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 .