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Unformatted text preview: (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
⎛ μ0i ⎞ μ0i (4π × 10 T ⋅ m/A)(10 A)
Bb = 2 ⎜
= 8.0 × 10−4 T.
⎟= R =
π (0.0050 m)
⎝ 2πR ⎠ π (d) This field, too, points out of the page.
→ 6. With the “usual” x and y coordinates used in Fig. 2937, then the vector r pointing
from a current element to P is r = − s ˆ + R ˆ . Since ds = ds ˆ , then  ds × r  = Rds.
i
i
j Therefore, with r = s 2 + R 2 , Eq. 293 gives
dB = μ0
iR ds
.
2
4π ( s + R 2 )3/ 2 (a) Clearly, considered as a function of s (but thinking of “ds” as some finitesized
constant value), the above expression is maximum for s = 0. Its value in this case is
dBmax = μ0i ds / 4π R 2 .
(b) We want to find the s value such that dB = dBmax /10 . This is a nontrivial algebra
exercise, but is nonetheless straightforward. The result is s =
R = 2.00 cm, then we obtain s = 3.82 cm. 10 2/3 − 1 R. If we set 7. (a) Recalling the straight sections discussion in Sample Problem — “Magnetic field at
the center of a circular arc of current,” we see that the current in the straight segments
collinear with P do not contribute to the field at that point. Using Eq. 299 (with φ = θ)
and the righthand rule, we find that the current in the semicircular arc of radius b
contributes μ 0iθ 4 pb (out of the page) to the field at P. Also, the current in the large
radius arc contributes μ 0iθ 4 pa (into the page) to the field there. Thus, the net field at P
is
μ iθ ⎛ 1 1 ⎞ (4p ×10 7 T ⋅ m A)(0.411A)(74°⋅π /180°) ⎛ 1
1⎞
B= 0 ⎜ − ⎟ =
−
⎜
⎟
4 ⎝b a⎠
4π
⎝ 0.107m 0.135m ⎠
= 1.02 ×10 7 T. 1129
(b) The direction is out of the page.
8. (a) Recalling the straight sections discussion in Sample Problem — “Magnetic field at
the center of a circular arc of current,” we see that the current in segments AH and JD do
not contribute to the field at point C. Usi...
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 Fall '08
 schuller
 Magnetism, Work

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