RECITATION 11
7.
Each of the semiinfinite straight wires contributes
0
4
i
R
μ
π
(Eq. 309) to the field at the
center of the circle (both contributions pointing “out of the page”). The current in the arc
contributes a term given by Eq. 3011 pointing into the page, and this is able to produce
zero total field at that location if
arc
straight
0
0
2
2
4
4
C
B
B
i
i
R
R
μ
φ
μ
π
π
=
=
which yields
2 rad
115 .
C
φ
=
≈
°
11.
Our
x
axis is along the wire with the origin at the midpoint. The current flows in the
positive
x
direction. All segments of the wire produce magnetic fields at
P
1
that are out of
the page. According to the BiotSavart law, the magnitude of the field any (infinitesimal)
segment produces at
P
1
is given by
0
2
sin
4
i
dB
dx
r
μ
φ
π
=
where
φ
(the angle between the segment and a line drawn from the segment to
P
1
) and
r
(the length of that line) are functions of
x
.
Replacing
r
with
2
2
x
R
+
and
sin
φ
with
2
2
,
R r
R
x
R
=
+
we integrate from
x = –L
/2 to
x = L
/2. The total field has a magnitude of
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 Spring '08
 Goksu
 Physics, Current, Magnetic Field, long straight wire, BARC

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