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
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '09
 Gangopashyaya
 Magnetism, Flux, Stokes' theorem, Prof. Asim Gangopadhyaya, Magnetism Prof. Asim

Click to edit the document details