hw6.12 - Solutions a.) To find v we can use the following...

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HW 6.12 Given: F i n d : kg C m q / 10 4 . 1 / 5 ? v T B 7 . 0 ? a ? m r 1 . 2 c f s m v z / 8 0 ? T s t 6 ? z A charged particle moves with speed v about a circle of radius r in the x - y plane. The charge-to- mass ratio of the particle is 1.4 × 10 5 C/kg. A uniform magnetic field B = 0.7 T points in the - z direction (into the page). (a) If the radius of the circular orbit is r = 2.1 m, what is the speed of the particle? (b) What is the magnitude of the acceleration of the particle? (c) Calculate the cyclotron frequency f c of this particle in this magnetic field. (d) Calculate the period T for one revolution. (e) Suppose that the particle also has an initial velocity component in the z -direction equal to v 0z = 8 m/s. (The resulting 3-D motion of the particle is called "helical".) How far in the z -direction does the particle move in a time interval t = 6 s?
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Unformatted text preview: Solutions a.) To find v we can use the following formula: qB mv R m RqB v m rqB v b.) To find a we can use the following formula: 2 2 2 m qB r r m rqB r v a 2 m qB r a c.) To find we can use the following formula: c f 2 2 4 rf a 2 2 2 4 rf m qB r m qB m qB f 2 4 2 2 m qB f 2 d.) To find T we can use the following formula: T f 1 1 2 2 1 1 m qB m qB f T 1 2 m qB T e.) To find we can use the following formula: z since q t v z z B v...
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hw6.12 - Solutions a.) To find v we can use the following...

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