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52.
(a) The binomial theorem (Appendix E) allows us to write
p
k
(1 +
x
)=
√
k
µ
1+
x
2
+
x
2
8
+
3
x
3
48
+
···
¶
≈
√
k
+
x
2
√
k
for
x
¿
1. Thus, the end result from the solution of problem 49 yields
r
m
=
s
Rλm
µ
1+
1
2
m
¶
≈
√
Rλm
+
1
4
m
√
Rλm
and
r
m
+1
=
s
Rλm
µ
1+
3
2
m
¶
≈
√
Rλm
+
3
4
m
√
Rλm
for very large values of
m
. Subtracting these, we obtain
∆
r
=
3
4
m
√
Rλm
−
1
4
m
√
Rλm
=
1
2
r
Rλ
m
.
(b) Wetakethed
iFerent
ia
lo
fthearea
:
dA
=
d
(
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This note was uploaded on 11/12/2011 for the course PHYS 2001 taught by Professor Sprunger during the Fall '08 term at LSU.
 Fall '08
 SPRUNGER
 Physics

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