P30_016.PDF
(
62 KB
)
Pobierz
Chapter 30 - 30.16
16. Our
y
axis is along the wire with the origin at the top endpoint, and the current is in the positive
y
direction. All segments of the wire produce magnetic fields at
P
that are into the page. According to
the Biot-Savart law, the magnitude of the field any (infinitesimal) segment produces at
P
is given by
dB
=
µ
0
i
4
π
sin
θ
r
2
dy
that line) are functions of
y
. Replacing
r
with
y
2
+
a
2
and sin
θ
with
a/r
=
a/
y
2
+
a
2
,weintegrate
from
y
=
−
a
to
y
= 0. The total field is
B
=
µ
0
ia
4
π
0
(
y
2
+
a
2
)
3
/
2
=
µ
0
ia
1
a
2
y
(
y
2
+
a
2
)
1
/
2
0
=
µ
0
i
4
πa
a
√
a
2
+
a
2
−
a
4
π
−a
which simplifies to the desired result (noting that
4
√
2
=
√
8
).
where
θ
(the angle between the segment and a li
ne draw
n from the segment to
P
)
and
r
(
the length of
dy
1
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Inne foldery tego chomika:
chap01
chap02
chap03
chap04
chap05
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