Tutorial Exercise A cosmic-ray proton in interstellar space has an energy of 16.8 MeV and executes a circular orbit having a radius equal to that of Mercury's orbit around the Sun (5.80 × 1010 m). What is the magnetic field in that region of space? Part 1 of 3 - Conceptualize A very large orbit radius indicates that the magnetic field in this interstellar space is a very small fraction of a tesla. Part 2 of 3 - Categorize When the proton, with a charge of the same magnitude as the electron charge, accelerates through a potential difference given in volts, the kinetic energy it receives is commonly expressed in electron volts. We will use the energy version of the isolated system model applied to the particle and the electric field that accelerates it from rest to allow us to find an expression for the speed of the particle. Then we will use the particle in a magnetic field model and the particle in uniform circular motion model to find the magnetic field. Part 3 of 3 - Analyze By conservation of energy for the system of proton and electric field, the kinetic energy of the proton is given by E=1m² = eAV, so solving for the speed, we have the following. v = 2eAV m By Newton's second law, for the circular motion of the proton in the magnetic field, we have mv2 R = evB sin 0, where R is the radius of the circular orbit and is 90°. Substituting the expression for v that we found above from the kinetic energy and solving for B, we have the following. B = mv eR eR m 2eAV 12mAV m R 2(1.67 x 10-27 kg) 107 V) 5.80 x 1010 m (1.6 x 10-19 c) x Your response differs significantly from the correct answer. Rework your solution from the beginning and
Tutorial Exercise A cosmic-ray proton in interstellar space has an energy of 16.8 MeV and executes a circular orbit having a radius equal to that of Mercury's orbit around the Sun (5.80 × 1010 m). What is the magnetic field in that region of space? Part 1 of 3 - Conceptualize A very large orbit radius indicates that the magnetic field in this interstellar space is a very small fraction of a tesla. Part 2 of 3 - Categorize When the proton, with a charge of the same magnitude as the electron charge, accelerates through a potential difference given in volts, the kinetic energy it receives is commonly expressed in electron volts. We will use the energy version of the isolated system model applied to the particle and the electric field that accelerates it from rest to allow us to find an expression for the speed of the particle. Then we will use the particle in a magnetic field model and the particle in uniform circular motion model to find the magnetic field. Part 3 of 3 - Analyze By conservation of energy for the system of proton and electric field, the kinetic energy of the proton is given by E=1m² = eAV, so solving for the speed, we have the following. v = 2eAV m By Newton's second law, for the circular motion of the proton in the magnetic field, we have mv2 R = evB sin 0, where R is the radius of the circular orbit and is 90°. Substituting the expression for v that we found above from the kinetic energy and solving for B, we have the following. B = mv eR eR m 2eAV 12mAV m R 2(1.67 x 10-27 kg) 107 V) 5.80 x 1010 m (1.6 x 10-19 c) x Your response differs significantly from the correct answer. Rework your solution from the beginning and
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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