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Optics 287, Math 287
March 4, 2008
2:00 to 3:15 pm
Midterm Exam
1.
a) (10 pts.) Calculate the gradient, divergence and/or curl (all that apply) of
φ
(
r
)
=
4
x
3
y
2
+
2
z
.
b) (10 pts.) Find the result of the following integral
I
=
F
(
r
)
⋅
d
v
λ
∫
.
where
F
(
r
) is a vector function given by one of your results from (a), and the
contour is the unit circle, centered at the origin, over the
xy
plane.
2.
a) (20 pts.) Calculate the gradient, divergence, curl, graddiv, and/or Laplacian
(whichever applies) of the following functions
E
(
r
,
t
)
=
E
0
e
i
(
k
⋅
r
−
ω
t
)
,
B
(
r
,
t
)
=
B
0
e
i
(
k
⋅
r
−
t
)
,
where
E
0
,
B
0
and
k
are constant vectors.
b) (20 pts.) Suppose that these functions are the electric and magnetic fields of a
freespace monochromatic plane wave. Maxwell’s equations are given by
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This note was uploaded on 03/23/2011 for the course OPT 287 taught by Professor Alonso during the Spring '11 term at Rochester.
 Spring '11
 alonso

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