Explanation Given info: Initially the proton is stationary. The proton and the alpha particle undergo elastic collision. Both the particles move perpendicular to the uniform magnetic field. The radius of the protons trajectory is R , Initially the proton is stationary. The proton and the alpha particle undergo elastic collision. Both the particles move perpendicular to the uniform magnetic field. The radius of the protons trajectory is R . Explanation: The mass of the alpha particle is four time that of the proton, m α m p = 4 (1) m α is the mass of the alpha particle m p is the mass of the proton The charge of alpha particle is twice of proton, q α q p = 2 (2) q α is the charge of the alpha particle q p is the charge of the proton Since the collision is elastic, the linear momentum as well as the kinetic energy in the collision is conserved. From conservation of linear momentum, m α v o = m α v α + m p v p (3) v o is the initial velocity of the alpha particle Re-arrange to get v o , v o = m α v α + m p v p m α (4) From conservation of kinetic energy, m α v o 2 = m α v α 2 + m p v p 2 (5) Combining (4) and (5), m α ( m α v α + m p v p m α ) 2 = m α v α 2 + m p v p 2 m α 2 v α 2 + m p 2 v p 2 + 2 m α v α m p v p = m α 2 v α 2 + m α m p v p 2 2 m α v α = v p ( m α − m p ) v α v p = m α − m p 2 m α Since m α = 4 m p , v α v p = 4 m p − m p 8 m p = 3 8 Hence the ratio of the velocities of the alpha particle and the proton is 3 8

10th Edition

ISBN: 9781285737027

Author: Raymond A. Serway, Chris Vuille

Publisher: Cengage Learning

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Magnetic Force

A magnetic force arises when a charged particle or a current-carrying conductor is placed in a magnetic field. It is created because of the movement of the charged particles.

Question

Chapter 19, Problem 19P

To determine

The radius of the alpha particles trajectory.

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Chapter 19 Solutions

College Physics

Ch. 19.3 - A charged particle moves in a straight line...Ch. 19.3 - The north-pole end of a bar magnet is held near a...Ch. 19.4 - As a charged particle moves freely in a circular...Ch. 19.6 - A square and a circular loop with the same area...Ch. 19.8 - Which of the following actions would double the...Ch. 19.8 - Prob. 19.6QQ Ch. 19 - Prob. 1CQ Ch. 19 - Prob. 2CQ Ch. 19 - How can the motion of a charged particle be used...Ch. 19 - Prob. 4CQ

Ch. 19 - The following statements are related to the force...Ch. 19 - Will a nail be attracted to either pole of a...Ch. 19 - Figure CQ19.7 shows a coaxial cable carrying...Ch. 19 - A magnet attracts a piece of iron. The iron can...Ch. 19 - Figure CQ19.9 shows four positive charges, A, B,...Ch. 19 - Is the magnetic field created by a current loop...Ch. 19 - Suppose you move along a wire at the same speed as...Ch. 19 - Why do charged particles from outer space, called...Ch. 19 - A hanging Slinky toy is attached to a powerful...Ch. 19 - How can a current loop he used to determine the...Ch. 19 - Prob. 15CQ Ch. 19 - Figure CQ19.16 shows four permanent magnets, each...Ch. 19 - Two charged particles are projected in the same...Ch. 19 - Prob. 18CQ Ch. 19 - A magnetic field exerts a torque on each of the...Ch. 19 - Consider an electron near the Earths equator. In...Ch. 19 - (a) Find the direction of the force on a proton (a...Ch. 19 - Find the direction of the magnetic field acting on...Ch. 19 - Prob. 4P Ch. 19 - A laboratory electromagnet produces a magnetic...Ch. 19 - Prob. 6P Ch. 19 - Electrons and protons travel from the Sun to the...Ch. 19 - An oxygen ion (O+) moves in the xy-plane with a...Ch. 19 - A proton moving at 4.00 106 m/s through a...Ch. 19 - Sodium ions (Na+) move at 0.851 m/s through a...Ch. 19 - At the equator, near the surface of Earth, the...Ch. 19 - A proton travels with a speed of 5.02 106 m/s at...Ch. 19 - An electron moves in a circular path perpendicular...Ch. 19 - Figure P19.14a is a diagram of a device called a...Ch. 19 - Prob. 15P Ch. 19 - A mass spectrometer is used to examine the...Ch. 19 - Jupiters magnetic field occupies a volume of space...Ch. 19 - Electrons in Earths upper atmosphere have typical...Ch. 19 - Prob. 19P Ch. 19 - A proton (charge +e, mass mp), a deuteron (charge...Ch. 19 - A particle passes through a mass spectrometer as...Ch. 19 - In Figure P19.2, assume in each case the velocity...Ch. 19 - A current I = 15 A is directed along the positive...Ch. 19 - A straight wire carrying a 3.0-A current is placed...Ch. 19 - In Figure P19.3, assume in each case the velocity...Ch. 19 - A wire having a mass per unit length of 0.500 g/cm...Ch. 19 - A wire carries a current of 10.0 A in a direction...Ch. 19 - At a certain location, Earth has a magnetic field...Ch. 19 - A wire with a mass of 1.00 g/cm is placed on a...Ch. 19 - Mass m = 1.00 kg is suspended vertically at rest...Ch. 19 - Consider the system pictured in Figure P19.31. A...Ch. 19 - A metal rod of mass m carrying a current I glides...Ch. 19 - In Figure P19.33, the cube is 40.0 cm on each...Ch. 19 - A horizontal power line of length 58 m carries a...Ch. 19 - A wire is formed into a circle having a diameter...Ch. 19 - A current of 17.0 mA is maintained in a single...Ch. 19 - An eight-turn coil encloses an elliptical area...Ch. 19 - A current-carrying rectangular wire loop with...Ch. 19 - A 6.00-turn circular coil of wire is centered on...Ch. 19 - The orientation of small satellites is often...Ch. 19 - Along piece of wire with a mass of 0.100 kg and a...Ch. 19 - A rectangular loop has dimensions 0.500 m by 0.300...Ch. 19 - A lightning bolt may carry a current of 1.00 104...Ch. 19 - A long, straight wire going through the origin is...Ch. 19 - Neurons in our bodies carry weak currents that...Ch. 19 - In 1962 measurements of the magnetic field of a...Ch. 19 - A cardiac pacemaker can be affected by a static...Ch. 19 - The two wires shown in Figure P19.48 are separated...Ch. 19 - Prob. 49P Ch. 19 - Two long, parallel wires carry currents of I1 =...Ch. 19 - Two long, parallel wires carry currents of I1 =...Ch. 19 - Prob. 52P Ch. 19 - The magnetic field 40.0 cm away from a long,...Ch. 19 - Prob. 54P Ch. 19 - Prob. 55P Ch. 19 - Prob. 56P Ch. 19 - A wire with a weight per unit length of 0.080 N/m...Ch. 19 - In Figure P19.58 the current in the long, straight...Ch. 19 - A long solenoid that has 1.00 103 turns uniformly...Ch. 19 - Prob. 60P Ch. 19 - It is desired to construct a solenoid that will...Ch. 19 - Certain experiments must be performed in the...Ch. 19 - Ail electron is moving at a speed of 1.0 104 in/s...Ch. 19 - Figure P19.64 is a setup that can be used to...Ch. 19 - Two coplanar and concentric circular loops of wire...Ch. 19 - An electron moves in a circular path perpendicular...Ch. 19 - Prob. 67AP Ch. 19 - A 0.200-kg metal rod carrying a current of 10.0 A...Ch. 19 - Using an electromagnetic flowmeter (Fig. P19.69),...Ch. 19 - A uniform horizontal wire with a linear mass...Ch. 19 - Prob. 71AP Ch. 19 - Two long, parallel wires, each with a mass per...Ch. 19 - Protons having a kinetic energy of 5.00 MeV are...Ch. 19 - A straight wire of mass 10.0 g and length 5.0 cm...Ch. 19 - A 1.00-kg ball having net charge Q = 5.00 C is...Ch. 19 - Two long, parallel conductors separated by 10.0 cm...

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