This preview shows page 1. Sign up to view the full content.
Unformatted text preview: g glass, we see that all but i2 are directed into the page. Wire 3 is
therefore attracted to all but wire 2. Letting d = 0.500 m, we find the net force (per meter
length) using Eq. 2913, with positive indicated a rightward force:
F = μ0i3 ⎛ i1 i2 i4 i5 ⎞
+++
⎜−
⎟
2π ⎝ 2d d d 2d ⎠ which yields  F  / = 8.00 ×10−7 N/m .
40. Using Eq. 2913, the force on, say, wire 1 (the wire at the upper left of the figure) is
along the diagonal (pointing toward wire 3, which is at the lower right). Only the forces
(or their components) along the diagonal direction contribute. With θ = 45°, we find the
force per unit meter on wire 1 to be
⎛ μ 0i 2 ⎞
μ0i 2
3 ⎛ μ 0i 2 ⎞
=
F1 =  F12 + F13 + F14  = 2 F12 cos θ + F13 = 2 ⎜
⎟ cos 45° +
⎜
⎟
2 2πa 2 2π ⎝ a ⎠
⎝ 2πa ⎠
−7
3 ( 4π ×10 T ⋅ m A ) (15.0A )
=
= 1.12 ×10−3 N/m.
−2
2 2π
(8.50 ×10 m )
2 ˆ ˆ j)
The direction of F1 is along r = (i − ˆ / 2 . In unitvector notation, we have
(1.12 ×10 3 N/m) ˆ ˆ
ˆ
ˆ
F1 =
(i − j) = (7.94 ×10 4 N/m)i + (−7.94 ×10 4 N/m)j
2 41. The magnitudes of the forces on the sides of the rectangle that are parallel to the long
straight wire (with i1 = 30.0 A) are computed using Eq. 2913, but the force on each of
the sides lying perpendicular to it (along our y axis, with the origin at the top wire and +y
downward) would be figured by integrating as follows: 1142 CHAPTER 29
F⊥ sides = z a +b a i2 μ 0i1
dy.
2 πy Fortunately, these forces on the two perpendicular sides of length b cancel out. For the
remaining two (parallel) sides of length L, we obtain
F= μ0i1i2 L ⎛ 1
μ0i1i2b
1⎞
⎜−
⎟=
2π ⎝ a a + d ⎠ 2π a ( a + b ) ( 4π ×10
= −7 T ⋅ m/A ) ( 30.0A )( 20.0A )( 8.00cm ) ( 300 ×10−2 m )
2π (1.00cm + 8.00cm ) = 3.20 ×10−3 N, j
j
and F points toward the wire, or + ˆ . That is, F = (3.20 ×10−3 N)ˆ in unitvector notation.
1
42. The area enclosed by the loop L is A = 2 (4d )(3d ) = 6d 2 . Thus ∫ B ⋅ ds = μ0i = μ0...
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