P114 Practice Final Exam
•
DO NOT SIT NEXT TO A STUDENT WITH THE SAME COLOR TEST.
•
THIS IS A CLOSED BOOK EXAM
•
Print your name on each sheet
•
Do all problems  Problems 17 count for 25 points each.
•
Answer on the sheet containing the problem  use the back of the sheet if necessary.
•
Making a diagram, when appropriate, usually aids in solving the problem.
•
SHOW WORK TO GET PARTIAL CREDIT FOR ALL QUESTIONS
•
Circle your answers and give units when appropriate.
•
An information sheet is given at the back of the examination
.
•
Calculators are allowed.
Physical Constants
ε
o
=8
.
85 10
−
12
C
2
/N.m
2
.μ
o
=4
π
10
−
7
N/A
2
c
=2
.
998 10
8
m/s
Electron charge
e
=
−
1
.
602 10
−
19
C
Avogadro’s Number
N
=6
.
022 10
23
per mole.
Planck’s constant:
h
.
626 10
−
34
J.s
.
136 10
−
15
eV.s
~
=
h
2
π
Uni
f
ed mass of nucleon:
m
N
=1
.
66 10
−
27
kg
m
N
c
2
= 931
.
5
MeV
Electron mass:
m
e
=
9.109 10
−
31
m
e
c
2
= 511
.
0
keV
1
eV
.
602 10
−
19
J
1
W
J/s
1
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A capacitor comprises two concentric spherical thinwalled conducting shells, the inner one has radius
a
=2
.
0
cm
and
the outer shell has a radius
b
=4
cm.
A voltage of
100
,
000
V
is applied between the inner and outer electrodes.
a;(5pts)
Derive the direction and magnitude of the electric
f
eld between the two spheres,
b(4pts)
Derive the direction and magnitude of the electric
f
eld inside the inner concentric sphere,
c(4pts)
Derive the direction and magnitude of the electric
f
eld outside the outer concentric sphere,
d(5pts)
What is the total capacitance?
e(2pts)
What is the stored energy?
f(5pts)
What would be the capacitance if the volume between the two electrodes was
f
lled with a dielectric of dielectric
constant
κ
e
?
2;
A toroid comprises 20,000 turns evenly wrapped on a ring having a radius
r
=1
meter with a
2
cm
radius circular cross
section, that is,
b
−
a
cm
. To simplify the mathematics assume that the
B
f
eld is uniformly constant inside the windings
of the solenoid since the
2
cm
radius of the circular cross section of the solenoid is small compared to the average radius of
the toroid. A current of
0
.
6
amperes passes through the winding.
a;(8pts)
Calculate the B
f
eld inside the windings.
b;(7 pts)
Calculate the self inductance.
c;(5pts)
Calculate the stored energy.
d;(5pts)
What would be the B
f
eld if the toroid was wrapped on an iron ring of relative permeability
κ
M
= 1000
.
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 Spring '08
 Jordan
 Electron, Magnetic Field, Electric charge

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