1. Chapter 20
Magnetism

2. Magnets
Poles of a magnet are the ends where objects are most strongly attracted
Two poles, called north and south
Like poles repel each other and unlike poles attract each other
Similar to electric charges
Magnetic poles cannot be isolated
If a permanent magnetic is cut in half repeatedly, you will still have a north and a south pole

3. More About Magnetism
An unmagnetized piece of iron can be magnetized by stroking it with a magnet
Somewhat like stroking an object to charge an object
Magnetism can be induced
If a piece of iron, for example, is placed near a strong permanent magnet, it will become magnetized

4. Types of Magnetic Materials
Soft magnetic materials, such as iron, are easily magnetized
They also tend to lose their magnetism easily
Hard magnetic materials, such as cobalt and nickel, are difficult to magnetize
They tend to retain their magnetism

5. Magnetic Fields A vector quantity Symbolized by B
Direction is given by the direction a north pole of a compass needle points in that location
Magnetic field lines can be used to show how the field lines, as traced out by a compass, would look

6. 20.1 Magnets and Magnetic Fields
Magnets have two ends – poles – called north and south.
Like poles repel; unlike poles attract.

7. 20.1 Magnets and Magnetic Fields
However, if you cut a magnet in half, you don’t get a north pole and a south pole – you get two smaller magnets.

8. 20.1 Magnets and Magnetic Fields
Magnetic fields can be visualized using magnetic field lines, which are always closed loops.

9. Magnetic Field Lines, sketch
A compass can be used to show the direction of the magnetic field lines (a)
A sketch of the magnetic field lines (b)

10. Magnetic Field Lines, Bar Magnet
Iron filings are used to show the pattern of the electric field lines
The direction of the field is the direction a north pole would point

11. Magnetic Field Lines, Unlike Poles
Iron filings are used to show the pattern of the electric field lines
The direction of the field is the direction a north pole would point
Compare to the electric field produced by an electric dipole

12. Magnetic Field Lines, Like Poles
Iron filings are used to show the pattern of the electric field lines
The direction of the field is the direction a north pole would point
Compare to the electric field produced by like charges

13. Domains, cont Random alignment, a, shows an unmagnetized material
When an external field is applied, the domains aligned with B grow, b

14. Earth’s Magnetic Field
The Earth’s magnetic field resembles that achieved by burying a huge bar magnet deep in the Earth’s interior

15. Earth’s Magnetic Declination
Declination is the difference between true north and
magnetic north as read by a compass
Earth’s magnetic field reverses every few million years
Migration patterns may be guided by Earth’s magnetic field

16. Magnetic Fields, cont
When moving through a magnetic field, a charged particle experiences a magnetic force.
One can define a magnetic field in terms of the magnetic force exerted on a test charge
Similar to the way electric fields are defined

17. Units of Magnetic Field
The SI unit of magnetic field is the Tesla (T)
Wb is a Weber
The cgs unit is a Gauss (G)
1 T = 104 G

18. Finding the Direction of Magnetic Force
Experiments show that the direction of the magnetic force is always perpendicular to both v and B
Fmax occurs when v is perpendicular to B
F = 0 when v is parallel to B

19. Right Hand Rule- for individual charges
Hold your right hand open
Place your fingers in the direction of B
Place your thumb in the direction of v
The direction of the force on a positive charge is directed out of your palm
If the charge is negative, the force is opposite that determined by the right hand rule

20. Force on a Wire
The blue x’s indicate the magnetic field is directed into the page
Blue dots would be used to represent the field directed out of the page
In this case, there is no current, so there is no force

21. Right Hand Rule- for current carrying wires
Hold your right hand open
Place your fingers in the direction of B
Place your thumb in the direction of I
The direction of the force is directed out of your palm

22. Force on a Wire B is into the page The current velocity is up the page
Point your fingers into the page
The current velocity is up the page
Point your thumb up the page
The force is to the left
Your palm should be pointing to the left

23. Force on a Wire, final B is into the page The current is down the page
Point your fingers into the page
The current is down the page
Point your thumb down the page
The force is to the right
Your palm should be pointing to the right

24. Force on a Wire, equation
The magnetic force is exerted on each moving charge in the wire
The total force is the sum of all the magnetic forces on all the individual charges producing the current
F = B I ℓ sin θ
θ is the angle between B and I
The direction is found by the right hand rule, pointing your thumb in the direction of I instead of v

25. 20.2 Electric Currents Produce Magnetic Fields
The direction of the field is given by a right-hand rule.

26. Electric Motor
An electric motor converts electrical energy to mechanical energy
The mechanical energy is in the form of rotational kinetic energy
An electric motor consists of a rigid current-carrying loop that rotates when placed in a magnetic field

27. Torque on a Current Loop
T = NBIAsinθ
Applies to any shape loop
N is the number of turns in the coil

28. Force on a Charged Particle in a Magnetic Field
Consider a particle moving in an external magnetic field so that its velocity is perpendicular to the field
The force is always directed toward the center of the circular path
The magnetic force causes a centripetal acceleration, changing the direction of the velocity of the particle

29. Force on a Charged Particle
Equating the magnetic and centripetal forces:
Solving for r:
r is proportional to the momentum of the particle and inversely proportional to the magnetic field

30. Bending an Electron Beam in an External Magnetic Field

31. Particle Moving in an External Magnetic Field, 2
If the particle’s velocity is not perpendicular to the field, the path followed by the particle is a spiral
The spiral path is called a helix

32. Magnetic Fields – Long Straight Wire
A current-carrying wire produces a magnetic field
The compass needle deflects in directions tangent to the circle
The compass needle points in the direction of the magnetic field produced by the current

33. Direction of the Field of a Long Straight Wire
Right Hand Rule #2
Grasp the wire in your right hand
Point your thumb in the direction of the current
Your fingers will curl in the direction of the field

34. Magnitude of the Field of a Long Straight Wire
The magnitude of the field at a distance r from a wire carrying a current of I is
µo = 4  x 10-7 T m / A
µo is called the permeability of free space
Equation for B is derived using Ampere’s Law

35. Magnetic Force Between Two Parallel Conductors
The force on wire 1 is due to the current in wire 1 and the magnetic field produced by wire 2
The force per unit length is:

36. Force Between Two Conductors, cont
Parallel conductors carrying currents in the same direction attract each other
Parallel conductors carrying currents in the opposite directions repel each other

37. Magnetic Field of a Current Loop – Total Field

38. Magnetic Field of a Solenoid
If a long straight wire is bent into a coil of several closely spaced loops, the resulting device is called a solenoid
It is also known as an electromagnet since it acts like a magnet only when it carries a current

39. 20.5 Magnetic Field Due to a Long Straight Wire
The field is inversely proportional to the distance from the wire:
(20-6)
The constant μ0 is called the permeability of free space, and has the value:

40. 20.6 Force between Two Parallel Wires
The magnetic field produced at the position of wire 2 due to the current in wire 1 is:
The force this field exerts on a length l2 of wire 2 is:
(20-7)

41. 20.6 Force between Two Parallel Wires
Parallel currents attract; antiparallel currents repel.

42. 20.7 Solenoids and Electromagnets
A solenoid is a long coil of wire. If it is tightly wrapped, the magnetic field in its interior is almost uniform:
(20-8)

43. 20.7 Solenoids and Electromagnets
If a piece of iron is inserted in the solenoid, the magnetic field greatly increases. Such electromagnets have many practical applications.

44. 20.10 Applications: Galvanometers, Motors, Loudspeakers
A galvanometer takes advantage of the torque on a current loop to measure current.

45. 20.10 Applications: Galvanometers, Motors, Loudspeakers
An electric motor also takes advantage of the torque on a current loop, to change electrical energy to mechanical energy.

46. 20.10 Applications: Galvanometers, Motors, Loudspeakers
Loudspeakers use the principle that a magnet exerts a force on a current-carrying wire to convert electrical signals into mechanical vibrations, producing sound.

47. 20.3 Force on an Electric Current in a Magnetic Field; Definition of B
A magnet exerts a force on a current-carrying wire. The direction of the force is given by a right-hand rule.

48. 20.11 Mass Spectrometer
A mass spectrometer measures the masses of atoms. If a charged particle is moving through perpendicular electric and magnetic fields, there is a particular speed at which it will not be deflected:

49. 20.11 Mass Spectrometer
All the atoms reaching the second magnetic field will have the same speed; their radius of curvature will depend on their mass.

50. Summary of Chapter 20 Magnets have north and south poles
Like poles repel, unlike attract
Unit of magnetic field: tesla
Electric currents produce magnetic fields
A magnetic field exerts a force on an electric current:

51. Summary of Chapter 20
A magnetic field exerts a force on a moving charge:
Magnitude of the field of a long, straight current-carrying wire:
Parallel currents attract; antiparallel currents repel

52. Summary of Chapter 20 Magnetic field inside a solenoid: Ampère’s law:
Torque on a current loop: