mcconnell (kam2342) – homework22 – Turner – (60230)
1
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001
(part 1 of 3) 10.0 points
An infinite sheet lying in
yz
plane is carrying a
current which is uniform along the
y
direction,
as illustrated below.
The current is flowing
along the negative
z
direction.
The permeability of free space is 1
.
25664
×
10
−
6
N
/
A
2
.
b
a
x
y
A
C
D
F
E
z
What is the direction of magnetic field
vector
B
at point A, which is located on the negative
x
axis (
i.e.
,
x <
0)?
Caution:
See the sketch
to confirm the location of the point A.
1.
hatwide
B
=
−
(
ˆ
i
−
ˆ
j
)
√
2
2.
hatwide
B
=
(
ˆ
i
+
ˆ
j
)
√
2
3.
hatwide
B
= ˆ
correct
4.
hatwide
B
=
−
ˆ
k
5.
hatwide
B
=
−
ˆ
ı
6.
hatwide
B
=
(
ˆ
i
−
ˆ
j
)
√
2
7.
hatwide
B
= ˆ
ı
8.
hatwide
B
=
ˆ
k
9.
hatwide
B
=
−
ˆ
10.
hatwide
B
=
−
(
ˆ
i
+
ˆ
j
)
√
2
Explanation:
Basic Concepts:
Righthand rule for de
termining the direction of
vector
B
.
Amp´
ere’s Law:
contintegraldisplay
vector
B
·
vector
ds
=
μ
0
I .
Solution:
Consider that the current sheet
consists of infinite number of current wires
connected in parallel.
We can easily deter
mine the direction of
vector
B
for one wire with
righthand rule. Then the direction of
vector
B
for
two wires set together in parallel can be found
(as illustrated below) by superposition prin
ciple.
By symmetry, the direction of
vector
B
due to
an infinite current sheet is therefore along
positive
y
direction (ˆ
) in the part of space
where
x <
0.
002
(part 2 of 3) 10.0 points
Ampere’s Law states that
contintegraldisplay
vector
B
·
dvectors
=
μ
0
I
Denote the magnetic field at A by
B
A
. Eval
uate the loop integral along the rectangular
loop
CDEFC ,
where
EF
=
a
and
FC
=
b .
The magnitude of this loop integral is given
by
1.
contintegraldisplay
vector
B
·
dvectors
=
b B
A
.
2.
contintegraldisplay
vector
B
·
dvectors
=
a
+
b
2
B
A
.
3.
contintegraldisplay
vector
B
·
dvectors
= (
a
+
b
)
B
A
.
4.
contintegraldisplay
vector
B
·
dvectors
=
a B
A
.
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 Spring '10
 Turner
 Magnetic Field, Correct Answer, McConnell, Wire

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