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Test I
Physics 351/Dr. Gangopadhyaya
February 22, 2005
To receive full credit your work needs to be a) correct, and b) neat. Do not write answer
to more than one problems in one sheet. When done, put problems in ascending order and
staple all pages.
1) Electric ﬁeld
~
E
(
~
r
) due to a point charge
q
sitting at
~a
≡
(
a,
0
,
0) is given by
~
E
(
~
r
) =
q
4
π²
0
~
r

~a

~
r

~a

3
.
Determine the divergence and the curl of this vector ﬁeld.
2) A vector ﬁeld
~
A
is given by
~
A
(
s,φ,z
) =
C
ˆ
e
φ
s
, where
C
is a constant and
(
s,φ,z
) are cylindrical components of the position vector
~
r
.
a) Compute
H
~
A
·
~
dl
for this ﬁeld around a circular loop of radius
R
centered
at the origin and lying on the
x

y
plane.
b) Determine the curl of this ﬁeld at all points
.
c) Are results from b) and a) supposed to be related to each other? If yes,
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This note was uploaded on 01/28/2010 for the course PHYS 351 taught by Professor Gangopashyaya during the Spring '09 term at Loyola Chicago.
 Spring '09
 Gangopashyaya
 Magnetism, Work

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