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Unformatted text preview: 1127 Chapter 29 1. (a) The magnitude of the magnetic field due to the current in the wire, at a point a distance r from the wire, is given by B i 2 r . With r = 20 ft = 6.10 m, we have B 4 10 7 T m A 100A 2 6.10m 3.3 10 6 T 3.3 T. (b) This is about onesixth the magnitude of the Earths field. It will affect the compass reading. 2. Equation 291 is maximized (with respect to angle) by setting = 90 ( = /2 rad). Its value in this case is max 2 4 i ds dB R . From Fig. 2934(b), we have 12 max 60 10 T. B We can relate this B max to our dB max by setting ds equal to 1 10 6 m and R = 0.025 m. This allows us to solve for the current: i = 0.375 A. Plugging this into Eq. 294 (for the infinite wire) gives B = 3.0 T. 3. (a) The field due to the wire, at a point 8.0 cm from the wire, must be 39 T and must be directed due south. Since B i r 2 , i 2 rB 2 0.080m 39?106 T 4p?107 T m A 16A. (b) The current must be from west to east to produce a field that is directed southward at points below it. 4. The straight segment of the wire produces no magnetic field at C (see the straight sections discussion in Sample Problem Magnetic field at the center of a circular arc of current). Also, the fields from the two semicircular loops cancel at C (by symmetry). Therefore, B C = 0. CHAPTER 29 1128 5. (a) We find the field by superposing the results of two semiinfinite wires (Eq. 297) and a semicircular arc (Eq. 299 with = rad). The direction of B is out of the page, as can be checked by referring to Fig. 296(c). The magnitude of B at point a is therefore 7 3 1 1 (4 10 T m/A)(10 A) 1 1 2 1.0 10 T 4 2 2 2(0.0050 m) 2 a i i i B R R R upon substituting i = 10 A and R = 0.0050 m. (b) The direction of this field is out of the page, as Fig. 296(c) makes clear. (c) The last remark in the problem statement implies that treating b as a point midway between two infinite wires is a good approximation. Thus, using Eq. 294, 7 4 (4 10 T m/A)(10 A) 2 8.0 10 T. 2 (0.0050 m) b i i B R R (d) This field, too, points out of the page. 6. With the usual x and y coordinates used in Fig. 2937, then the vector r pointing from a current element to P is ? i j. r s R Since i ds ds , then   . ds r Rds Therefore, with 2 2 r s R , Eq. 293 gives 2 2 3/ 2 4 ( ) iR ds dB s R ....
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