HW7solutions - Physics 2213 HW #7 Solutions Spring 2009 #1...

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Physics 2213 HW #7 – Solutions Spring 2009 F B 30 o 60 o B down up N S #1 [Magnetic Force on an Electron] (a) In order for vB Fe   to be up (out of page), v must have a North component. The East-West component won’t affect the force, so it could be anything. There are two possible directions for v : North of West or North of East. (See diagram at right.) 14 vBsin 4 10 N   14 19 5 4 10 N 56.4 (1.6 10 C)(5 10 m/s)(0.6T) sin F e   (b) The greatest magnetic force occurs when the electron is moving perpendicular to the magnetic field. Then F max =evB=(1.6x10 -19 C)(5x10 5 m/s)(0.6T)=4.8x10 -14 N If we want this force to be up, then the electron should be moving due North. (See diagram at right.) #2 [Magnetic Force on a Cable] (a) The force on the cable due to the Earth’s magnetic field is F IL B   . The direction will be due South and 30 o below the horizontal (see diagram on right). The magnitude of this force is F B =ILBsin90 o (90 o is the angle between B and L .) =(120A)(30m)(0.5x10 -4 T)(1)=0.18N (b) The weight of the cable is given by F g =mg= Vg=r( r 2 L)g=(8.9x10 3 kg/m 3 )( )(0.0025 2 m 2 )(30m)(9.8N/kg) =51.4N The magnetic force is much smaller than the cable’s weight, so it can be ignored when designing the cables. 27.19. [Fusion Reactor] In part (a), apply conservation of energy to the motion of the two nuclei. In part (b) apply 2 /. q vB mv R (a) Let point 1 be when the two nuclei are far apart and let point 2 be when they are at their closest separation. Apply conservation of energy to the motion of the two nuclei. 1 1 2 2 K U K U . 12 0, UK  so KU . Now U 2 =ke 2 /r , while 2 1 1 2 2 K mv (because there are two deuterium nuclei, each of mass m , moving at speed v ) so 22 mv ke r . 19 6 27 15 (1.602 10 C) 8.4 10 m s (3.34 10 kg)(1.0 10 m) kk ve mr  (3% of the speed of light!) (b) Recall that a charged particle moving perpendicular to a uniform magnetic field will travel in a circle with 2 q vB mv R Then 27 6 19 (3.34 10 kg)(8.4 10 m/s) 0.14 T (1.602 10 C)(1.25 m) mv B qr
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HW7solutions - Physics 2213 HW #7 Solutions Spring 2009 #1...

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