# solutions_chapter20 - 20 MAGNETIC FIELD AND MAGNETIC FORCES...

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20-1 M AGNETIC F IELD AND M AGNETIC F ORCES 20 Answers to Multiple-Choice Problems 1. E 2. C 3. C 4. B 5. D 6. A 7. C 8. C 9. B 10. A 11. C 12. B 13. A 14. B 15. A Solutions to Problems 20.1. Set Up: The force on the particle is in the direction of the deflection of the particle. The directions of and are shown in Figure 20.1. Apply the right-hand rule to the directions of and See if your thumb is in the direction of or opposite to that direction. Use with to calculate F . Figure 20.1 Solve: (a) When you apply the right-hand rule to and your thumb points east. is in this direction, so the charge is positive. (b) 20.2. Set Up: The force on the ion is downward, in the direction of the deflection. The directions of and are shown in Figure 20.2a. Use the right-hand rule to relate the directions of and The charge is positive. Use with to calculate B. Figure 20.2 ( a ) ( b ) v S v S F S F S B S e 5 1.60 3 10 2 19 C. f 5 90° F 5 0 q 0 v B sin f F S . B S , v S , F S v S F S F 5 0 q 0 v B sin f 5 1 8.50 3 10 2 6 C 21 4.75 3 10 3 m / s 21 1.25 T 2 sin 90° 5 0.0505 N F S B S , v S E N S W v S F S B S f 5 90° F 5 0 q 0 v B sin f F S , B S . v S F S B S v S , F S
Solve: is perpendicular to both and so is either toward the top of the page or toward the bottom of the page. If is toward the top of the page, as shown in Figure 20.2b, then when you apply the right-hand rule your thumb points into the page. This is the specified direction of so is directed as shown in Figure 20.2b. gives 20.3. Set Up: The directions of and are shown in Figure 20.3. A proton has charge In part (a), An electron has charge Figure 20.3 Solve: (a) The right-hand rule says is into the page in Figure 20.3. (b) F is maximum when when is perpendicular to F is minimum when or when is either parallel or antiparallel to (c) is the same for an electron and a proton, so the same as for a proton. Since the proton and electron have charges of opposite sign, the forces on them are in opposite directions. The force on the electron is directed out of the page in Figure 20.3. Reflect: Only the component of perpendicular to contributes to the magnetic force. Therefore, this force is zero when the charged particle moves along the direction of and the force is maximum when the particle moves in a direction perpendicular to When the sign of the charge changes, the force reverses direction. And, even though the force magnitude is the same for the electron and proton, the effect of the force (the acceleration) for the electron would be much greater, because of its smaller mass. 20.4. Set Up: The gravity force is downward so the force from the magnetic field must be upward. The charge’s velocity and the forces are shown in Figure 20.4. Since the charge is negative, the magnetic force is opposite to the right-hand rule direction. The minimum magnetic field is when the field is perpendicular to The force is also perpendicular to so is either eastward or westward.
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