Physics 21
Fall, 2007
Practice Hour Exam #1
1
2
3
4
5
Total
Name:
Recitation Time
Recitation Leader
This exam is closed notes and closed book. You must show enough work on all problems to convince the grader you
understand how to solve the problem. You may use a calculator, but you must show a full solution to simultaneous
algebraic equations. Give units. There is an equation sheet on the last page. All problems count 20 points.
Problem 1.
8
Ω
3
Ω
6
Ω
I
3
I
2
I
1
36 V
27 V
b
a
(a) (10 pts.) Write the loop and junction equations
needed to determine the currents
I
1
,
I
2
,and
I
3
in
the circuit shown. Indicate clearly the loop used
to determine each loop equation.
(b) (6 pts.)
Determine the currents
I
1
,
I
2
,and
I
3
(including the correct sign) by explicit solution
of the equations. You must show your work.
(c) (4 pts.) What is the potential diFerence
V
b

V
a
between the points marked
a
and
b
on the dia
gram? Use the calculated values of the currents
and show how you get your answer.
Problem 2.
The circular ring of charge shown in the
diagram is in the
xy
plane centered at the origin and
has a radius
R
. The charge is spread uniformly around
the ring with linear density
λ
.
R
P (x
=0,y=0,
z)
y
z
x
λ
ı
φ
(a) (4 pts.) Write an expression for the total charge
Q
on the ring.
(b) (3 pts.) Give the components of the vector (
r

r
±
)
from the point on the ring at angle
φ
(with respect
to the
x
axis) to the point
P
.
(c) (6 pts.) Determine the electric potential
dV
at
the point
P
due to the element
dQ
of charge at
the point
φ
on the ring. Express
dQ
in terms of
λ
and
dφ
.
(d) (3 pts.) Integrate to ±nd the electric potential
V
at the point
P
due to the ring of charge. Your
answer should be in terms of
λ
,
R
,and
z
.
(e) (4 pts.) Use the expression for
V
to ±nd the
z
component of the electric ±eld at the point
P
.
Work out the value of the electric ±eld numeri
cally if
R
=0
.
03 m,
λ
=3
.
68nC/m(1nC=
10
−
9
C), and
z
=0
.
04 m. Don’t forget the units.
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View Full DocumentProblem 3.
A nonconducting sphere of radius
R
0
possesses a uniform volume charge density
ρ
. For this
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 Spring '08
 Hickman
 Work, Trigraph, Electric charge, Dielectric

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