79. (a) The energy density at any point is given by
u
B
=
B
2
/
2
µ
0
,where
B
is the magnitude of the magnetic
Feld. The magnitude of the Feld inside a toroid, a distance
r
from the center, is given by Eq. 3026:
B
=
µ
0
iN/
2
πr
,where
N
is the number of turns and
i
is the current. Thus
u
B
=
1
2
µ
0
µ
µ
0
iN
2
πr
¶
2
=
µ
0
i
2
N
2
8
π
2
r
2
.
(b) We evaluate the integral
U
B
=
R
u
B
d
V
over the volume of the toroid. A circular strip with radius
r
,he
ight
h
,andth
ickness
dr
has volume
d
V
=2
πrhdr
,so
U
B
=
µ
0
i
2
N
2
8
π
2
2
πh
Z
b
a
dr
r
=
µ
0
i
2
N
2
h
4
π
ln
µ
b
a
¶
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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, Energy

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