Chapter 22: MagnetismAnswers to Even-Numbered Conceptual Questions2. Yes. If an electric field exists in this region of space, and no magnetic field is present, the electric field willexert a force on the electron and cause it to accelerate.4. In a uniform electric field the force on a charged particle is always in one fixed direction, as with gravity nearthe earth's surface, leading to parabolic trajectories. In a uniform magnetic field the force of a chargedparticle is always at right angles to the motion, resulting in circular or helical trajectories. Perhaps even moreimportant, a charged particle experiences a force due to an electric field whether it is moving or at rest; in amagnetic field, the particle must be moving to experience a force.6. A current-carrying wire in a uniform magnetic field can experience zero force only if the wire points in thesame or opposite direction as the magnetic field. In such a case, the angle  in equation 22-4 will be either 0˚or 180˚, in which case F = ILB sin  = 0.Solutions to Problems and Conceptual Exercises1. Picture the Problem: Proton 1 moves with a speed v from the east coast to the west coast in the continental United States; and proton 2 moves with the same speed from the southern United States toward Canada. Strategy: The magnetic field of Earth points roughly north over the entire continental United States. Each particle experiences a magnetic force given by F =qvBsinθ(equation 22-1), where θ is the angle between the velocity and magnetic field vectors. Use these principles to determine the relative magnitudes of the forces experienced by the two protons. Solution: 1. (a) Proton 1 moves east to west, roughly perpendicular to the magnetic field, so that θ is close to 90°, whereas proton 2 moves roughly parallel to the magnetic field, so that θ is close to 0°. We conclude that the magnitude of the magnetic force experienced by proton 2 is less than the force experienced by proton 1.2. (b) The best explanation is II. Proton 1 experiences the greater force because it moves at right angles to the magnetic field. Statement I ignores the importance of the relative directions of the velocity and the magnetic field, and statement III would only be true if the force depended upon the cosine of the angle θ.Insight: The magnetic field of the Earth changes the trajectories of charged particles from the Sun according to equation22-1. Many of the particles spiral around the Earth’s magnetic field lines and collide with atmospheric molecules, creating colorful displays called aurora.2. Picture the Problem: An electron moves west to east in the continental United States and experiences a magnetic force.Strategy: The magnetic force exerted on a charged particle is F =qvBsinθ(equation 22-1), where θ is the angle between the velocity and magnetic field vectors. The direction of this force is given by the Right-Hand Rule for positiveparticles, and points in the opposite direction for negative particles. Solution: The magnetic field in the continental United States points primarily toward the north. According to the Right-Hand Rule, the direction of the magnetic force on a positively charged particle moving toward the east is upward. Therefore, a negatively charged electron moving toward the east experiences a downward magnetic force. Insight: Another way to remember the direction of the magnetic force on a negatively charged particle is to use your lefthand instead of your right hand in the manner described in section 22-2.Copyright © 2010 Pearson Education, Inc. All rights reserved. This material is protected under all copyright laws as they currently exist. Noportion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.22 – 1Chapter 22: Magnetism James S. Walker, Physics, 4th Edition3. Picture the Problem: An electron moving in the positive x direction, at right angles to a magnetic field, experiences a magnetic force in the positive y direction.Strategy: The magnetic force exerted on a charged particle is F =qvBsinθ(equation 22-1), where θ is the angle between the velocity and magnetic field vectors. The direction of this force is given by the Right-Hand Rule for positiveparticles, and points in the opposite direction for negative particles. Solution: The direction of the magnetic force on a negatively charged particle will be opposite to that given by the Right-Hand Rule. We therefore suppose that the force on a positive charge that is moving in the positive x direction would be in the negative y direction, A little practice with the Right-Hand Rule reveals that the magnetic field must therefore point in the positive z direction. Insight: Another way to remember the direction of the magnetic force on a negatively charged particle is to use your lefthand instead of your right hand in the manner described in section 22-2.4. Picture the Problem: Particles A, B, and C in the figure at right have identical masses and charges of the same magnitude.Strategy: The magnetic force exerted on a charged particle that moves perpendicular to a magnetic field produces a curved path of radius r =mv qB (equation 22-3). Use this expression to determine the ranking of the speeds of the three particles.Solution: Because the radius of the curved path is proportional to the speed, it follows that the particle with the larger radius has the greater speed. In this case, the ranking of the speeds is A < B < C.Insight: An analysis of the curved paths and the direction of the magnetic field reveals that charges A and B are negative and charge C is positive.5. Picture the Problem: Particles A, B, and C in the figure at right have identical masses and charges of the same magnitude.Strategy: The direction of the magnetic force exerted on a charged particlethat moves perpendicular to a magnetic field is given by the Right-Hand Rule. Solution: The Right-Hand Rule for particles moving to the right in a uniform magnetic field that points out of the page predicts a force in the downward direction. Particle C is deflected downward, but particles A and B are deflected upward. We conclude that the signs of the charges are:A, negative; B, negative; C, positive.Insight: An electrically neutral particle, such as a neutron, would not be deflected at all by the magnetic field.6. Picture the Problem: Particles A, B, and C in the figure at right have identical masses and speeds