1
Class Examples for Chapter 29
5.
(a) We find the field by superposing the results of two semiinfinite wires (Eq. 297)
and a semicircular arc (Eq. 299 with
=
rad). The direction of
B
is out of the page, as
can be checked by referring to Fig. 296(c). The magnitude of
B
at point
a
is therefore
7
3
0
0
0
1
1
(4
10 T m/A)(10 A) 1
1
2
1.0 10 T
4
2
2
2(0.0050 m)
2
a
i
i
i
B
R
R
R
upon substituting
i
= 10 A and
R
= 0.0050 m.
(b) The direction of this field is out of the page, as Fig. 296(c) makes clear.
(c) The last remark in the problem statement implies that treating
b
as a point midway
between two infinite wires is a good approximation. Thus, using Eq. 294,
7
4
00
(4
10 T m/A)(10 A)
2
8.0 10 T.
2
(0.0050 m)
b
ii
B
RR
(d) This field, too, points out of the page.
8.
In the one case we have
B
small
+
B
big
= 47.25
T, and the other case gives
B
small
–
B
big
=
15.75
T (cautionary note about our notation:
B
small
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 Fall '08
 IASHVILI
 Force, René Descartes, Magnetic Field

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