PHY 3323
September 28, 2009
Exam #1
Thucydides V.99
(1) Evaluate the following integrals:
a)
R
6
2
dx
(3
x
2

2
x

1)
δ
(
x

3)
(7 points)
.
b)
R
5
0
dx
cos(
x
)
δ
(
x

π
)
(7 points)
.
c)
R
3
0
dx x
3
δ
(
x
+1)
(7 points)
.
d)
R
∞
∞
dx
ln(
x
+3)
δ
(
x
+2)
(7 points)
.
(2) Compute the line integral of
~v
=
r
cos
2
(
θ
)
b
r

r
cos(
θ
) sin(
θ
)
b
θ
+ 3
r
b
φ
around the 3step
path:
a) Along the
x
axis from the origin to
b
x
(7 points)
;
b) Counterclockwise along the unit circle of radius 1 in the
xy
plane from
b
x
to
b
y
(7
points)
; and
c) Along the
y
axis from
b
y
back to the origin
(7 points)
.
d) Check your answer using Stokes’ theorem
(7 points)
.
(3) Suppose the charge density is given in cylindrical coordinates (
s, φ, z
) as
ρ
=
n
ks
for 0
≤
s
≤
R
0
for
R < s
.
a) What are the dimensions of the constant
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 12/15/2011 for the course PHY 3323 taught by Professor Staff during the Spring '08 term at University of Florida.
 Spring '08
 Staff
 Magnetism

Click to edit the document details