Magnetism
161
19.47
The magnetic field inside a long solenoid is
00
N
I
L
µµ
==
Bn
. Thus, the required
current is
I
( )( )
()
4
2
-7
0
1.00
10
T
0.400 m
3.18
10
A
31.8 mA
4
10
T m A
1000
BL
I
N
µ
π
−
−
×
=×
=
×⋅
19.48
(a) From
RL
A
ρ
=
, the required length of wire to be used is
2
3
8
5.00
0.500
10
m
4
57.7 m
1.70
10
m
RA
L
−
−
Ω×
⋅
=
×Ω
⋅
The total number of turns on the solenoid (that is, the number of times this length of
wire will go around a 1.00 cm radius cylinder) is
2
57.7 m
919
2
21
.
0
01
0
m
L
N
r
−
=
×
(b) From
B
0
n
I
=
, the number of turns per unit length on the solenoid is
2
3
-7
0
4.00
10
T
7.96
10 turns m
41
0
T
m
A
4
.
0
0
A
B
n
I
−
×
Thus, the required length of the solenoid is

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