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Chapter 28 HW Solutions

# Chapter 28 HW Solutions - PHYS 241 28.3 Ch 28 Homework...

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PHYS 241 Ch. 28 Homework Solutions 28.3. I DENTIFY : A moving charge creates a magnetic field. S ET U P : The magnetic field due to a moving charge is 0 2 sin 4 qv B r μ φ π = . E XECUTE : Substituting numbers into the above equation gives (a) 7 19 7 0 2 6 2 sin 4 10 T m/A (1.6 10 C)(3.0 10 m/s)sin30 . 4 4 (2.00 10 m) qv B r μ φ π π π - - - × × × ° = = × B = 6.00 × 10 –8 T, out of the paper, and it is the same at point B . (b) B = (1.00 × 10 –7 T m/A)(1.60 × 10 –19 C)(3.00 × 10 7 m/s)/(2.00 × 10 –6 m) 2 B = 1.20 × 10 –7 T, out of the page. (c) B = 0 T since sin(180°) = 0. E VALUATE : Even at high speeds, these charges produce magnetic fields much less than the Earth’s magnetic field. 28.9.I DENTIFY : A current segment creates a magnetic field. S ET U P : The law of Biot and Savart gives 0 2 sin 4 Idl dB r μ φ π = . E XECUTE : Applying the law of Biot and Savart gives (a) 7 2 10 T m/A (10.0 A)(0.00110 m) sin90° (0.0500 m) dB - × = = 4.40 × 10 –7 T, out of the paper. (b) The same as above, except 2 2 (5.00 cm) (14.0 cm) r = + and φ = arctan(5/14) = 19.65°, giving dB = 1.67 × 10 –8 T, out of the page. (c) dB = 0 since φ = 0°. E VALUATE : This is a very small field, but it comes from a very small segment of current. 28.13. I DENTIFY : A current segment creates a magnetic field. S ET U P : The law of Biot and Savart gives 0 2 sin . 4 Idl dB r μ φ π = Both fields are into the page, so their magnitudes add. E XECUTE : Applying the Biot and Savart law, where 2 2 1 2 (3.00 cm) (3.00 cm) r = + = 2.121 cm, we have 7 2 10 T m/A (28.0 A)(0.00200 m)sin 45.0° 2 (0.02121 m) dB - × = = 1.76 × 10 –5 T, into the paper. E VALUATE : Even though the two wire segments are at right angles, the magnetic fields they create are in the same direction. 28.15. I DENTIFY : We can model the lightning bolt and the household current as very long current-carrying wires. S ET U P : The magnetic field produced by a long wire is 0 2 I B r μ π = . E XECUTE : Substituting the numerical values gives (a) B = 7 (4π 10 T m/A)(20,000 A) 2π(5.0 m) - × = 8 × 10 –4 T (b) 7 (4π 10 T m/A)(10 A) 2π(0.050 m) B - × = = 4.0 × 10 –5 T. E VALUATE : The field from the lightning bolt is about 20 times as strong as the field from the household current. 28.21. I DENTIFY : 0 2 I B r μ π = . The direction of B r is given by the right-hand rule in Section 20.7. 1

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S ET U P : Call the wires a and b , as indicated in Figure 28.21. The magnetic fields of each wire at points P 1 and P 2 are shown in Figure 28.21a. The fields at point 3 are shown in Figure 28.21b.
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Chapter 28 HW Solutions - PHYS 241 28.3 Ch 28 Homework...

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