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Magnetism
171
Thus, the downward magnetic force acting on the wire is
()
( )
23
2
19.6 N m
0.80
10
m
10.0
10
kg
9.80 m s
5.9
10
N
m
total
Fk
x m
g
−−
−
=−
=×
−
×
sin90
m
2
Since the magnetic force is given by
F
BIL
=
°
, the magnetic field is
( )( )
2
2
12
5.9
10
N
0.59 T
24 V
5.0
10
m
mm
FF
B
IL
V R L
−
−
Ω×
==
=
=
∆
×
19.67
Each turn of wire occupies a length of the solenoid equal to the diameter of the wire.
Thus, the number of turns on the solenoid is
75.0 cm
750
0.100 cm
solenoid
wire
L
N
d
=
The length of wire required to make this number of turns on the solenoid is
( ) ( ) ( )
2
750
10.0
10
m
75.0
m
solenoid
id
N
d
ππ
−
=
×
N circumference of soleno
l
π
=
and this copper wire has a resistance of
( )
8
Cu
Cu
2
2

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