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Unformatted text preview: song (shs546) Homework 12 weathers (22202) 1 This printout should have 10 questions. Multiplechoice questions may continue on the next column or page find all choices before answering. 001 10.0 points What is the radius of the smallest possible cir cular orbit that a proton with energy 4 . 6 MeV 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 . 103004 m. Explanation: Let : m = 1 . 67 10 27 kg , Q = 1 . 609 10 19 C , B = 3 T , and E = 4 . 6 MeV . The energy of a proton is E = 1 2 mv 2 v = radicalbigg 2 E m = radicalBigg 2(4 . 6 MeV) 1 . 67 10 27 kg 1 10 6 MeV / eV 1 MeV radicalbigg 1 . 609 10 19 J / eV 1 eV = 2 . 97724 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 = mv B q = (1 . 67 10 27 kg) (2 . 97724 10 7 m / s) (3 T) (1 . 609 10 19 C) = . 103004 m . 002 10.0 points A singly charged positive ion has a mass of 2 . 85 10 26 kg. After being accelerated through a potential difference of 341 V, the ion enters a magnetic field of 0 . 37 T, in a direction perpendicular to the field. Calculate the radius of the path of the ion in the field. Correct answer: 2 . 97685 cm. Explanation: Let : m = 2 . 85 10 26 kg , q = 1 . 60218 10 19 C , V = 341 V , and B = 0 . 37 T . We use conservation of energy to find the velocity of the ion upon entering the field, 1 2 mv 2 = q V , v = radicalbigg 2 q V m = radicalBigg 2 (1 . 60218 10 19 C) (341 V) 2 . 85 10 26 kg = 61919 . 2 m / s . Therefore, the radius is r = mv q B = (2 . 85 10 26 kg) (61919 . 2 m / s) (1 . 60218 10 19 C) (0 . 37 T) = 0 . 0297685 m = 2 . 97685 cm . 003 (part 1 of 2) 10.0 points A cyclotron designed to accelerate protons has a magnetic field of magnitude 0 . 74 T over a region of radius 3 . 3 m. The charge on a proton is 1 . 60218 10 19 C and its mass is 1 . 67262 10 27 kg. What is the cyclotron frequency? Correct answer: 7 . 08834 10 7 rad / s....
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 Spring '00
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