solutions 12 - Patel Kinal Homework 12 Due Mar 4 2008 7:00...

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Unformatted text preview: Patel, Kinal Homework 12 Due: Mar 4 2008, 7:00 pm Inst: Weathers 1 This print-out should have 10 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. The due time is Central time. 001 (part 1 of 1) 10 points What is the radius of the smallest possible circular orbit that a 2 . 9 MeV proton can have in a 3 T magnetic field? The mass of a proton is 1 . 67 10- 27 kg and its charge is 1 . 609 10- 19 C. Correct answer: 0 . 0817849 m. Explanation: Let : m = 1 . 67 10- 27 kg , Q = 1 . 609 10- 19 C , B = 3 T , and E = 2 . 9 MeV . The energy of a proton is E = 1 2 m v 2 , so v = r 2 E m = s 2 (2 . 9 MeV) (1 . 609 10- 19 J / eV) (1 10- 6 MeV / eV) (1 . 67 10- 27 kg) = 2 . 36393 10 7 m / s . If the proton is shot into the magnetic field with a velocity at right angles to the direction of the field, we will get the smallest radius r = m v B q = (1 . 67 10- 27 kg) (2 . 36393 10 7 m / s) (3 T) (1 . 609 10- 19 C) = . 0817849 m . keywords: 002 (part 1 of 1) 10 points A singly-charged positive ion has a mass of 6 . 5 10- 26 kg. After being accelerated through a potential difference of 374 V, the ion enters a magnetic field of 1 . 31 T along a direction perpendicular to the direction of the electric field. The charge on an electron is 1 . 60218 10- 19 C. Calculate the radius of the path of the ion in the magnetic field. Correct answer: 0 . 0132978 m. Explanation: Let : m = 6 . 5 10- 26 kg , B = 1 . 31 T , V = 42938 . 8 m / s , and q = 1 . 60218 10- 19 C . Energy conservation: 1 2 m v 2 = q U so the speed of the ion is: v = r 2 q U m = s 2 (1 . 60218 10- 19 C) (374 V) 6 . 5 10- 26 kg = 42938 . 8 m / s The magnetic force provides the centripetal force: q v B = m v 2 r r = m v q B = (6 . 5 10- 26 kg) (42938 . 8 m / s) (1 . 60218 10- 19 C) (1 . 31 T) = . 0132978 m . keywords: 003 (part 1 of 2) 10 points A cyclotron with a magnetic field of 0 . 39 T is designed to accelerate protons in a circle with a radius 1 . 5 m. Patel, Kinal Homework 12 Due: Mar 4 2008, 7:00 pm Inst: Weathers 2 What is the angular frequency of the pro- ton?...
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solutions 12 - Patel Kinal Homework 12 Due Mar 4 2008 7:00...

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