061
12-10-04
Name:_______________________ ___
4. [6 points] The electric field just outside of a spherical electric conductor of radius 3
cm is E  C rˆ , where C  5 104 N/C . What is the net electric charge contained in
the conductor?
Page 6 of 12
PHY2061
12-10-04
Name:_______________________ ___
5. The electric field in a certain region of space is given by E  xy 2 xˆ  yx 2 yˆ .
(a) [6 points] What is electric charge density in this region?
(b) [6 points] What is the electric potential difference between 2 points on the x
axis: x = 0 and x = a ?
Page 7 of 12
PHY2061
12-10-04
Name:_______________________ ___
6. [6 points] Aluminum has a resistivity of 2.75 108   m . A length of wire is made
by extruding 7 m of aluminum through a hole of diameter 4 mm. What will be the
resistance of the wire?
7. [8 points] A flat nonconducting surface infinite in extent carries a uniform charge
density of   7 109 C/m 2 . A small circular hole of radius R  1.5 m has been cut
in the middle of the sheet as shown. Calculate the electric field at a point z = 5 m
away from the center of the hole along an axis perpendicular to the surface. (In other
words, consider z R , but don’t set z / R exactly equal to zero. You may find the
superposition principle handy.)
Z
R
(Space provided on next page)
Page 8 of 12
PHY2061
12-10-04
Name:_______________________ ___
7. continued
Page 9 of 12
Name:_______________________ ___
PHY2061
12-10-04
8. [6 points] Two infinitely long straight wires have a circular cross section and are
parallel to each other. One has a radius of 3mm and the other has a radius of 2mm.
They are covered with an insulating material of negligible thickness. The two wires
are parallel to each other, but carry a current of 5A in opposite directions. If the
central axes of each wire are separated by 5mm, calculate the magnitude of the
magnetic field at a point 5mm to right of the center of the 2mm radius wire along the
line joining the two axes, as shown:
2mm radius,
current out
3mm radius,
current in

5mm 5mm
Page 10 of 12
Find field here
Name:_______________________ ___
PHY2061
12-10-04
9. A square loop of wire with a side length of 50 cm is rotated about an axis that bisects
the square and that is perpendicular to a constant magnetic field of 0.5 T as shown
(the square loop extends into the plane of the paper). The rotational frequency is 60
revolutions per second.
i
B

axis
(a) [6 points] Calculate the induced EMF in the loop of wire.
(b) [6 points] If the wire has a resistance of 0.5 , calculate the average power
dissipated in the circuit.
Page 11 of 12
Name:_______________________ ___
PHY2061
12-10-04
10. Consider the circuit below. Each capacitor has a capacitance of 2 F, and each
resistor has a resistance of 300 .

+
(a) [6 points] Calculate the RC time constant of the circuit.
(b) [6 points] Once a 6 V battery is connected, how much time must elapse before
the charge on the capacitors has reached half of the maximum value
(assuming they are initially uncharged)?
Page 12 of 12