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80. If the solenoid is long and thin, then when it is bent into a toroid (
b
−
a
)
/a
is much less than 1. Therefore,
L
toroid
=
µ
0
N
2
h
2
π
ln
µ
b
a
¶
=
µ
0
N
2
h
2
π
ln
µ
1+
b
−
a
b
¶
≈
µ
0
N
2
h
(
b
−
a
)
2
πb
.
Since
A
=
h
(
b
−
a
) is the crosssectional area and
l
=2
πb
is the length of the toroid, we may rewrite
this expression for the toroid selfinductance as
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Unformatted text preview: L toroid l ≈ µ N 2 A l 2 = µ n 2 A , which indeed reduces to that of a long solenoid. Note that the approximation ln(1 + x ) ≈ x is used for very small  x  ....
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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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