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Physics 2220
Spring 2012
Ben Bromley
FINAL EXAM
PLEASE FILL IN THE INFORMATION BELOW
Name (printed):
Name (signed):
Student ID Number
Discussion Instructor:
U __ __ __ __ __ __ __
Chad
Jon Paul
Maria
Peter
Physics 2220
Spring 2012
Ben Bromley
Data: Use these constants (where it states, for example, 1 ft, the 1 is exact for significant figure purposes).
1 ft = 12 in (exact)
1 m = 3.28 ft
1 mile = 5280 ft (exact)
1 hour = 3600 sec = 60 min (exact)
1 day = 24 hr (exact)
2
2
gearth = 9.80 m/s = 32.2 ft/s
gmoon = 1.67 m/s2 = 5.48 ft/s2
1 year = 365.25 days
1 kg = 0.0685 slug
1 N = 0.225 pound
1 horsepower = 550 ft‫ڄ‬pounds/s (exact)
Mearth = 5.98 × 1024 kg
3
Rearth = 6.38 × 10 km
Msun = 1.99 × 1030 kg
Rsun = 6.96 × 108 m
Mmoon = 7.35 × 1022 kg
Rmoon = 1.74 × 103 km
G = 6.67 × 10-11 N‫ڄ‬m2/kg2
k = 8.99 × 109 N‫ڄ‬m2/C2

x







melectron = 9.11 × 10-31 kg





















μo = 4π × 10-7 T‫ڄ‬m/A (exact)
N(Avogadro's No.) = 6.02 × 1023 atoms/gm‫ڄ‬mole
= 6.02 × 1026 atoms/kg‫ڄ‬mole
1 Tesla = 10,000 gauss (exact)
ρ(H2O) = 1000 kg/m3
cos(a ± b) = cos a cos b ‫ ט‬a sin b
sin(a ± b) = sin a cos b ± sin b
mproton = 1.67 × 10−27 kg
h = 6.64 × 10-34 J
π = 3.14
8
c = 3.00 × 10 m/s
dx
 x 2  a 2 3/2
  ax
e
dx


εo = 8.85 × 10-12 F/m
eelectron charge = -1.60 × 10-19 C
x 2  a 2 dx 


1
3
 x2  a2 
3
x
a2 x2  a2
1
  eax
a
xdx
x2  a2

xdx
a2  x2
3/2

1
x2  a2
  a2  x2
dx
 n  x  x 2  a 2 


x2  a2
1  a  x2  a2
  n 
a 
x
x x2  a2

dx









x2  a2





x
x
 sin 1   , or  cos 1  
a
a
a2  x2









xdx
 x2  a2
dx
dx
1
 n  a  bx 
a  bx b
dx
 a  bx 2

1
b  a  bx 
Physics2220
2220
Physics
Spring 2012
Fall 2009
Name: __________________________________
Unid: ___________________________________
Discussion TA: ___________________________
Final Exam
Show all work!! Report all numbers to three (3) significant figures.
A.
A parallel plate capacitor has two oppositely charged sheets separated by a
distance d, and containing a vacuum (see diagram above). The capacitor is
charged to V = 12 V. An electron is placed at rest immediately to the inside
of the negatively charged sheet. I t is then released, accelerating toward the
positively charged sheet. What is the speed v of the electron when it reaches
the positively charged sheet? [Hint: Don’t Force this one and it will Work
out better….]
V = __________________________
B.
A spherically symmetric cloud of charge contained in a sphere of radius R has a
volume charge density  = +A/r2, where A is a constant and r < R is the distance from
the center of the cloud. Find electric field E at a radius r = R/2.
E = _________________________
Ben Bromley
1
PhysicsPhysics
2220 2220 Fall 2009
Spring 2012
Name: __________________________________
Unid: ___________________________________
Discussion TA: ___________________________
Final Exam
Ben Bromley
2
Show all work!! Report all numbers to three (3) significant figures.
A.
A particle of mass m = 0.01 kg and charge q = 0.008 C has a velocity
ˆ . It is observed to travel
v  1.2iˆ 1.6ˆj m/s in a uniform magnetic field B  0.75kT
in a circular path of radius R. Find that radius.
R = _____________________________
B.
Based on the figure shown, find the infinitesimal element of magnetic field
dB at the point P (distance a above the x-axis), from the current I (flowing
along the x-axis) through an element of length dx. Give your answer in
terms of a and variable x.
dB magnitude:_______________________, direction [+x,-x,+y,-y, in/out of page]:____________________
Find the B-field, Bsegment from a wire segment of length 2a, at a distance a from the center of the segment.
[Hint: integrate your result for dB from x = -a to a.]
Bsegment (magnitude):____________________
Finally, find the strength of the magnetic field at the center of a square wire loop (length 2a to a side, carrying
current I) in terms of Bsegment:
Bsquare (magnitude)_____________________
Physics2220
2220
Physics
Spring 2012
Fall 2009
Name: __________________________________
Unid: ___________________________________
Discussion TA: ___________________________
Final Exam
Show all work!! Report all numbers to three (3) significant figures.
A.
A square wire loop (length A to a side) has a resistor with resistance R on one
leg, and it travels with speed v to the right, as shown. At time t = 0 it crosses
into a small, square region (length a to a side) which contains a uniform
magnetic field of strength B and oriented perpendicular to the square wire
loop. What is the power P dissipated through the resistor immediately after
t = 0, when the larger loop is moving into the smaller square region?
P = _____________________________
B.
Find the three currents, I1, I2, and I3, in the circuit shown.
I1 = ________________
I2 = ________________
I3=_________________
Ben Bromley
3
Physics2220
2220 Fall 2009
Physics
Spring 2012
Name: __________________________________
Unid: ___________________________________
Discussion TA: ___________________________
Final Exam
Ben Bromley
4
Show all work!! Report all numbers to three (3) significant figures.
A.
Coherent light of wavelength  travels inside two optical fibers. The
length of the straight fiber is L, while the other fiber has two straight
segments of total length L plus a circular segment of radius R in
between (see figure). If the light entering both fibers is in phase,
what is the condition in terms of (L, R, , as needed) for constructive
interference when the light coming out of the ends of the fibers is
recombined? (Assume that light is a plane wave traveling along the
axis of the wire, even if the wire is not straight.)
B.
In the optical/thin lens set-up shown, find the image location (relative to the first lens), orientation and height.
Image location (distance left of right of lens)_______________________
Image orientation (upright or inverted)______________________
Image height________________________