This preview shows page 1. Sign up to view the full content.
Unformatted text preview: 3rad ) ˆ
ˆ
B= 0
k−
k = −(1.7 × 10−6 T)k
4π ( 0.050 m )
4π ( 0.040 m )
or  B  = 1.7 ×10−6 T .
ˆ
(b) The direction is − k , or into the page.
(c) If the direction of i1 is reversed, we then have
B=− μ0 ( 0.40 A )(π rad ) ˆ μ0 ( 0.80 A ) ( 2π / 3rad ) ˆ
ˆ
k−
k = −(6.7 × 10−6 T)k
4π ( 0.050 m )
4π ( 0.040 m ) or  B  = 6.7 × 10−6 T.
ˆ
(d) The direction is − k , or into the page.
16. Using the law of cosines and the requirement that B = 100 nT, we have
2
⎛ B12 + B2 − B 2 ⎞
⎟ = 144° ,
⎝ −2 B1 B2 ⎠ θ = cos −1 ⎜ where Eq. 2910 has been used to determine B1 (168 nT) and B2 (151 nT).
17. Our x axis is along the wire with the origin at the right endpoint, and the current is in
the positive x direction. All segments of the wire produce magnetic fields at P2 that are
out of the page. According to the BiotSavart law, the magnitude of the field any
(infinitesimal) segment produces at P2 is given by
dB = μ 0i sin θ
4p r 2 dx 1132 CHAPTER 29 where θ (the angle between the segment and a line drawn from the segment to P2) and r
x 2 + R 2 and sin θ with (the length of that line) are functions of x. Replacing r with
R r=R x 2 + R 2 , we integrate from x = –L to x = 0. The total field is B= μ 0iR
4p ∫ dx 0 −L ( 4p ×10
= (x
7 2 +R ) 2 32 = μ 0iR 1
4p R 2 (x x
2 +R T ⋅ m A ) ( 0.693 A ) 4p ( 0.251 m ) 0 ) 2 1 2 −L = μ 0i L 4pR L2 + R 2 0.136m
(0.136m) + (0.251m)
2 2 = 1.32 × 10−7 T. 18. In the one case we have Bsmall + Bbig = 47.25 μT, and the other case gives Bsmall – Bbig
= 15.75 μT (cautionary note about our notation: Bsmall refers to the field at the center of
the smallradius arc, which is actually a bigger field than Bbig!). Dividing one of these
equations by the other and canceling out common factors (see Eq. 299) we obtain
(1/ rsmall ) + (1/ rbig )
(1/ rsmall ) − (1/ rbig ) = 1 + (rsmall / rbig )
1 − (rsmall / rbig ) =3 . The solution of this is straightforward: rsmall = rbig /2. Using the given fact that the
rbig = 4.00 cm, then we conclude that th...
View
Full
Document
This document was uploaded on 02/26/2014 for the course PHYS 2b at UCSD.
 Fall '08
 schuller
 Magnetism, Work

Click to edit the document details