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Physics 351
Electricity and Magnetism
Test1
Prof. Asim Gangopadhyaya
I will not divulge any information about this exam to any one for any reason.
Name
1) The integral
~a
≡
Z
S
d~a
is sometimes called the
vector area
of the surface S. Use problem 60
a
to show
that
~a
= 0 for any closed surface.
problem 60a :
•Z
V
±
~
∇
T
¶
d
3
r
=
I
S
T d
~
S
‚
.
2) Find the surface integral [
H
~v
·
d~a
] of the vector ﬁeld
~v
=
r
2
sin
θ
ˆ
r
+ 4
r
2
cos
θ
ˆ
θ
+
r
2
tan
θ
ˆ
φ
over a closed surface formed by an inverted hemispherical bowl of radius
R
h
x
2
+
y
2
+
z
2
=
R
2
i
resting on the
xy
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 Spring '09
 Gangopashyaya
 Magnetism

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