The Magnetic Field

1
The Magnetic Field

• Physics
• Montwood High School
• R. Casao

2

• Our most familiar experience of magnetism is
  through permanent magnets.
• Inside a magnetized body, such as a permanent
  magnet, there is a coordinated motion of certain
  electrons in an unmagnetized body, the electron
  motions are not coordinated.
• These are made of materials which exhibit a
  property we call ferromagnetism - i.e., they
  can be magnetized.
• An unmagnetized piece of iron can become a
  permanent magnet by being stroked with a
  permanent magnet
• If a piece of unmagnetized iron is placed near a
  strong permanent magnet, the piece of iron will
  eventually become magnetized.
• A magnetized object can lose its magnetic
  properties by heating and cooling the iron or by
  hammering the iron.

3

• Magnetic materials can be described as hard or
  soft, depending upon the extent to which they
  retain their magnetism.
• Soft magnetic materials, such as iron, are easily
  magnetized but also tend to lose their magnetism
  easily.
• Hard magnetic materials, like cobalt and nickel,
  are difficult to magnetize, but once they are
  magnetized, they tend to retain their magnetism.
• The magnetic properties of many materials are
  explained in terms of a model in which an
  electron is said to spin on its axis (remember
  the up and down arrows in the orbital notation
  you used in chemistry ??).
• The spinning electron is a charge in motion that
  produces a magnetic field.

4

• In atoms with many electrons, the electrons
  usually pair up with their spins opposite each
  other, and their magnetic fields cancel each
  other. This is why most substances are not
  magnetic.
• In ferromagnetic materials such as iron, cobalt,
  and nickel, the magnetic fields produced by the
  electron spins do not cancel completely.
• Strong coupling occurs between neighboring atoms
  to form large groups of atoms whose net spins are
  aligned these groups are called domains.
• In an unmagnetized substance, the magnetic
  domains are randomly oriented.
• In magnetized materials, whether
• permanent or temporary, the domains
• are aligned.

5

• unmagnetized
• magnetized

6

• In hard magnetic materials, the domain alignment
  remains after the external magnetic field is
  removed.
• In soft magnetic materials, once the magnetic
  field is removed, the random motion of the
  particles in the material changes the orientation
  of the domains back to a random arrangement.
• Heating and hammering can cause the domains in
  hard magnetic materials to become randomly
  arranged, resulting in a loss of the permanent
  magnetic properties.
• Depending on how we position two magnets, they
  will attract or repel, i.e. they exert forces on
  each other.
• Thus, a magnet must have an associated field
• a magnetic field.
• We describe magnets as having two magnetic poles
  North (N) and South (S).
• Magnetic poles always occur in pairs.

7

• When a magnet is broken in half, equal and
  opposite poles appear at either side of the break
  point.
• The result is two magnets, each with a north and
  south pole.

8

• A compass is used to detect the presence of a
  magnetic field.
• The needle of a compass is a piece of magnetized
  iron.
• The compass needle aligns with the magnetic field
  at the needles position.
• The north pole of a compass needle is attracted
  toward the geographic north pole of the Earth and
  repelled by the Earths geographic south pole.
• An object that contains iron but is not itself
  magnetized (shows no tendency to point north or
  south) is attracted by either pole of a permanent
  magnet.
• This is the attraction that acts between a magnet
  and the unmagnetized steel door of a refrigerator.

9

• Only iron and a few other materials, such as
  cobalt, nickel, gadolinium, and some of their
  oxides and alloys, show strong magnetic effects
  and are said to be ferromagnetic.
• Other materials show more slight magnetic effect.
• The Earth itself is a large magnet.
• Geophysicists generally agree
• that the Earths magnetic poles
• arise from currents in its molten
• iron core.
• The magnetic poles are offset
• slightly from the geographic
• poles of the Earths rotation axis.
• The geographic north pole is actually a
• south magnetic pole.

10
(No Transcript)
11

• We used the concept of an electric field
  surrounding an electric charge.
• Similarly, we can imagine a magnetic field
  surrounding a magnet.
• The force one magnet exerts on another can be
  described as the interaction between one magnet
  and the magnetic field of the other.
• We can also draw magnetic field lines.
• For magnetic field lines
• The number of lines per unit area is proportional
  to the strength of the magnetic field. The field
  lines are closer together where the magnetic
  field is stronger.
• The direction of the magnetic field is tangent to
  a field line at any point.

12

• The direction of the magnetic field at a given
  point is defined as the direction that the north
  pole of a compass needle would point if placed at
  that point.
• Magnetic field lines always point out from the
  north pole and toward the south pole of a
  magnet.
• Magnetic field lines continue inside the magnet
  to form closed loops.

13
(No Transcript)
14
(No Transcript)
15

• The origin of magnetism lies in moving electric
  charges.
• Moving (or rotating) charges generate magnetic
  fields in the surrounding space in addition to
  its electric field.
• An electric current generates a magnetic field.
• A magnetic field will exert a force on a moving
  charge that is present in the field.
• A magnetic field will exert a force on a
• conductor that carries an electric current
• in the field.
• The magnetic field is a vector field
• associated with each point in space.
• The symbol for the magnetic field if B.

16

• We can define a magnetic field B at a point in
  space in terms of the magnetic force FB that the
  field exerts on a charged particle moving with a
  velocity v.
• Experiments on charged particles moving in a
  magnetic field give the following results
• The magnitude FB of the magnetic force exerted on
  the particle is proportional to the magnitude of
  the charge q.
• If a 1 µC charge and a 2 µC charge move through
  the same magnetic field with the same velocity,
  experiments show that the force on the 2 µC
  charge is twice as great as the force on the 1 µC
  charge.
• The magnitude FB of the magnetic force exerted on
  the particle is proportional to the magnitude, or
  strength, of the field B.
• If we double the magnitude of the field without
  changing the charge or its velocity, the force
  doubles.

17

• The magnitude FB of the magnetic force exerted on
  the particle is proportional to the speed v of
  the particle.
• A charged particle at rest experiences no
  magnetic force.
• The magnetic force FB does not have the same
  direction as the magnetic field B but instead is
  always perpendicular to both B and the velocity
  v.
• The magnitude FB of the magnetic force is
  proportional to the component of the velocity
  perpendicular to the field. The maximum magnetic
  force FB occurs when the magnetic field B and the
  velocity v are at right angles to each other.
• The magnetic force FB is zero when the magnetic
  field B and the velocity v are parallel (0º) or
  antiparallel (180º).

18
(No Transcript)
19

• The direction of FB is always perpendicular to
  the plane containing B and v.
• Equation
• q is the magnitude of the charge (drop any
  negative signs on charges)
• ? is the angle between the direction of v and the
  direction of B.

20

• The direction of the magnetic force FB is given
  by the right hand rule
• Point the fingers of your right hand in the
  direction of the velocity vector v.
• Point the palm of your right hand in the
  direction of the magnetic field vector B.
• The thumb of your right hand points in the
  direction of the magnetic force FB.

21
Casaos Version of the Right-Hand Rule

• I use the right hand as described for positive
  charges. No change here.
• I use the left hand for negative
• charges.
• Point the fingers of the left hand
• in the direction of the velocity
• vector v.
• Point the palm of the left hand
• in the direction of the magnetic
• field vector B.
• The thumb of the left hand points
• in the direction of the magnetic
• force FB.

22

• If the magnetic field B is directed into the
  page, crosses represent the tail of the vector
  arrow.
• If the magnetic field B is directed out of the
  page, dots represent the head of the vector
  arrow.
• The units of the magnetic field B is the Tesla
  and the abbreviation is T.
• An older unit for the magnetic field is the Gauss
  (1 G 0.0001 T).

23
Magnetic Force on a Current-Carrying Conductor

• A magnetic force is exerted on a single charged
  particle when the particle moves through a
  magnetic field, so a current-carrying wire placed
  in a magnetic field also experiences a magnetic
  force.
• Current is a collection of many charged particles
  in motion, so the resultant force exerted by the
  magnetic field in the wire is the sum of the
  individual forces exerted on all the charged
  particles making up the current.
• The force exerted on the particles is transmitted
  to the wire when the particles collide with the
  atoms making up the wire.

24

• The force on a current-carrying conductor can be
  demonstrated by hanging a wire between the poles
  of a magnet.

25

• Equation
• l is the length of the wire in the magnetic
  field.
• ? is the angle between the length of the wire (or
  the direction of the current) and the magnetic
  field.
• The direction of the magnetic force is found
  using the right hand rule.
• Fingers in the direction of I.
• Palm in direction of B.
• Thumb points in direction of FB.

26

• A current consists of charge carriers q moving
  with velocity v.

27
Magnetic field around a long, straight
current-carrying wire
28
Forces Between Two Current-Carrying Wires

• Currents traveling in the same direction result
  in an attractive force acting between the two
  wires.
• Currents traveling in opposite directions through
  two wires produce a repulsive force between the
  two wires.

29

• Force between two parallel
• 
  wires
• µo 4p x 10-7 Tm/A
• l length of conducting wire
• d distance between wires

30
Motion of a Charged Particle in a Uniform
Magnetic Field

• When a charged particle traveling with velocity v
  enters a uniform magnetic field perpendicular to
  the magnetic field, the particle moves in a
  circle in a plane perpendicular to the magnetic
  field.
• The particle moves in a circle
• because the magnetic force FB is
• at right angles to v and B and has
• a constant magnitude qvB.
• As the force deflects the particle,
• the directions of v and FB change
• continuously.

31

• Because FB always points toward the center of the
  circle, it changes only the direction of the
  velocity and does not affect the magnitude of the
  velocity.
• Motion of a charged particle under the action of
  a magnetic field alone is always motion with
  constant speed.
• The right hand rule can be used to
• determine the direction of the force
• acting on the charged particle.
• Because the particle moves under
• the influence of a constant force
• that is always at right angles to the
• velocity of the particle, the path
• is a circle of constant speed v.

32

• The inward directed magnetic force FB provides
  the centripetal force FC to keep the particle
  traveling in a circular path.

33
Magnetic Field of a Current-Carrying Wire

• A current-carrying wire produces a magnetic field
  and can be detected by a compass needle placed
  near the wire.
• When no current is in the wire, all needles point
  in the direction of the Earths magnetic field.
• When the wire carries a strong, steady current,
  the needles deflect in directions tangent to the
  circle around the wire, pointing in the direction
  of the magnetic field B due to the wire.

34

• A current-carrying wire produces a magnetic field
  and can be detected by a compass needle placed
  near the wire.
• When no current is in the wire, all needles point
  in the direction of the Earths magnetic field.
• When the wire carries a strong, steady current,
  the needles deflect in directions tangent to the
  circle around the wire, pointing in the direction
  of the magnetic field B due to the wire.
• If the current is reversed, the needles reverse
  directions.

35

• Right hand rule for determining the direction of
  the magnetic field around a current carrying
  wire if the wire is grasped in the right hand
  with the thumb in the direction of the current I,
  the fingers will curl around the wire in the
  direction of the magnetic field B.
• The magnetic field lines form concentric circles
  around the wire.

36

• The magnitude of B is the same everywhere on a
  circular path centered on the wire and lying in a
  plane perpendicular to the wire.

37

• The magnetic field strength increases as the
  current I increases.
• The magnetic field strength decreases as the
  distance from the wire increases.
• Equation where
  r is the distance from the
• 
  wire to the location of the
• 
  magnetic field

38
Current Loops and Solenoids

• The right hand rule can also be applied to find
  the direction of the magnetic field of a
  current-carrying loop.
• No matter where on the loop you apply the right
  hand rule, the field within the loop points in
  the same direction.

39

• If a long, straight wire is bent into a coil of
  several closely spaced loops, the resulting
  device is called a solenoid.

40

• Solenoids produce a strong magnetic field by
  combining several loops.
• The solenoid has many applications because it
  acts as a magnet when it carries a current.
• The magnetic field inside a solenoid increases
  with the current and the number of coils per unit
  length.
• The magnetic field of a solenoid can be increased
  by inserting an iron rod through the center of
  the coil this device is often called an
  electromagnet.
• The magnetic field that is induced in the iron
  rod adds to the magnetic field of the solenoid,
  creating a more powerful magnet.

41

• In a car or truck, the starter solenoid helps to
  start the vehicle. The starter solenoid receives
  a large electric current from the battery and a
  small electric current from the ignition switch.
• When the ignition switch is turned on (when the
  key is turned to start the car), the small
  electric current forces the starter solenoid to
  close a pair of heavy contacts, thus relaying the
  large electric current to the starter motor.
• If a starter solenoid receives insufficient power
  from the battery, it will fail to start the
  motor, and may produce a rapid 'clicking' or
  'clacking' sound.
• This can be caused by a low or dead battery, by
  corroded or loose connections in the cable, or by
  a broken or damaged positive (red) cable from the
  battery.

42

• Any of these will result in some power to the
  solenoid, but not enough to hold the heavy
  contacts closed, so the starter motor itself
  never spins, and the engine is not rotated and
  does not start.

43

• Magnetic field inside a solenoid
• ?o 4p x 10-7
• The quantity is the number of turns per
  unit length l
• Magnetic field B inside a solenoid