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Chapter 8 Review

Key Terms

cosmic rays
comprised of particles that originate mainly from outside the solar system and reach Earth

cyclotron
device used to accelerate charged particles to large kinetic energies

dees
large metal containers used in cyclotrons that serve contain a stream of charged particles as their speed is increased



gauss

unit of the magnetic field strength;



Hall effect
creation of voltage across a current-carrying conductor by a magnetic field



helical motion
superposition of circular motion with a straight-line motion that is followed by a charged particle moving in a region of magnetic field at an angle to the field



magnetic dipole
closed-current loop



magnetic dipole moment
term

of the magnetic dipole, also called



magnetic field lines
continuous curves that show the direction of a magnetic field; these lines point in the same direction as a compass points, toward the magnetic south pole of a bar magnet



magnetic force
force applied to a charged particle moving through a magnetic field



mass spectrometer
device that separates ions according to their charge-to-mass ratios



motor (dc)
loop of wire in a magnetic field; when current is passed through the loops, the magnetic field exerts torque on the loops, which rotates a shaft; electrical energy is converted into mechanical work in the process



north magnetic pole
currently where a compass points to north, near the geographic North Pole; this is the effective south pole of a bar magnet but has flipped between the effective north and south poles of a bar magnet multiple times over the age of Earth



right-hand rule-1
using your right hand to determine the direction of either the magnetic force, velocity of a charged particle, or magnetic field



south magnetic pole
currently where a compass points to the south, near the geographic South Pole; this is the effective north pole of a bar magnet but has flipped just like the north magnetic pole



tesla
SI unit for magnetic field:



velocity selector
apparatus where the crossed electric and magnetic fields produce equal and opposite forces on a charged particle moving with a specific velocity; this particle moves through the velocity selector not affected by either field while particles moving with different velocities are deflected by the apparatus



Key Equations

Force on a charge in a magnetic field
Magnitude of magnetic force
Radius of a particle’s path in a magnetic field
Period of a particle’s motion in a magnetic field
Force on a current-carrying wire in a uniform magnetic field
Magnetic dipole moment
Torque on a current loop
Energy of a magnetic dipole
Drift velocity in crossed electric and magnetic fields
Hall potential
Hall potential in terms of drift velocity
Charge-to-mass ratio in a mass spectrometer
Maximum speed of a particle in a cyclotron



Summary

8.1 Magnetism and Its Historical Discoveries

  • Magnets have two types of magnetic poles, called the north magnetic pole and the south magnetic pole. North magnetic poles are those that are attracted toward Earth’s geographic North Pole.
  • Like poles repel and unlike poles attract.
  • Discoveries of how magnets respond to currents by Oersted and others created a framework that led to the invention of modern electronic devices, electric motors, and magnetic imaging technology.



8.2 Magnetic Fields and Lines

  • Charges moving across a magnetic field experience a force determined by The force is perpendicular to the plane formed by and
  • The direction of the force on a moving charge is given by the right hand rule 1 (RHR-1): Sweep your fingers in a velocity, magnetic field plane. Start by pointing them in the direction of velocity and sweep towards the magnetic field. Your thumb points in the direction of the magnetic force for positive charges.
  • Magnetic fields can be pictorially represented by magnetic field lines, which have the following properties:
    1. The field is tangent to the magnetic field line.
    2. Field strength is proportional to the line density.
    3. Field lines cannot cross.
    4. Field lines form continuous, closed loops.
  • Magnetic poles always occur in pairs of north and south—it is not possible to isolate north and south poles.



8.3 Motion of a Charged Particle in a Magnetic Field

  • A magnetic force can supply centripetal force and cause a charged particle to move in a circular path of radius
  • The period of circular motion for a charged particle moving in a magnetic field perpendicular to the plane of motion is
  • Helical motion results if the velocity of the charged particle has a component parallel to the magnetic field as well as a component perpendicular to the magnetic field.



8.4 Magnetic Force on a Current-Carrying Conductor

  • An electrical current produces a magnetic field around the wire.
  • The directionality of the magnetic field produced is determined by the right hand rule-2, where your thumb points in the direction of the current and your fingers wrap around the wire in the direction of the magnetic field.
  • The magnetic force on current-carrying conductors is given by where is the current and is the length of a wire in a uniform magnetic field



8.5 Force and Torque on a Current Loop

  • The net force on a current-carrying loop of any plane shape in a uniform magnetic field is zero.
  • The net torque on a current-carrying loop of any shape in a uniform magnetic field is calculated using where is the magnetic dipole moment and is the magnetic field strength.
  • The magnetic dipole moment is the product of the number of turns of wire the current in the loop and the area of the loop or



8.6 The Hall Effect

  • Perpendicular electric and magnetic fields exert equal and opposite forces for a specific velocity of entering particles, thereby acting as a velocity selector. The velocity that passes through undeflected is calculated by
  • The Hall effect can be used to measure the sign of the majority of charge carriers for metals. It can also be used to measure a magnetic field.



8.7 Applications of Magnetic Forces and Fields

  • A mass spectrometer is a device that separates ions according to their charge-to-mass ratios by first sending them through a velocity selector, then a uniform magnetic field.
  • Cyclotrons are used to accelerate charged particles to large kinetic energies through applied electric and magnetic fields.



Answers to Check Your Understanding

8.1 a.

b.

c.

d.



8.2 a.

toward the south; b.



8.3 a. bends upward; b. bends downward



8.4 a. perpendicular ; b. anti-aligned



8.5 a.



b.



8.6



Conceptual Questions

8.2 Magnetic Fields and Lines


1. Discuss the similarities and differences between the electrical force on a charge and the magnetic force on a charge.



2. (a) Is it possible for the magnetic force on a charge moving in a magnetic field to be zero? (b) Is it possible for the electric force on a charge moving in an electric field to be zero? (c) Is it possible for the resultant of the electric and magnetic forces on a charge moving simultaneously through both fields to be zero?



8.3 Motion of a Charged Particle in a Magnetic Field


3. At a given instant, an electron and a proton are moving with the same velocity in a constant magnetic field. Compare the magnetic forces on these particles. Compare their accelerations.



4. Does increasing the magnitude of a uniform magnetic field through which a charge is traveling necessarily mean increasing the magnetic force on the charge? Does changing the direction of the field necessarily mean a change in the force on the charge?



5. An electron passes through a magnetic field without being deflected. What do you conclude about the magnetic field?



6. If a charged particle moves in a straight line, can you conclude that there is no magnetic field present?



7. How could you determine which pole of an electromagnet is north and which pole is south?



8.4 Magnetic Force on a Current-Carrying Conductor


8. Describe the error that results from accidently using your left rather than your right hand when determining the direction of a magnetic force.

9. Considering the magnetic force law, are the velocity and magnetic field always perpendicular? Are the force and velocity always perpendicular? What about the force and magnetic field?



10. Why can a nearby magnet distort a cathode ray tube television picture?



11. A magnetic field exerts a force on the moving electrons in a current carrying wire. What exerts the force on a wire?



12. There are regions where the magnetic field of earth is almost perpendicular to the surface of Earth. What difficulty does this cause in the use of a compass?



8.6 The Hall Effect


13. Hall potentials are much larger for poor conductors than for good conductors. Why?



8.7 Applications of Magnetic Forces and Fields


14. Describe the primary function of the electric field and the magnetic field in a cyclotron.



Problems

8.2 Magnetic Fields and Lines


15. What is the direction of the magnetic force on a positive charge that moves as shown in each of the six cases?



16. Repeat previous exercise for a negative charge.



17. What is the direction of the velocity of a negative charge that experiences the magnetic force shown in each of the three cases, assuming it moves perpendicular to



18. Repeat previous exercise for a positive charge.



19. What is the direction of the magnetic field that produces the magnetic force on a positive charge as shown in each of the three cases, assuming

is perpendicular to

?



20. Repeat previous exercise for a negative charge.



21. (a) Aircraft sometimes acquire small static charges. Suppose a supersonic jet has a

charge and flies due west at a speed of

over Earth’s south magnetic pole, where the

magnetic field points straight up. What are the direction and the magnitude of the magnetic force on the plane? (b) Discuss whether the value obtained in part (a) implies this is a significant or negligible effect.



22. (a) A cosmic ray proton moving toward Earth at

experiences a magnetic force of

What is the strength of the magnetic field if there is a

angle between it and the proton’s velocity? (b) Is the value obtained in part a. consistent with the known strength of Earth’s magnetic field on its surface? Discuss.



23. An electron moving at

in a

magnetic field experiences a magnetic force of

What angle does the velocity of the electron make with the magnetic field? There are two answers.



24. (a) A physicist performing a sensitive measurement wants to limit the magnetic force on a moving charge in her equipment to less than

What is the greatest the charge can be if it moves at a maximum speed of

in Earth’s field? (b) Discuss whether it would be difficult to limit the charge to less than the value found in (a) by comparing it with typical static electricity and noting that static is often absent.



8.3 Motion of a Charged Particle in a Magnetic Field


25. A cosmic-ray electron moves at

perpendicular to Earth’s magnetic field at an altitude where the field strength is

What is the radius of the circular path the electron follows?



26. (a) Viewers of Star Trek have heard of an antimatter drive on the Starship Enterprise. One possibility for such a futuristic energy source is to store antimatter charged particles in a vacuum chamber, circulating in a magnetic field, and then extract them as needed. Antimatter annihilates normal matter, producing pure energy. What strength magnetic field is needed to hold antiprotons, moving at

in a circular path

in radius? Antiprotons have the same mass as protons but the opposite (negative) charge. (b) Is this field strength obtainable with today’s technology or is it a futuristic possibility?



27. (a) An oxygen-

ion with a mass of

travels at

perpendicular to a

magnetic field, which makes it move in a circular arc with a

radius. What positive charge is on the ion? (b) What is the ratio of this charge to the charge of an electron? (c) Discuss why the ratio found in (b) should be an integer.



28. An electron in a TV CRT moves with a speed of

in a direction perpendicular to Earth’s field, which has a strength of

(a) What strength electric field must be applied perpendicular to the Earth’s field to make the electron moves in a straight line? (b) If this is done between plates separated by

what is the voltage applied? (Note that TVs are usually surrounded by a ferromagnetic material to shield against external magnetic fields and avoid the need for such a correction.)



29. (a) At what speed will a proton move in a circular path of the same radius as the electron in the previous exercise? (b) What would the radius of the path be if the proton had the same speed as the electron? (c) What would the radius be if the proton had the same kinetic energy as the electron? (d) The same momentum?



30. (a) What voltage will accelerate electrons to a speed of

? (b) Find the radius of curvature of the path of a proton accelerated through this potential in a

field and compare this with the radius of curvature of an electron accelerated through the same potential.



31. An alpha-particle

travels in a circular path of radius

in a uniform magnetic field of magnitude

(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?



32. A particle of charge