lin (gdl353) – Homework 9 – shubeita – (58390)
1
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print-out
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have
16
questions.
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before answering.
001(part1of2)10.0points
Given a current segment which flows along
the edges of a cube as shown in the figure.
The conventional Cartesian notation of ˆ
ı
(a
unit vector along the positive
x
axis), ˆ
(a unit
vector along the positive
y
axis), and
ˆ
k
(a unit
vector along the positive
z
axis), is used.
The cube has sides of length
a
. The current
flows along the path
A→C→D→E→G
.
There is a uniform magnetic field
vector
B
=
B
ˆ
ı
.
x
y
z
B
B
B
A
C
D
E
G
a
a
Find the direction
hatwide
F
≡
vector
F
bardbl
vector
F
bardbl
of the resul-
tant magnetic force on the current segment
ACDEG
.
1.
hatwide
F
=
1
√
2
parenleftBig
ˆ
−
ˆ
k
parenrightBig
2.
Undetermined, since the magnitude of the
force is zero.
3.
hatwide
F
= ˆ
4.
hatwide
F
=
−
ˆ
k
5.
hatwide
F
=
−
ˆ
correct
6.
hatwide
F
= ˆ
ı
7.
hatwide
F
=
ˆ
k
8.
hatwide
F
=
1
√
2
parenleftBig
ˆ
+
ˆ
k
parenrightBig
9.
hatwide
F
=
1
√
2
parenleftBig
ˆ
k
−
ˆ
parenrightBig
10.
hatwide
F
=
−
ˆ
ı
Explanation:
Note:
The force on wire segment
AC
is
canceled by the force on wire segment
EG
.
The current in wire segment
CD
flows in the ˆ
ı
direction and the current in wire segment
DE
flows in the
−
ˆ
k
direction.
x
z
A
G
a
a
TopView
B
B
B
ˆ
ı
−
ˆ
k
ˆ
ı
−
ˆ
k
B
B
B
The magnetic force on a wire is given by
vector
F
mag
=
I
vector
ℓ
×
vector
B .
The vector
vector
ℓ
is given by the sum of the
current segments
vector
ℓ
=
−→
AC
+
−→
CD
+
−→
DE
+
−→
EG
,
and this is the vector
−→
AG
,
(see figure above).
The magnitude is given by
vector
F
≃
vector
ℓ
×
vector
B
≃
(ˆ
ı
−
ˆ
k
)
×
(ˆ
ı
)
= (ˆ
ı
×
ˆ
ı
)
−
(
ˆ
k
×
ˆ
ı
)
= 0
−
ˆ
hatwide
F
=
−
ˆ
.
002(part2of2)10.0points
Find the magnitude
bardbl
vector
F
magnetic
bardbl
the magnetic

lin (gdl353) – Homework 9 – shubeita – (58390)
2
field exerts on the current segment
ACDEG
if
the.
Magnetic field is 1
.
78 T,
a
is 3
.
81 m, and
the current is 5
.
14 A.
◦
with the
vertical when in equilibrium (
v
= 0 m
/
s),
determine the strength of the magnetic field.
003
10.0points
If the wires make an angle of 22
◦
with the
vertical when in equilibrium (
v
= 0 m
/
s),
determine the strength of the magnetic field.

A metal rod having a mass per unit length of
0
.
0424 kg
/
m carries a current of 4
.
9 A
.
The
rod hangs from two wires (in the same plane
as the rod) in a uniform vertical magnetic
field as in the figure.