PHYS2020, Fall 2006
CAPA Set 9
1.
[1pt] A vertical straight wire carrying an upward 11.3
A
current exerts an attractive force per unit length of
8
.
00
×
10

4
N/m
on a second parallel wire 7.70
cm
away. What is the magnitude of the current that flows in the second
wire?
The current in the first wire creates a magnetic field which acts on the current in the second wire. The
magnetic field created by a current along a long straight wire is given by
B
=
μI
2
πr
. Labeling the current
in the first wire as
I
1
the field is
B
=
μ
0
I
1
2
πr
. The force that this magnetic field exerts on the second wire
is given by
F
=
IlscriptB
. Here the current is that which is carried in the second wire
I
2
so the force on the
second wire is
F
2
=
I
2
lscript
2
B
where
B
is given from before so we have
F
2
=
I
2
lscript
2
μ
0
I
1
2
πr
. We are asked to find
the current flowing in the second wire so we solve for
I
2
to get
I
2
=
F
2
·
2
πr
lscript
2
μ
0
I
1
. We don’t know
F
2
or
lscript
2
but we
do know
F
2
/lscript
2
which is all that is necessary to solve the problem. For the numbers given here, the final
answer is
I
2
=
F
2
lscript
2
2
πr
μ
0
I
1
= 8
.
00
×
10

4
N/m
2
π
0
.
0770
m
4
π
×
10

7
T m/A
·
11
.
3
A
= 8
.
00
×
10

4
N/m
0
.
0770
m
2
×
10

7
T m/A
·
11
.
3
A
= 27
.
3
A
.
2.
[1pt] Determine the magnitude of the magnetic field midway between two long straight wires 1.80
cm
apart when
one wire carries 5.40
A
and the other carries 15.5
A
. Assume these currents are in the same direction.
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 Spring '06
 DUBSON
 Physics, Current, Force, Magnetic Field, Wire

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