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chapter19-1 - Magnetism 195 is the same as the pole on the...

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PROBLEM SOLUTIONS 19.1 Consider a three-dimensional coordinate system with the xy plane in the plane of this page, the + x -direction toward the right edge of the page and the + y -direction toward the top of the page. Then, the z -axis is perpendicular to the page with the + z -direction being upward, out of the page. The magnetic fi eld is directed in the + x -direction, toward the right. (a) When a proton (positively charged) moves in the + y -direction, the right-hand rule number 1 gives the direction of the magnetic force as into the page or in the z -direction . (b) With r v in the y -direction , the right-hand rule number 1 gives the direction of the force on the proton as out of the page, in the + -direction z . (c) When the proton moves in the + x -direction, parallel to the magnetic field, the magnitude of the magnetic force it experiences is F q B = ( ) = v sin 0 0 ° , or there is a zero force in this case . 19.2 (a) For a positively charged particle, the direction of the force is that predicted by the right-hand rule number one. These are: (a ) in plane of page and to left (b ) into the page (c ) out of the page (d ) in plane of page and toward the top (e ) into the page (f ) out of the page (b) For a negatively charged particle, the direction of the force is exactly opposite what the right-hand rule number 1 predicts for positive charges. Thus, the answers for part (b) are reversed from those given in part (a) . 19.3 Since the particle is positively charged, use the right-hand rule number 1. In this case, start with the fingers of the right hand in the direction of r v and the thumb pointing in the direction of r F . As you start closing the hand, the fingers point in the direction of r B after they have moved 90°. The results are (a) into the page (b) toward the right (c) toward bottom of page 19.4 Hold the right hand with the fingers in the direction of r v so that as you close your hand, the fingers move toward the direction of r B . The thumb will point in the direction of the force (and hence the deflection) if the particle has a positive charge. The results are (a) toward top of page (b) out of the page , since the charge is negative. (c) θ = ° 180 zero force (d) into the page
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196 Chapter 19 19.5 (a) The proton experiences maximum force when it moves perpendicular to the magnetic field, and the magnitude of this maximum force is F q B max sin . . = = × ( ) × ( ) v 90 1 60 10 6 00 10 1 19 6 ° C m s . . 50 1 1 44 10 12 T N ( ) ( ) = × (b) a F m p max max . . = = × × = × 1 44 10 10 8 62 12 N 1.67 kg 27 10 14 m s 2 (c) Since the magnitude of the charge of an electron is the same as that of a proton, the force experienced by the electron would hav e the same magnitude , but would be in the opposite direction due to the negative charge of the electron. The acceleration of the elec- tron would be much greater than that of the proton because of the mass of the electron is much smaller.
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