**Problem Statement:**A proton moves with a velocity of \(\vec{v} = (5\hat{i} - 4\hat{j} + \hat{k}) \, \text{m/s}\) in a region in which the magnetic field is \(\vec{B} = (\hat{i} + 2\hat{j} - \hat{k}) \, \text{T}\). What is the magnitude of the magnetic force this particle experiences?**Solution Explanation:**The magnetic force \(\vec{F}\) experienced by a charged particle moving in a magnetic field is given by the equation:\[\vec{F} = q (\vec{v} \times \vec{B})\]where \(q\) is the charge of the proton, \(\vec{v}\) is the velocity vector, and \(\vec{B}\) is the magnetic field vector.**Cross Product Calculation:**To find \(\vec{v} \times \vec{B}\), use the determinant method:\[\vec{v} \times \vec{B} = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \\5 & -4 & 1 \\1 & 2 & -1 \\\end{vmatrix}\]Calculate each component of the cross product:- \(\hat{i}\) component: \((-4)(-1) - (1)(2) = 4 - 2 = 2\)- \(\hat{j}\) component: \(-( (5)(-1) - (1)(1) ) = -(-5 - 1) = 6\)- \(\hat{k}\) component: \((5)(2) - (-4)(1) = 10 + 4 = 14\)Thus, \(\vec{v} \times \vec{B} = (2\hat{i} + 6\hat{j} + 14\hat{k})\).**Magnitude of the Magnetic Force:**The magnitude \(|\vec{F}|\) is given by:\[|\vec{F}| = q |\vec{v} \times \vec{B}|\]The charge of a proton \(q = 1.6 \times 10^{-19}

Given: The velocity vector is 5i⏜-4j⏜+k⏜ m/s. The magnetic field vector is i⏜+2j⏜-k⏜ T.…

A proton moves with a velocity of v = (Sî – 4j + k) m/s in a region in which the magnetic field is B = (î + 2j – k) T. What is the magnitude of the magnetic force this particle experiences? %3D %3D

A proton moves with a velocity of v = (Sî – 4j + k) m/s in a region in which the magnetic field is B = (î + 2j – k) T. What is the magnitude of the magnetic force this particle experiences? %3D %3D

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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