62. We use B(x, y, z) = (µ
0
/4π)i ∆
s
× r/r
3
, where ∆
s = ∆sˆj and
r = xˆi + yˆj + z
k. Thus,
B(x, y, z) =
µ
0
4π
i ∆sˆj
× (xi + yˆj+ zk)
(x
2
+ y
2
+ z
2
)
3/2
=
µ
0
i ∆s (zˆi
− xˆk)
4π(x
2
+ y
s
+ z
2
)
3/2
.
(a) The field on the z axis (at z = 5.0m) is
B(0, 0, 5.0m)
=
(4π
× 10
−7
T
· m/A)(2.0A)(3.0 × 10
−2
m)(5.0m)ˆi
4π (0
2
+ 0
2
+ (5.0m)
2
)
3/2
=
2.4
× 10
−10
T ˆi .
(b)
B(0, 6.0 m, 0), since x = z = 0 .
(c) The field in the xy plane, at (x, y) = (7, 7), is
B(7.0 m, 7.0 m, 0 )
=
(4π
× 10
−7
T
· m/A)(2.0A)(3.0 × 10
−2
m)(
−7.0m)ˆk
4π ((7.0m)
2
+ (7.0m)
2
+ 0
2
)
3/2
=
4.3
× 10
−11
T ˆ
k .
(d) The field in the xy plane, at (x, y) = (
−3, −4), is
B(
−3.0 m, −4.0 m, 0 ) =
(4π
× 10
−7
T
· m/A)(2.0A)(3.0 × 10
−2
m)(3.0m)ˆ
k
4π ((
−3.0m)
2
+ (
−4.0m)
2
+ 0
2
)
3/2
=
1.4
× 10
−10
T ˆ
k .