Name:_______________________ ___
PHY2061
11-9-06
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 at least 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
1
1
q
di
dq
V 
V   L
i
 
Ceff  C1  C2
C
dt
dt
Ceff C1 C2
1
1
1
L
L
R
 LR 
 
 RC  RC
Reff  R1  R2
A
R
Reff R1 R2
P  Vi  i 2 R 
V  iR
 
1
1 v / c
2
ux  v
vu
1  2x
c
2
V2
R
t   t0
U
Q2
2C
L
L0
1 2
1
Li
  2 f 
2
LC
x    x  vt 
y  y
2
t     t  vx / c 
z  z
U

uy
E  mc2
EK    1 mc2
 vu 
 1  2x 
c 

p  mu
F  q(E  v  B)
m2 c4  E 2  p 2 c2
F  dp / dt
F  i L×B
 i ds ×r
i
i
dB  0
Bwire  0
Barc  0 
p  qBr
B  ds  0 ienc
3

C
4 r
2 r
4 R
dB
Fz   z z
μ  NiA
τ  μ×B
U  μ  B
τ  r ×F
dz
u x 
 B   B  dΑ
S
u y 
dB
  N
dt
a  b  axbx  a y by  az bz

LN B
i
u
0 E
2
2
2
B

2 0
a  b   a y bz  by az  x   axbz  bx az  y   axby  bx a y  z
Page 1 of 13
Name:_______________________ ___
PHY2061
11-9-06
1. [8 points] In the circuit shown, the resistance R1  12 . The battery voltages are
identical: 1   2   3  1 V . What is the current (in amps) flowing through the middle
branch from a to b?
1
Page 2 of 13
Name:_______________________ ___
PHY2061
11-9-06
2. [6 points] A capacitor of capacitance C  2 1010 F contains a charge q on one of its
plates (and –q on the other). It is connected in to a resistor of resistance R = 200 such that it
forms a closed circuit. How much time must elapse so that the charge on the capacitor is
reduced to only 10% of its starting value?
3. [6 points] A stationary flat conductor carries a constant current i >0 in the direction from
top to bottom ( yˆ ) in the presence of a magnetic field B that points into plane the paper
( zˆ ). If the electrons that make up the current are not allowed to leave the conductor, and the
magnitude of their drift velocity is vd , indicate the direction and determine the magnitude of
any electric field created inside the conductor.
i
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
B
y
x
z
Page 3 of 13
PHY2061
11-9-06
Name:_______________________ ___
4. [6 points] An electron is accelerated from rest between 2 electric plates with a potential
difference of V  5 105 V . What is the velocity of the electron upon reaching the far
plate? (Careful!) The mass of the electron is me  9.111031 kg .
Page 4 of 13
PHY2061
11-9-06
Name:_______________________ ___
5. [6 points] A long wire has an electric charge density of   2.5 C / m , where
1C  106 C , as measured in the rest frame of the wire. What is the magnitude of the electric
field in the rest frame of an electron traveling at a velocity of v  2.8 108 m/s parallel to the
wire at a distance r  1 cm from the wire?
Page 5 of 13
PHY2061
11-9-06
Name:_______________________ ___
6. [6 points] A long cylindrical wire of radius r = 3mm carries 100A of current. If the current
density is uniform throughout the cross-section of the wire, what is the magnitude of the
magnetic field at a radius of r = 1mm within the wire?
Page 6 of 13
Name:_______________________ ___
PHY2061
11-9-06
7. [8 points] An infinitely long insulated wire carrying a current I = 50 A is bent into a 270º
arc ( 3 / 2 radians) of radius R=2 cm. The current comes in from infinitely far away from
above, and exits to the left infinitely far away. Find the magnitude of the field B at the center
of the arc. The wire begins and ends its turn at the locations indicated.
I
y
I
x
z
R
R
I
Page 7 of 13
PHY2061
11-9-06
Name:_______________________ ___
8. A stationary neutral atom resides at the center of a Cartesian coordinate system and has a
magnetic dipole moment of 2.11023 J/T aligned in the yˆ direction.
(a) [6 points] What is the ratio of the magnitude of the magnetic field from the atomic dipole
at y = 100 nm to that at y = 25 nm? (The radius of the atom is about 0.1 nm, where 1 nm =
10-9 m)
(b) [6 points] If a magnetic field is present everywhere with the form
B  B0 y yˆ , where B0  0.5 T/m , what is the magnitude of the acceleration of the dipole if
the mass of the atom is 10-25 kg.
Page 8 of 13
PHY2061
11-9-06
Name:_______________________ ___
9. [6 points] The magnetic field of a large solenoid is used to keep a proton in a perfect
circular orbit. The solenoid has 1000 windings per meter of length and has a radius of 1 m. If
the proton has a velocity of v  1.5 106 m/s , what is the minimum current needed to keep
the proton orbiting within the confines of the solenoid in a plane perpendicular to the
solenoid axis? The proton mass is mp  1.67 1027 kg and its charge is q  1.6 1019 C .
r
p
Page 9 of 13
Name:_______________________ ___
PHY2061
11-9-06
10. [6 points] A rod of length L = 0.5 m and mass m = 0.5 kg carries a current I = 20 A in the
direction shown. The rod is aligned parallel to the z axis, and a uniform magnetic field is
present: B   B0 yˆ , B0  0.5 T . The rod is suspended by two massless wires which bring the
current to and away from the rod. The acceleration due to gravity is 10 m/s2 in the yˆ
direction. What is the angle  that the suspension wires make with respect to the magnetic
field direction?
B
y
z
x

I
Page 10 of 13
PHY2061
11-9-06
Name:_______________________ ___
11. An oscillating LC circuit consists of a 0.002 H inductive coil and a 4 F capacitor.
The capacitor has a voltage drop of 0.75 V when the current through the coil is
0.03A.
(a) [6 points] Find the maximum charge on the capacitor.
(b) [6 points] Find the maximum current through the coil.
Page 11 of 13
PHY2061
11-9-06
Name:_______________________ ___
12. [6 points] A circular conducting loop of wire increases in radius with time according to
r  vt where v is a constant. It is immersed in a constant magnetic field B perpendicular to
the plane of the loop. What is the induced EMF in the loop as a function of time?
Page 12 of 13
PHY2061
11-9-06
Name:_______________________ ___
13. A solenoid 21 cm long has a circular cross-section of 17 cm2. There are 210 turns of wire
carrying a current of 2.5A.
(a) [6 points] Find the magnitude of the magnetic field inside the solenoid assuming that
it is essentially infinite in length (neglect end effects).
(b) [6 points] Find the total energy stored in the magnetic field inside the volume of the
solenoid. Neglect end effects.
Page 13 of 13