7. A charged particle, q, is moving with speed v perpendicular to a uniform magnetic field. A second identical charged particle is moving with speed 2v perpendicular to the same magnetic field. The time to complete one full circular revolution for the first particle is T1. The time to complete one full circular revolution for the particle moving with speed 2v

7. A charged particle, q, is moving with speed v perpendicular to a uniform magnetic field. A second identical charged particle is moving with speed 2v perpendicular to the same magnetic field. The time to complete one full circular revolution for the first particle is T1. The time to complete one full circular revolution for the particle moving with speed 2v

University Physics Volume 2

18th Edition

ISBN:9781938168161

Author:OpenStax

Publisher:OpenStax

Chapter11: Magnetic Forces And Fields

Section: Chapter Questions

Problem 31P: An alpha-particle ( m=6.641027kg , q=3.21019C ) travels in a circular path of radius 25 cm in a...

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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 alpha-particle ( m=6.641027kg , q=3.21019C ) travels in a circular path of radius 25 cm in a uniform magnetic field of magnitude 1.5 T. (a) What is the speed of the particle? (b) What is the kinetic energy in electron-volts? (c) Through what potential difference must the particle be accelerated in order to give it this kinetic energy?
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 p. In terms of p, determine (a) the radius rd of the circular orbit for the deuteron and (b) the radius r for the alpha particle.
A spacecraft is in 4 circular orbit of radius equal to 3.0 104 km around a 2.0 1030 kg pulsar. The magnetic field of the pulsar at that radial distance is 1.0 102 T directed perpendicular to the velocity of the spacecraft. The spacecraft is 0.20 km long with a radius of 0.040 km and moves counter-clockwise in the xy-plane around the pulsar. (a) What is the speed of the spacecraft? (b) If the magnetic field points in the positive z-direction, is the emf induced from the back to the front of the spacecraft or from side to side? (c) Compute the induced emf. (d) Describe the hazards for astronauts inside any spacecraft moving in the vicinity of a pulsar.
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?
One long wire carries current 30.0 A to the left along the x axis. A second long wire carries current 50.0 A to the right along the line (y = 0.280 m, z = 0). (a) Where in the plane of the two wires is the total magnetic field equal to zero? (b) A particle with a charge of 2.00 C is moving with a velocity of 150iMm/s along the line (y = 0.100 m, z = 0). Calculate the vector magnetic force acting on the particle. (c) What If? A uniform electric field is applied to allow this particle to pass through this region undetected. Calculate the required vector electric field.
Why is the following situation impossible? Figure P28.46 shows an experimental technique for altering the direction of travel for a charged particle. A particle of charge q = 1.00 C and mass m = 2.00 1015 kg enters the bottom of the region of uniform magnetic field at speed = 2.00 105 m/s, with a velocity vector perpendicular to the field lines. The magnetic force on the particle causes its direction of travel to change so that it leaves the region of the magnetic field at the top traveling at an angle from its original direction. The magnetic field has magnitude B = 0.400 T and is directed out of the page. The length h of the magnetic field region is 0.110 m. An experimenter performs the technique and measures the angle at which the particles exit the top of the field. She finds that the angles of deviation are exactly as predicted. Figure P28.46
Two long, straight, parallel wires carry currents that are directed perpendicular to the page as shown in Figure P30.9. Wire 1 carries a current I1, into the page (in the negative z direction) and passes through the x axis at x = +. Wire 2 passes through the x axis at x = 2a and carries an unknown current I2. The total magnetic field at the origin due to the current-carrying wires has the magnitude 20I1(2a). The current I2 can have either of two possible values, (a) Find the value of with the smaller magnitude, stating it in terms of I1, and giving its direction. (b) Find the other possible value of I2.
A uniform magnetic Held of magnitude 0.150 T is directed along the positive x axis. A positron moving at a speed of 5.00 106 m/s enters the Held along a direction that makes an angle of = 85.0 with the x axis (Fig. P29.73). The motion of the particle is expected to be a helix as described in Section 29.2. Calculate (a) the pitch p and (b) the radius r of the trajectory as defined in Figure P29.73.
A spacecraft is in 4 circular orbit of radius equal to 3.0 104 km around a 2.0 1030 kg pulsar. The magnetic field of the pulsar at that radial distance is 1.0 102 T directed perpendicular to the velocity of the spacecraft. The spacecraft is 0.20 km long with a radius of 0.040 km and moves counter-clockwise in the xy-plane around the pulsar. (a) What is the speed of the spacecraft? (b) If the magnetic field points in the positive z-direction, is the emf induced from the back to the front of the spacecraft or from side to side? (c) Compute the induced emf. (d) Describe the hazards for astronauts inside any spacecraft moving in the vicinity of a pulsar.
Review. A rod of mass 0.720 kg and radius 6.00 cm rests on two parallel rails (Fig. P28.23) that are d = 12.0 cm apart and L = 45.0 cm long. The rod carries a current of I = 48.0 A in the direction shown and rolls along the rails without slipping. A uniform magnetic field of magnitude 0.240 T is directed perpendicular to the rod and the rails. If it starts from rest, what is the speed of the rod as it leaves the rails? Figure P28.23 Problems 23 and 24.
An oxygen ion (O+) moves in the xy-plane with a speed of 2.50 103 m/s. If a constant magnetic field is directed along the z-axis with a magnitude of 2.00 105 T, find (a) the magnitude of the magnetic force acting on the ion and (b) the magnitude of the ions acceleration.