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A potential difference V exists between two parallel plates that are separated by a distance d. A particle of mass m and charge +q is accelerated from rest through the potential difference, and as a result moves between the plates in a straight line in the plane of the page, as shown above. The particle reaches the right-hand plate with a speed v, passes through a hole in the plate, and enters a region containing a uniform magnetic field. The particle then follows the semicircular path shown. Gravitational effects are negligible. (a) Would the speed v of the particle be greater, smaller, or the same if the magnitude of the potential difference was greater? Explain your answer. Hole +q 01117 m Plates Region of Magnetic Field (b) A student derives the equation v = 2 for the speed of the particle. Whether or not the equation md is correct, is it consistent with your answer to part (a)? Explain your reasoning. (c) A student equates the following two expressions to determine how an increase in the magnitude of the particle's charge affects the radius of its path in the field. mv/r for the magnitude of the net force on an object in uniform circular motion with radius r qvB for the magnitude of the force on a charged particle in a magnetic field of magnitude B Describe the relationship between the particle's charge and the radius of its path indicated by these expressions, and indicate how an increase in charge affects the radius.

A potential difference V exists between two parallel plates that are separated by a distance d. A particle of mass m and charge +q is accelerated from rest through the potential difference, and as a result moves between the plates in a straight line in the plane of the page, as shown above. The particle reaches the right-hand plate with a speed v, passes through a hole in the plate, and enters a region containing a uniform magnetic field. The particle then follows the semicircular path shown. Gravitational effects are negligible. (a) Would the speed v of the particle be greater, smaller, or the same if the magnitude of the potential difference was greater? Explain your answer. Hole +q 01117 m Plates Region of Magnetic Field (b) A student derives the equation v = 2 for the speed of the particle. Whether or not the equation md is correct, is it consistent with your answer to part (a)? Explain your reasoning. (c) A student equates the following two expressions to determine how an increase in the magnitude of the particle's charge affects the radius of its path in the field. mv/r for the magnitude of the net force on an object in uniform circular motion with radius r qvB for the magnitude of the force on a charged particle in a magnetic field of magnitude B Describe the relationship between the particle's charge and the radius of its path indicated by these expressions, and indicate how an increase in charge affects the radius.

College Physics
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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A potential difference V exists between two parallel plates that are separated by a distance d. A particle of mass m and charge +q is accelerated from rest through the potential difference, and as a result moves between the plates in a straight line in the plane of the page, as shown above. The particle reaches the right-hand plate with a speed v, passes through a hole in the plate, and enters a region containing a uniform magnetic field. The particle then follows the semicircular path shown. Gravitational effects are negligible. (a) Would the speed v of the particle be greater, smaller, or the same if the magnitude of the potential difference was greater? Explain your answer. +q m 2qV - md (b) A student derives the equation v is correct, is it consistent with your answer to part (a)? Explain your reasoning. Hole Plates Region of Magnetic Field for the speed of the particle. Whether or not the equation (c) A student equates the following two expressions to determine how an increase in the magnitude of the particle's charge affects the radius of its path in the field. mv²/r for the magnitude of the net force on an object in uniform circular motion with radius r qvB for the magnitude of the force on a charged particle in a magnetic field of magnitude B Describe the relationship between the particle's charge and the radius of its path indicated by these expressions, and indicate how an increase in charge affects the radius.
Transcribed Image Text:A potential difference V exists between two parallel plates that are separated by a distance d. A particle of mass m and charge +q is accelerated from rest through the potential difference, and as a result moves between the plates in a straight line in the plane of the page, as shown above. The particle reaches the right-hand plate with a speed v, passes through a hole in the plate, and enters a region containing a uniform magnetic field. The particle then follows the semicircular path shown. Gravitational effects are negligible. (a) Would the speed v of the particle be greater, smaller, or the same if the magnitude of the potential difference was greater? Explain your answer. +q m 2qV - md (b) A student derives the equation v is correct, is it consistent with your answer to part (a)? Explain your reasoning. Hole Plates Region of Magnetic Field for the speed of the particle. Whether or not the equation (c) A student equates the following two expressions to determine how an increase in the magnitude of the particle's charge affects the radius of its path in the field. mv²/r for the magnitude of the net force on an object in uniform circular motion with radius r qvB for the magnitude of the force on a charged particle in a magnetic field of magnitude B Describe the relationship between the particle's charge and the radius of its path indicated by these expressions, and indicate how an increase in charge affects the radius.
(d) For the values m = 5.04 x 10-27 kg, q = 3.20 x 10-1⁹ C, v = 2.20 x 106 m/s, and B = 0.30 T, compute the radius of the particle's circular motion. 2Vm (e) Another student writes the equation r = √ for the radius of the path. Whether or not the (B²+qV) equation is correct, is it consistent with your answers to part (c) and (d)? Explain your reasoning. (f) If the particle had a charge of -q, would its motion be the same? Justify your answer. -d The region of the magnetic field is replaced +V by a wire that is in the page and has a current directed toward the right. The positively charged particle still moves in a straight line between the plates. (g) With respect to the coordinate axes shown, in what direction is the acceleration of the particle at the instant it passes through the hole? Explain your reasoning. +q m Hole Plates Wire +y +Z +X (out of page)
Transcribed Image Text:(d) For the values m = 5.04 x 10-27 kg, q = 3.20 x 10-1⁹ C, v = 2.20 x 106 m/s, and B = 0.30 T, compute the radius of the particle's circular motion. 2Vm (e) Another student writes the equation r = √ for the radius of the path. Whether or not the (B²+qV) equation is correct, is it consistent with your answers to part (c) and (d)? Explain your reasoning. (f) If the particle had a charge of -q, would its motion be the same? Justify your answer. -d The region of the magnetic field is replaced +V by a wire that is in the page and has a current directed toward the right. The positively charged particle still moves in a straight line between the plates. (g) With respect to the coordinate axes shown, in what direction is the acceleration of the particle at the instant it passes through the hole? Explain your reasoning. +q m Hole Plates Wire +y +Z +X (out of page)
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