Magnetism

1
Chapter 19

• Magnetism

2
Magnets

• In each magnet there are two poles present (the
  ends where objects are most strongly attracted)
  north and south
• Like (unlike) poles repel (attract) each other
  (similar to electric charges)
• Magnetic poles cannot be isolated if a
  permanent magnetic is cut in half, you will still
  have a north and a south pole (unlike electric
  charges)
• There is some theoretical basis for monopoles,
  but none have been detected

3
Magnetism

• An unmagnetized piece of iron can be magnetized
  by stroking it with a magnet (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
• Soft magnetic materials (such as iron) are easily
  magnetized and also tend to lose their magnetism
  easily
• Hard magnetic materials (such as cobalt and
  nickel) are difficult to magnetize and they tend
  to retain their magnetism

4
Magnetic Fields

• The region of space surrounding a moving charge
  includes a magnetic field (the charge will also
  be surrounded by an electric field)
• A magnetic field surrounds a properly magnetized
  magnetic material
• A magnetic field is a vector quantity symbolized
  by B
• Its direction is given by the direction a north
  pole of a compass needle pointing in that
  location
• Magnetic field lines can be used to show how the
  field lines, as traced out by a compass, would
  look

5
Magnetic Field Lines

• A compass can be used to show the direction of
  the magnetic field lines

6
Magnetic Field Lines

• Iron filings can also be used to show the pattern
  of the magnetic field lines
• The direction of the field is the direction a
  north pole would point
• Unlike poles (compare to the electric field
  produced by an electric dipole)

7
Magnetic Field Lines

• Iron filings can also be used to show the pattern
  of the magnetic field lines
• The direction of the field is the direction a
  north pole would point
• Unlike poles (compare to the electric field
  produced by an electric dipole)
• Like poles (compare to the electric field
  produced by like charges)

8
Earths Magnetic Field

• The Earths geographic north (south) pole
  corresponds to a magnetic south (north) pole a
  north (south) pole should be a north- (south-)
  seeking pole

• The Earths magnetic field resembles that
  achieved by burying a huge bar magnet deep in the
  Earths interior
• The most likely source of the Earths magnetic
  field electric currents in the liquid part of
  the core

9
Earths Magnetic Field

• The magnetic and geographic poles are not in the
  same exact location magnetic declination is the
  difference between true north (geographic north
  pole) and magnetic north pole

• The amount of declination varies by location on
  the earths surface
• The direction of the Earths magnetic field
  reverses every few million years (the origin of
  these reversals is not understood)

10
Earths Magnetic Field

• If a compass is free to rotate vertically as well
  as horizontally, it points to the earths surface
• The angle between the horizontal and the
  direction of the magnetic field is called the dip
  angle
• The farther north the device is moved, the
  farther from horizontal the compass needle would
  be
• The compass needle would be horizontal at the
  equator and the dip angle would be 0
• The compass needle would point straight down at
  the south magnetic pole and the dip angle would
  be 90

11
Magnetic Fields

• When moving through a magnetic field, a charged
  particle experiences a magnetic force
• This force has a maximum (zero) value when the
  charge moves perpendicularly to (along) the
  magnetic field lines
• Magnetic field is defined in terms of the
  magnetic force exerted on a test charge moving in
  the field with velocity v
• The SI unit Tesla (T)

12
Magnetic Fields

• Conventional laboratory magnets 2.5 T
• Superconducting magnets 30 T
• Earths magnetic field 5 x 10-5 T

13
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 and F
  0 when v is parallel to B
• Right Hand Rule 1 (for a charge) Place your
  fingers in the direction of v and curl the
  fingers in the direction of B your thumb points
  in the direction of F
• If the charge is negative, the force points in
  the opposite direction

14
Direction of Magnetic Force

• The blue xs indicate the magnetic field when it
  is directed into the page (the x represents the
  tail of the arrow)
• Blue dots would be used to represent the field
  directed out of the page (the represents the
  head of the arrow)

15
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

16
Force on a Charged Particle in a Magnetic Field

• This expression is known as the cyclotron
  equation
• r is proportional to the momentum of the particle
  and inversely proportional to the magnetic field
• If the particles velocity is not perpendicular
  to the field, the path followed by the particle
  is a spiral (helix)

17
Chapter 19Problem 9

• A proton moves perpendicularly to a uniform
  magnetic field at 1.0 107 m/s and exhibits an
  acceleration of 2.0 1013 m/s2 in the
  x-direction when its velocity is in the
  z-direction. Determine the magnitude and
  direction of the field.

18
Chapter 19Problem 28

• A cosmic-ray proton in interstellar space has an
  energy of 10.0 MeV and executes a circular orbit
  having a radius equal to that of Mercurys orbit
  around the Sun (5.80 1010 m). What is the
  magnetic field in that region of space?

19
Magnetic Force on a Current Carrying Wire

• The current is a collection of many charged
  particles in motion
• 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
• Therefore a force is exerted on a
  current-carrying wire placed in a magnetic field

20
Magnetic Force on a Current Carrying Wire

• The direction of the force is given by right hand
  rule 1, placing your fingers in the direction of
  I instead of v

21
Chapter 19Problem 19

• An unusual message delivery system is pictured in
  the figure. A 15-cm length of conductor that is
  free to move is held in place between two thin
  conductors. When a 5.0-A current is directed as
  shown in the figure, the wire segment moves
  upward at a constant velocity. If the mass of the
  wire is 15 g, find the magnitude and direction of
  the minimum magnetic field that is required to
  move the wire. (The wire slides without friction
  on the two vertical conductors.)

22
Torque on a Current Loop
23
Torque on a Current Loop

• Applies to any shape loop
• Torque has a maximum value when q 90
• Torque is zero when the field is perpendicular to
  the plane of the loop

24
Chapter 19Problem 26

• A copper wire is 8.00 m long and has a
  cross-sectional area of 1.00 10-4 m2. The wire
  forms a one-turn loop in the shape of square and
  is then connected to a battery that applies a
  potential difference of 0.100 V. If the loop is
  placed in a uniform magnetic field of magnitude
  0.400 T, what is the maximum torque that can act
  on it? The resistivity of copper is 1.70 10-8 O
  m.

25
Magnetic Moment

• The vector is called the magnetic moment of
  the coil
• Its magnitude is given by µ IAN
• The vector always points perpendicular to the
  plane of the loop(s)
• The equation for the magnetic torque can be
  written as t BIAN sin? µB sin?
• The angle is between the moment and the field

26
Electric Motor

• An electric motor converts electrical energy to
  mechanical energy (rotational kinetic energy)
• An electric motor consists of a rigid
  current-carrying loop that rotates when placed in
  a magnetic field

• The torque acting on the loop will tend to rotate
  the loop to smaller values of ? until the torque
  becomes 0 at ? 0

27
Electric Motor

• If the loop turns past this point and the current
  remains in the same direction, the torque
  reverses and turns the loop in the opposite
  direction
• To provide continuous rotation in one direction,
  the current in the loop must periodically reverse

• In ac motors, this reversal naturally occurs
• In dc motors, a split-ring commutator and brushes
  are used

28
Electric Motor

• Just as the loop becomes perpendicular to the
  magnetic field and the torque becomes 0, inertia
  carries the loop forward and the brushes cross
  the gaps in the ring, causing the current loop to
  reverse its direction

• This provides more torque to continue the
  rotation
• The process repeats itself
• Actual motors would contain many current loops
  and commutators

29
Magnetic Fields Long Straight Wire

• A current-carrying wire produces a magnetic field
• The compass needle points in the direction of the
  magnetic field produced by the current
  (tangential to the circle)
• Right Hand Rule 2 Grasp the wire in your right
  hand and point your thumb in the direction of the
  current
• Your fingers will curl in the direction of the
  field

30
Magnetic Fields 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 permeability of free
  space

31
Ampères Law

• Ampères Circuital Law a procedure for deriving
  the relationship between the current in an
  arbitrarily shaped wire and the magnetic field
  produced by the wire
• Choose an arbitrary closed path around the
  current and sum all the products of B ?l
  around the closed path
• ? B ?l µo I

32
Ampères Law for a Long Straight Wire

• Use a closed circular path
• The circumference of the circle is 2? r
• ? B ?l µo I
• B ? ?l B 2? r µo I

33
Chapter 19Problem 42

• A long, straight wire lies on a horizontal table
  and carries a current of 1.20 µA. In a vacuum, a
  proton moves parallel to the wire (opposite the
  direction of the current) with a constant
  velocity of 2.30 104 m/s at a constant distance
  d above the wire. Determine the value of d. (You
  may ignore the magnetic field due to Earth.)

34
Magnetic Force Between Two Parallel Conductors
35
Magnetic Force Between Two Parallel Conductors

• The force (per unit length ) on wire 1 due to the
  current in wire 1 and the magnetic field produced
  by wire 2
• Parallel conductors carrying currents in the same
  direction attract each other
• Parallel conductors carrying currents in the
  opposite directions repel each other

36
Ampere and Coulomb revisited

• The force between parallel conductors can be used
  to define the Ampere (A) If two long, parallel
  wires 1 m apart carry the same current, and the
  magnitude of the magnetic force per unit length
  is 2 x 10-7 N/m, then the current is defined to
  be 1 A
• The SI unit of charge, the Coulomb (C), can be
  defined in terms of the Ampere If a conductor
  carries a steady current of 1 A, then the
  quantity of charge that flows through any cross
  section in 1 second is 1 C

37
Chapter 19Problem 45

• A wire with a weight per unit length of 0.080 N/m
  is suspended directly above a second wire. The
  top wire carries a current of 30.0 A and the
  bottom wire carries a current of 60.0 A. Find the
  distance of separation between the wires so that
  the top wire will be held in place by magnetic
  repulsion.

38
Magnetic Field of a Current Loop

• The strength of a magnetic field produced by a
  wire can be enhanced by forming the wire into a
  loop
• All the segments, ?x, contribute to the field,
  increasing its strength

39
Magnetic Field of a Current Loop

• The magnitude of the magnetic field at the center
  of a circular loop with a radius R and carrying
  current I is
• With N loops in the coil, this becomes

40
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
• The field inside the solenoid is nearly uniform
  and strong the field lines are nearly parallel,
  uniformly spaced, and close together
• The exterior field is nonuniform, much weaker,
  and in the opposite direction to the field inside
  the solenoid

41
Magnetic Field of a Solenoid

• The field lines of the solenoid resemble those of
  a bar magnet
• The magnitude of the field inside a solenoid is
  approximately constant at all points far from its
  ends
• B µo n I
• n N / l the number of turns per unit length
• The same result can be obtained by applying
  Ampères Law to the solenoid

42
Magnetic Field of a Solenoid

• A cross-sectional view of a tightly wound
  solenoid
• If the solenoid is long compared to its radius,
  we assume the field inside is uniform and outside
  is zero
• Apply Ampères Law to the blue dashed rectangle

43
Magnetic Effects of Electrons Orbits

• An individual atom should act like a magnet
  because of the motion of the electrons about the
  nucleus
• Each electron circles the atom once in about
  every 10-16 seconds this would produce a current
  of 1.6 mA and a magnetic field of about 20 T at
  the center of the circular path
• However, the magnetic field produced by one
  electron in an atom is often canceled by an
  oppositely revolving electron in the same atom
• The net result is that the magnetic effect
  produced by electrons orbiting the nucleus is
  either zero or very small for most materials

44
Magnetic Effects of Electrons Spins

• Electrons also have spin (it is a quantum effect)
• The classical model is to consider the electrons
  to spin like tops
• The field due to the spinning is generally
  stronger than the field due to the orbital motion
• Electrons usually pair up with their spins
  opposite each other, so their fields cancel each
  other, hence most materials are not naturally
  magnetic

45
Magnetic Effects of Electrons Domains

• In some materials ferromagnetic the spins do
  not naturally cancel
• Large groups of atoms in which the spins are
  aligned are called domains
• When an external field is applied, it causes the
  material to become magnetized the domains that
  are aligned with the field tend to grow at the
  expense of the others

46
Domains and Permanent Magnets

• In hard magnetic materials, the domains remain
  aligned after the external field is removed
• The result is a permanent magnet
• In soft magnetic materials, once the external
  field is removed, thermal agitation causes the
  materials to quickly return to an unmagnetized
  state
• With a core in a loop, the magnetic field is
  enhanced since the domains in the core material
  align, increasing the magnetic field

47

• Answers to Even Numbered Problems
• Chapter 19
• Problem 2
• in plane of page and to left into the page out
  of the page in plane of page and toward the top
  into the page out of the page
• the answers for part (b) are reversed from those
  given in part (a)

48
Answers to Even Numbered Problems Chapter 19
Problem 22 4.33 10-3 N m
49

• Answers to Even Numbered Problems
• Chapter 19
• Problem 34
• toward the left
• out of the page
• lower left to upper right

50

• Answers to Even Numbered Problems
• Chapter 19
• Problem 38
• 40.0 µT into the page
• 5.00 µT out of the page
• 1.67 µT out of the page

51

• Answers to Even Numbered Problems
• Chapter 19
• Problem 44
• 2.00 10-4 N / m, attracted
• 2.00 10-4 N / m, repelled