A proton (charge +e, mass m), a deuteron (charge +e, mass 2m), and an alpha particle (charge +2e, mass 4m) are accelerated from rest through a common potential difference AV. Each of the particles enters a uniform magnetic field B, with its velocity in a direction perpendicular to B. The proton moves in a circular path of radius r (a) In terms of r. determine the radius r of the circular orbit for the deuteron. (b) In terms of r determine the radius r for the alpha particle. p

A proton (charge +e, mass m), a deuteron (charge +e, mass 2m), and an alpha particle (charge +2e, mass 4m) are accelerated from rest through a common potential difference AV. Each of the particles enters a uniform magnetic field B, with its velocity in a direction perpendicular to B. The proton moves in a circular path of radius r (a) In terms of r. determine the radius r of the circular orbit for the deuteron. (b) In terms of r determine the radius r for the alpha particle. p

Physics for Scientists and Engineers with Modern Physics

10th Edition

ISBN:9781337553292

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter28: Magnetic Fields

Section: Chapter Questions

Problem 9P: A proton (charge + e, mass mp), a deuteron (charge + e, mass 2mp), and an alpha particle (charge...

See similar textbooks

Similar questions

An electron is accelerated through 2.40 103 V from rest and then enters a uniform 1.70-T magnetic field. What are (a) the maximum and (b) the minimum values of the magnetic force this particle experiences?
, A proton, deuteron, and an alpha-particle ae all accelerated from rest through the same potential difference. They then enter the same magnetic field, moving perpendicular to it. Compute the ratios of the radii of their circular paths. Assume that md= 2wmp and ma= 4mp.
A singly charged ion of mass m is accelerated from rest by a potential difference V. It is then deflected by a uniform magnetic field (perpendicular to the ions velocity) into a semicircle of radius R. Now a doubly charged ion of mass m' is accelerated through the same potential difference and dellected by the same magnetic field into a semicircle of radius R' = 2R. What is the ratio of the masses of the ions?
(a) An oxygen16 ion with a mass at 2.661026kg travels at 5.00106m/s perpendicular to a 1.20T magnetic field, which makes it move in a circular arc with a 0.231-m radius. What positive charge is on the ion? (b) What is the radio of this charge to the charge of an electron? (c) Discuss why the radio found in (b) should be an integer.
Review. Rail guns have been suggested for launching projectiles into space without chemical rockets. A tabletop model rail gun (Fig. P29.42) consists of two long, parallel, horizontal rails = 3.50 cm apart, bridged by a bar of mass m = 3.00 g that is free to slide without friction. The rails and bar have low electric resistance, and the current is limited to a constant I = 24.0 A by a power supply that is far to the left of the figure, so it has no magnetic effect on the bar. Figure P29.42 shows the bar at rest at the midpoint of the rails at the moment the current is established. We wish to find the speed with which the bar leaves the rails after being released from the midpoint of the rails. (a) Find the magnitude of the magnetic field at a distance of 1.75 cm from a single long wire carrying a current of 2.40 A. (b) For purposes of evaluating the magnetic field, model the rails as infinitely long. Using the result of part (a), find the magnitude and direction of the magnetic field at the midpoint of the bar. (c) Argue that this value of the field will be the same at all positions of the bar to the right of the midpoint of the rails. At other points along the bar, the field is in the same direction as at the midpoint, but is larger in magnitude. Assume the average effective magnetic field along the bar is five times larger than the field at the midpoint. With this assumption, find (d) the magnitude and (e) the direction of the force on the bar. (f) Is the bar properly modeled as a particle under constant acceleration? (g) Find the velocity of the bar after it has traveled a distance d = 130 cm to the end of the rails. Figure P29.42
Unreasonable Results A charged particle having mass 6.641027kg (that of a helium atom) moving at 8.70105m/s perpendicular to a 1.50T magnetic field travels in a circular path of radius 16.0 mm. (a) What is the charge of the particle? (b) What is unreasonable about this result? (c) Which assumptions are responsible?
A particle’s path is bent when it passes through a region of non-zero magnetic field although its speed remains unchanged. This is very useful for “beam steering’’ in particle accelerators. Consider a proton of speed 4106m/s entering a region of uniform magnetic field 0.2 T over a 5-cm-wide region. Magnetic field is perpendicular to the velocity of the particle. By how much angle will the path of the proton be bent? (Hint: the particle comes out tangent to a circle.
A proton (charge + e, mass mp), a deuteron (charge + e, mass 2mp), and an alpha particle (charge +2e, mass 4mp) are accelerated from rest through a common potential difference V. Each of the particles enters a uniform magnetic field B, with its velocity in a direction perpendicular to B. The proton moves in a circular path of radius rp. In terms of rp, determine (a) the radius rd of the circular orbit for the deuteron and (b) the radius ra for the alpha particle.
An electron is projected into a uniform magnetic field (0.5i+0.8k)T with a velocity of (3.0i+4.0j)106 m/s . What is the magnetic force on the electron?
An electron moving at 4.00103m/s in a 1.25T magnetic field experiences a magnetic force of 1.401016N. What angle does the velocity at the electron make with the magnetic field? There are two answers.
Review. A particle with a mass of 2.00 1016 kg and a charge of 30.0 nC starts from rest, is accelerated through a potential difference V, and is fired from a small source in a region containing a uniform, constant magnetic field of magnitude 0.600 T. The particle's velocity is perpendicular to the magnetic field lines. The circular orbit of the panicle as it returns to the location of the source encloses a magnetic flux of 15.0 Wb. (a) Calculate the particles speed. (b) Calculate the potential difference through which the particle was accelerated inside the source.
A charged particle is traveling through a uniform magnetic field. Which of the following statements are true of the magnetic field? There may be more than one correct statement. (a) It exerts a force on the particle parallel to the field. (b) It exerts a force on the particle along the direction of its motion. (c) It increases the kinetic energy of the particle. (d) It exerts a force that is perpendicular to the direction of motion. (e) It does not change the magnitude of the momentum of the particle.