Physics 21
Fall, 2004
Solution to HW15
29
P 21
Determine the magnetic ﬂux through a square loop
of side
a
if one side is parallel to, and a distance
a
from, a
straight wire that carries a current
I
.
The field of the wire is
B
(
r
) =
µ
0
I/
2
πr
, directed perpen
dicular to the loop. The ﬂux is
Φ =
2
a
a
B
(
r
)
a dr
=
µ
0
I
2
π
a
2
a
a
dr
r
The definite integral is
2
a
a
dr
r
= ln
r

2
a
a
= ln 2
a
−
ln
a
= ln
2
a
a
= ln 2
Combining terms, we obtain
Φ =
µ
0
Ia
2
π
ln 2
≈
0
.
6931
µ
0
Ia
2
π
.
One can get a pretty good approximate answer by assuming
B
(
r
) is constant over the loop and taking the value at the
middle, where
r
= 1
.
5
a
. Then
Φ =
B
(1
.
5
a
)
a
2
=
µ
0
I
2
π
(1
.
5
a
)
a
2
=
2
3
µ
0
Ia
2
π
≈
0
.
6667
µ
0
Ia
2
π
.
29
P 40
Neon signs require 12 kV for their operation. To
operate from a 220 V line, what must be the ratio of sec
ondary to primary turns of the transformer? What would be
the voltage output if the transformer were connected back
ward?
Given that
V
P
= 12 kV and
V
S
= 220 V, we can use
V
S
V
P
=
12
,
000
220
=
N
S
N
P
= 54
.
5
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 Fall '07
 Hickman
 Physics, Current, Magnetic Field, rod, Faraday's law of induction, frictionless parallel rails

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