**Problem:**A proton having a speed of \(3.0 \times 10^6 \, \text{m/s}\) in a direction perpendicular to a uniform magnetic field moves in a circle of radius \(0.20 \, \text{m}\) within the field. What is the magnitude of the magnetic field?(The charge and mass of a proton are \(q = 1.60 \times 10^{-19} \, \text{C}\) and \(m = 1.67 \times 10^{-27} \, \text{kg}\).)**Options:**a) \(0.080 \, \text{T}\) b) \(0.16 \, \text{T}\) c) \(0.24 \, \text{T}\) d) \(0.32 \, \text{T}\) e) \(0.36 \, \text{T}\) **Explanation:**To solve this problem, we use the formula for the radius of the circular path of a charged particle in a magnetic field:\[r = \frac{mv}{qB}\]Where:- \(r\) is the radius of the circle,- \(m\) is the mass of the proton,- \(v\) is the speed of the proton,- \(q\) is the charge of the proton,- \(B\) is the magnetic field.Rearranging the formula to solve for \(B\):\[B = \frac{mv}{qr}\]Substitute the known values:\[B = \frac{(1.67 \times 10^{-27} \, \text{kg})(3.0 \times 10^6 \, \text{m/s})}{(1.60 \times 10^{-19} \, \text{C})(0.20 \, \text{m})}\]Calculate \(B\) to find the magnitude of the magnetic field.

Answered: Image /qna-images/answer/12d5c83a-67f0-47dd-89bf-8dd97ec1d61f.jpg

4. A proton having a speed of 3.0 x 106 m/s in a direction perpendicular to a uniform magnetic field moves in a circle of radius 0.20 m within the field. What is the magnitude of the magnetic field? (The charge and mass of a proton are q = 1.60 x 10-19 C and m = 1.67 x 10-27 kg). a) 0.080 T b) 0.16 T c) 0.24 T d) 0.32 T e) 0.36 T

4. A proton having a speed of 3.0 x 106 m/s in a direction perpendicular to a uniform magnetic field moves in a circle of radius 0.20 m within the field. What is the magnitude of the magnetic field? (The charge and mass of a proton are q = 1.60 x 10-19 C and m = 1.67 x 10-27 kg). a) 0.080 T b) 0.16 T c) 0.24 T d) 0.32 T e) 0.36 T

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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