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# ch21 - CHAPTER 21 MAGNETIC FORCES AND MAGNETIC FIELDS...

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CHAPTER 21 MAGNETIC FORCES AND MAGNETIC FIELDS ANSWERS TO FOCUS ON CONCEPTS QUESTIONS ____________________________________________________________________________________________ 1. (d) Right-Hand Rule No. 1 gives the direction of the magnetic force as - x for both drawings A and B. In drawing C, the velocity is parallel to the magnetic field, so the magnetic force is zero. 2. (b) Using Right-Hand Rule No. 1 (see Section 21.2), we find that the direction of the magnetic force on a positively charged particle is to the west. Reversing this direction because the particle is a negative electron, we see that the magnetic force acting on it points to the east. 3. (a) Using Right-Hand Rule No. 1 (see Section 21.2), we find that the direction of the magnetic force on a positively charged particle is straight down toward the bottom of the screen. 4. B = 1.1 × 10 - 1 T, south 5. (c) The electric force points out of the screen, in the direction of the electric field. An application of Right-Hand Rule No. 1 shows that the magnetic force also points out of the screen, parallel to the electric force. When two forces have the same direction, the magnitude of their sum has the largest possible value. 6. (e) In this situation, the centripetal force, F c = mv 2 / r (Equation 5.3), is provided by the magnetic force, F = qvB sin 90.0 ° (Equation 21.1), so mv 2 / r = qvB sin 90.0 ° . Thus, ( 29 / q mv rB = , and the charge magnitude q is inversely proportional to the radius r . Since the radius of curve 1 is smaller than that of curve 2, and the radius of curve 2 is smaller than that of curve 3, we conclude that q 1 is larger than q 2 , which is larger than q 3 . 7. (a) The magnetic force that acts on the electron in regions 1 and 2 is always perpendicular to its path, so the force does no work. According to the work-energy theorem, Equation 6.3, the kinetic energy, and hence speed, of the electron does not change when no work is done. 8. (d) According to Equation 21.2, the radius r of the circular path is given by ( 29 / r mv qB = . Since v , q , and B are the same for the proton and the electron, the more-massive proton travels on the circle with the greater radius. The centripetal force F c acting on the proton must point toward the center of the circle. In this case, the centripetal force is provided by

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111 MAGNETIC FORCES AND MAGNETIC FIELDS the magnetic force F . According to Right-Hand Rule No. 1, the direction of F is related to the velocity v and the magnetic field B . An application of this rule shows that the proton must travel counterclockwise around the circle in order that the magnetic force point toward the center of the circle. 9. r proton / r electron = 1835 10. (c) When, for example, a particle moves perpendicular to a magnetic field, the field exerts a force that causes the particle to move on a circular path. Any object moving on a circular path experiences a centripetal acceleration. 11. F = 3.0 N, along the - y axis 12. (e) The magnetic field is directed from the north pole to the south pole (Section 21.1).
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