This preview shows page 1. Sign up to view the full content.
Unformatted text preview: thand rule) the
only region in which their fields might cancel is between them. Thus, if the point at
which we are evaluating their field is r away from the wire carrying current i and is d – r
away from the wire carrying current 3.00i, then the canceling of their fields leads to μ 0i
μ (3i )
=0
⇒
2π r 2π (d − r ) r= d 16.0 cm
=
= 4.0 cm.
4
4 (b) Doubling the currents does not change the location where the magnetic field is zero.
13. Our x axis is along the wire with the origin at the midpoint. The current flows in the
positive x direction. All segments of the wire produce magnetic fields at P1 that are out of
the page. According to the BiotSavart law, the magnitude of the field any (infinitesimal)
segment produces at P1 is given by
dB = μ 0i sin θ
4p r 2 dx where θ (the angle between the segment and a line drawn from the segment to P1) and r
(the length of that line) are functions of x. Replacing r with
R r=R x 2 + R 2 and sin θ with x 2 + R 2 , we integrate from x = –L/2 to x = L/2. The total field is B= μ 0iR
4p ∫ dx L2 −L 2 ( 4p × 10
= 7 (x = μ 0iR 1 4p R ( x
)
T ⋅ m A ) ( 0.0582 A )
2 +R 2 32 2 2p ( 0.131 m ) x
2 L2 +R ) 2 1 2 −L 2 = μ 0i L 2pR L2 + 4 R 2 0.180m (0.180m) + 4(0.131m)
2 2 = 5.03 × 10−8 T. 14. We consider Eq. 296 but with a finite upper limit (L/2 instead of ∞). This leads to
B= μ0i L/2 2πR ( L / 2) 2 + R 2 . In terms of this expression, the problem asks us to see how large L must be (compared
with R) such that the infinite wire expression B∞ (Eq. 294) can be used with no more
than a 1% error. Thus we must solve
B∞ – B
B = 0.01. 1131 This is a nontrivial algebra exercise, but is nonetheless straightforward. The result is
L= 200 R
L
≈ 14.1R ⇒
≈ 14.1 .
R
201 15. (a) As discussed in Sample Problem — “Magnetic field at the center of a circular arc
of current,” the radial segments do not contribute to BP and the arc segments contribute
according to Eq. 299 (with angle in radians). If k designates the direction “out of the
page” then
μ ( 0.40 A )(π rad ) ˆ μ0 ( 0.80 A ) ( 2π /...
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