SM_chapter29 - 29 Magnetic Fields CHAPTER OUTLINE 29.1 29.2...

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29 Magnetic Fields CHAPTER OUTLINE 29.1 Magnetic Fields and Forces 29.2 Motion of a Charged Particle in a Uniform Magnetic Field 29.3 Applications Involving Charged Particles Moving in a Magnetic Field 29.4 Magnetic Force Acting on a Current-Carrying Conductor 29.5 Torque on a Current Loop in a Uniform Magnetic Field 29.6 The Hall Effect ANSWERS TO QUESTIONS *Q29.1 (a) Yes, as described by F E = q . (b) No, as described by F v B = × q (c) Yes. (d) Yes. (e) No. The wire is uncharged. (f) Yes. (g) Yes. (h) Yes. *Q29.2 (i) (b). (ii) (a). Electron A has a smaller radius of curvature, as described by q v B = m v 2 / r. *Q29.3 (i) (c) (ii) (c) (iii) (c) (iv) (b) (v) (d) (vi) (b) (vii) (b) (viii) (b) *Q29.4 We consider the quantity | q v B sin q |, in units of e (m/s)(T). For (a) it is 1 × 10 6 10 3 1 = 10 3 . For (b) it is 1 × 10 6 10 3 0 = 0. For (c) 2 × 10 6 10 3 1 = 2 000. For (d) 1 × 10 6 2 × 10 3 1 = 2 000. For (e) 1 × 10 6 10 3 1 = 10 3 . For (f) 1 × 10 6 10 3 0.707 = 707. The ranking is then c = d > a = e > f > b. *Q29.5 ˆ ( ˆ ) ˆ i k j × − = . Answer (c). *Q29.6 Answer (c). It is not necessarily zero. If the magnetic field is parallel or antiparallel to the velocity of the charged particle, then the particle will experience no magnetic force. Q29.7 If they are projected in the same direction into the same magnetic field, the charges are of opposite sign. Q29.8 Send the particle through the uniform field and look at its path. If the path of the particle is parabolic, then the field must be electric, as the electric field exerts a constant force on a charged particle, independent of its velocity. If you shoot a proton through an electric field, it will feel a constant force in the same direction as the electric field—it’s similar to throwing a ball through a gravitational field. If the path of the particle is helical or circular, then the field is magnetic. If the path of the particle is straight, then observe the speed of the particle. If the particle accelerates, then the field is electric, as a constant force on a proton with or against its motion will make its speed change. If the speed remains constant, then the field is magnetic. *Q29.9 Answer (d). The electrons will feel a constant electric force and a magnetic force that will change in direction and in magnitude as their speed changes. Q29.10 Yes. If the magnetic field is perpendicular to the plane of the loop, then it exerts no torque on the loop. 151
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152 Chapter 29 Q29.11 If you can hook a spring balance to the particle and measure the force on it in a known electric field, then q F E = will tell you its charge. You cannot hook a spring balance to an electron. Measuring the acceleration of small particles by observing their deflection in known electric and magnetic fields can tell you the charge-to-mass ratio, but not separately the charge or mass. Both an acceleration produced by an electric field and an acceleration caused by a magnetic field depend on the properties of the particle only by being proportional to the ratio q m .
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