YF_ISM_27

YF_ISM_27 - MAGNETIC FIELD AND MAGNETIC FORCES 27 27.1....

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27-1 M AGNETIC F IELD AND M AGNETIC F ORCES 27.1. IDENTIFY and SET UP: Apply Eq.(27.2) to calculate . F G Use the cross products of unit vectors from Section 1.10. EXECUTE: () 44 ˆˆ 4.19 10 m/s 3.85 10 m/s =+ × +− × vij G (a) ˆ 1.40 T = Bi G 84 4 1.24 10 C 1.40 T q ⎡⎤ =×= − × × × × × ⎣⎦ F vB ii ji GG G ˆˆ ˆ 0, ×= ×=− ji k 4 6.68 10 N =− × × − =− × F kk G EVALUATE: The directions of and G G are shown in Figure 27.1a. The right-hand rule gives that × G G is directed out of the paper (+ z -direction). The charge is negative so F G is opposite to ; × G G Figure 27.1a F G is in the - z direction. This agrees with the direction calculated with unit vectors. (b) EXECUTE: ˆ 1.40 T = Bk G ( ) 4 q + × ×− × × F ik jk G ˆˆˆ , − ×= jjk i 4 4 ˆ 7.27 10 N −− × − + × = × + × F ij G EVALUATE: The directions of and G G are shown in Figure 27.1b. The direction of F G is opposite to × G G since q is negative. The direction of F G computed from the right-hand rule agrees qualitatively with the direction calculated with unit vectors. Figure 27.1b 27.2. IDENTIFY: The net force must be zero, so the magnetic and gravity forces must be equal in magnitude and opposite in direction. 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 27.2. 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 v G . The force is also perpendicular to B G , so B G is either eastward or westward. EXECUTE: If B G is eastward, the right-hand rule direction is into the page and B F G is out of the page, as required. Therefore, B G is eastward. sin mg q vB φ = . 90 = ° and 32 48 (0.195 10 kg)(9.80 m/s ) 1.91 T (4.00 10 m/s)(2.50 10 C) mg B vq × == = ×× . 27
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27-2 Chapter 27 EVALUATE: The magnetic field could also have a component along the north-south direction, that would not contribute to the force, but then the field wouldn’t have minimum magnitude. Figure 27.2 27.3. IDENTIFY: The force F G on the particle is in the direction of the deflection of the particle. Apply the right-hand rule to the directions of v G and B G . See if your thumb is in the direction of F G , or opposite to that direction. Use sin Fq v B φ = with 90 = ° to calculate F . SET UP: The directions of v G , B G and F G are shown in Figure 27.3. EXECUTE: (a) When you apply the right-hand rule to v G and B G , your thumb points east. F G is in this direction, so the charge is positive. (b) 63 sin (8.50 10 C)(4.75 10 m/s)(1.25 T)sin90 0.0505 N v B == × × = ° EVALUATE: If the particle had negative charge and v G and B G are unchanged, the particle would be deflected toward the west. Figure 27.3 27.4. IDENTIFY: Apply Newton’s second law, with the force being the magnetic force.
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This note was uploaded on 03/14/2012 for the course MAE 162D taught by Professor Shaefer during the Spring '11 term at UCLA.

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YF_ISM_27 - MAGNETIC FIELD AND MAGNETIC FORCES 27 27.1....

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