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# Week 4 short assignments 1220

Mizzou

GPA 3.0

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## Popular in Physics 2

This 9 page Bundle was uploaded by Dragon Note on Thursday March 24, 2016. The Bundle belongs to 1220 at University of Missouri - Columbia taught by Y Zhang in Spring 2016. Since its upload, it has received 13 views. For similar materials see College Physics II in Physics 2 at University of Missouri - Columbia.

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Date Created: 03/24/16

Short Assignment By 2/17/2016 https://session.masteringphysics.com/myct/assignmentPrintView?displ... Short Assignment By 2/17/2016 Due: 11:00am on Wednesday, February 17, 2016 To understand how points are awarded, read therading Policy for this assignment. Magnetic Force on Charged Particles Conceptual Question For each of the situations below, a charged particle enters a region of uniform magnetic field. Determine the direction of the force on each charge due to the magnetic field. Part A Determine the direction of the force on the charge due to the magnetic field. Hint 1. Determining the direction of a magnetic force A charged particle moving through a region of magnetic field experiences a magnetic force, unless the velocity and magnetic field are parallel. If the velocity is parallel to the magnetic field, then the force is zero. Otherwise, the direction of the force can be found by using the right-hand rule. To employ the right hand rule: 1. Open your hand so that it is completely flat, and point the fingers of your right hand in the direction of the velocity vector. 2. Rotate your wrist until you can bend your fingers to point in the direction of the magnetic field. 3. The direction of your outstretched thumb is the direction of the magnetic force on a positive charge. ANSWER: points into the page. points out of the page. points neither into nor out of the page and . . Correct Short Assignment By 2/17/2016 https://session.masteringphysics.com/myct/assignmentPrintView?displ... Part B Determine the direction of the force on the charge due to the magnetic field. Hint 1. Determining the direction of a magnetic force A charged particle moving through a region of magnetic field experiences a magnetic force, unless the velocity and magnetic field are parallel. If the velocity is parallel to the magnetic field, then the force is zero. Otherwise, the direction of the force can be found by using the right-hand rule. To employ the right hand rule: 1. Open your hand so that it is completely flat, and point the fingers of your right hand in the direction of the velocity vector. 2. Rotate your wrist until you can bend your fingers to point in the direction of the magnetic field. 3. The direction of your outstretched thumb is the direction of the magnetic force on a positive charge. ANSWER: points out of the page. points into the page. points neither into nor out of the page and . . Correct Part C Determine the direction of the force on the charge due to the magnetic field. Note that the charge is negative. Short Assignment By 2/17/2016 https://session.masteringphysics.com/myct/assignmentPrintView?displ... Hint 1. Effect of a magnetic field on a negative charge You can use the right-hand rule to determine the direction of the force exerted on a positive charge. Once you find the direction of the force that would be exerted on a positive charge, the force on a negative charge will point in the opposite direction. ANSWER: points out of the page. points into the page. points neither into nor out of the page and . . Correct Problem 22.11 A 0.40 particle moves with a speed of 16 through a region where the magnetic field has a strength of 0.95 . Part A At what angle to the field is the particle moving if the force exerted on it is ? Express your answer using two significant figures. ANSWER: = 52 Correct Part B At what angle to the field is the particle moving if the force exerted on it is ? Express your answer using two significant figures. Short Assignment By 2/17/2016 https://session.masteringphysics.com/myct/assignmentPrintView?displ... ANSWER: = 30 Correct Part C At what angle to the field is the particle moving if the force exerted on it ?s Express your answer using two significant figures. ANSWER: = 0.94 Correct Score Summary: Your score on this assignment is 100%. You received 1.75 out of a possible total of 1.75 points. Short Assignment By 2/19/2016 https://session.masteringphysics.com/myct/assignmentPrintView?displ... Short Assignment By 2/19/2016 Due: 11:00am on Friday, February 19, 2016 To understand how points are awarded, read therading Policy for this assignment. Charge Moving in a Cyclotron Orbit Learning Goal: To understand why charged particles move in circles perpendicular to a magnetic field and why the frequency is an invariant. A particle of charge \texttip{q}{q} and mass \texttip{m}{m} moves in a region of space where there is a uniform magnetic field \vec{B}=B_0\hat{z} (i.e., a magnetic field of magnitude \texttip{B_{\rm 0}}{B_0} in the +z direction). In this problem, neglect any forces on the particle other than the magnetic force. Part A At a given moment the particle is moving in the +x direction (and the magnetic field is always in the +z direction). If \texttip{q}{q} is positive, what is the direction of the force on the particle due to the magnetic field? Hint 1. The right-hand rule for magnetic force A charged particle moving through a region of magnetic field experiences a magnetic force. This force is directed perpendicular to both the velocity vector and the magnetic field vector at the point of interaction. The requirement that the force be perpendicular to both of the other vectors specifies the direction of the force to within an algebraic sign. This algebraic sign is determined by the right-hand rule. To employ the right-hand rule: 1. Straighten your fingers so that they point in the direction of the velocity. 2. Bend your fingers and orient your hand, so that your fingers curl in the direction of the magnetic field. 3. Your thumb should be maintained perpendicular to your fingers. If the charge is positive, your thumb is now pointing in the direction of the force, \vec {v} \times \vec {B}, as shown in the figure. Short Assignment By 2/19/2016 https://session.masteringphysics.com/myct/assignmentPrintView?displ... If the charge is negative, the force is in the direction opposite your thumb. ANSWER: + x direction -x direction + y direction -y direction + z direction - z direction Correct Part B This force will cause the path of the particle to curve. Therefore, at a later time, the direction of the force will ____________. ANSWER: have a component along the direction of motion remain perpendicular to the direction of motion have a component against the direction of motion first have a component along the direction of motion; then against it; then along it; etc. Loading [MathJax]/jax/output/HTML-CSS/autoload/maction.js Short Assignment By 2/19/2016 https://session.masteringphysics.com/myct/assignmentPrintView?displ... Correct Part C The fact that the magnetic field generates a force perpendicular to the instantaneous velocity of the particle has implications for the work that the field does on the particle. As a consequence, if only the magnetic field acts on the particle, its kinetic energy will ____________. ANSWER: increase over time decrease over time remain constant oscillate Correct Part D If the resulting trajectory of the charged particle is a circle, what is \texttip{\omega }{omega}, the angular frequency of the circular motion? Express \texttip{\omega }{omega} in terms of \texttip{q}{q}, \texttip{m}{m}, and \texttip{B_{\rm 0}}{B_0}. Hint 1. How to approach the problem This is a circular dynamics problem. Set F_{\rm mag} = ma to solve the problem. Note that angular speed and angular frequency are the same physical quantity. Hint 2. Determine the magnetic force If the particle is moving with velocity of magnitude \texttip{v}{v}, what is \texttip{F_{\rm mag}}{F_mag}, the magnitude of the magnetic force on the particle? Express \texttip{F_{\rm mag}}{F_mag} in terms of \texttip{v}{v} and other given variables. ANSWER: \texttip{F_{\rm mag}}{F_mag} = q v B_{0} Loading [MathJax]/jax/output/HTML-CSS/autoload/maction.js Short Assignment By 2/19/2016 https://session.masteringphysics.com/myct/assignmentPrintView?displ... Hint 3. Determine the acceleration of the particle If the particle moves in a circular orbit of radius \texttip{R}{R} with uniform speed \texttip{v}{v}, what is the radial component of the particle's acceleration \texttip{a_{\rm r}}{a_r}? Express \texttip{a_{\rm r}}{a_r} in terms of \texttip{v}{v} and other given variables ANSWER: \texttip{a_{\rm r}}{a_r} = \large{\frac{v^{2}}{R}} Hint 4. Express the angular speed in terms of the linear speed What is the angular speed \texttip{\omega }{omega} in terms of \texttip{v}{v}, the tangential speed? Express \texttip{v}{v} in terms of \texttip{\omega }{omega} and \texttip{R}{R}, the radius of the circle. Hint 1. Relationship between \texttip{v}{v} and \texttip{\omega }{omega} The linear speed \texttip{v}{v} of a particle located a distance \texttip{R}{R} from the center of rotation is given by v = \omega R, where \texttip{\omega }{omega} is the angular speed of the particle. ANSWER: \texttip{v}{v} = {\omega} R ANSWER: \texttip{\omega }{omega} = \large{\frac{qB_{0}}{m}} Correct Note that this result for the frequency does not depend on the radius \texttip{R}{R} of the circle. Although it appeared in the equations of force and motion, it canceled out. This implies that the frequency (but not the linear speed) of the particle is invariant with orbit size. The first particle accelerator built, the cyclotron, was based on the fact that the frequency of a charged particle orbiting in a uniform field is independent of the radius. In the cyclotron, radio frequency voltage is applied across a gap between the two sides of the conducting vacuum chamber in which the protons circulate owing to an external magnetic field. Particles in phase with this voltage are accelerated each time they cross the gap (because the field reverses while they make half a circle) and reach energies of millions of electron volts after several thousand round trips. Problem 22.34 The long, thin wire shown in the figure is in a region of constant magnetic field {{\vec B}}. The wire carries a current of 6.2 {\rm A} and is oriented at an angle of 7.5 {\rm ^\circ} to the direction of the magnetic field. Loading [MathJax]/jax/output/HTML-CSS/autoload/maction.js Short Assignment By 2/19/2016 https://session.masteringphysics.com/myct/assignmentPrintView?displ... Part A If the magnetic force exerted on this wire per meter is 3.3×{\rm N} , what is the magnitude of the magnetic field? Express your answer using two significant figures. ANSWER: B = 41 \rm mT Correct Part B At what angle will the force exerted on the wire per meter be equal to 1.5{\rm N} ? Express your answer using two significant figures. ANSWER: \theta = 3.4 ^\circ All attempts used; correct answer displayed Score Summary: Your score on this assignment is 75.0%. You received 1.5 out of a possible total of 2 points. Loading [MathJax]/jax/output/HTML-CSS/autoload/maction.js

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