HW 12 solution

HW 12 solution - song (shs546) Homework 12 weathers (22202)...

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Unformatted text preview: song (shs546) Homework 12 weathers (22202) 1 This print-out should have 10 questions. Multiple-choice 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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HW 12 solution - song (shs546) Homework 12 weathers (22202)...

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