Magnetic Fields and Electromagnetism

1
Magnetic Fields and Electromagnetism

• Chapter 24 and 26

2
Magnetism

• The word magnetism comes from the Greek word for
  a certain type of stone (lodestone) containing
  iron oxide found in Magnesia, a district in
  northern Greece.
• The Greeks and the Chinese found lodestone could
  exert forces on similar stones and could impart
  this property (magnetize) to a piece of iron it
  touched
• And that a small sliver of lodestone suspended
  with a string will always align itself in a
  north-south directionit detects the earths
  magnetic field
• Use of magnets to aid in navigation can be traced
  back to at least the eleventh century

3
Magnetism - History

• Not until 1819 was a connection between
  electrical and magnetic phenomena shown. Danish
  scientist Hans Christian Oersted observed that a
  compass needle in the vicinity of a wire carrying
  electrical current was deflected!
• In 1831, Michael Faraday discovered that a
  momentary current existed in a circuit when the
  current in a nearby circuit was started or
  stopped
• Shortly thereafter, he discovered that motion of
  a magnet toward or away from a circuit could
  produce the same effect.

4
All magnetic phenomena result from forces between
electric charges in motion.
5
Magnetic Poles

• Magnets have at least one north pole and one
  south pole.  By convention, we say that the
  magnetic field lines leave the North end of a
  magnet and enter the South end of a magnet. 
• Like electric field lines, increased density
  indicates increased magnetic field.
• The ends of a magnet are where the magnetic
  effect is the strongest. These are called
  poles.

Magnetic Field Lines of a bar magnet
6
For every North, there is a South

• Poles of a magnet always come in pairs!
• Even an individual electron has a magnetic
  dipole!
• Although there have been many searches for
  magnetic monopolesNo monopoles have ever been
  found!
• If you take a bar magnet and break it into two
  pieces, each piece will again have a North pole
  and a South pole.  If you take one of those
  pieces and break it into two, each of the smaller
  pieces will have a North pole and a South pole. 
  No matter how small the pieces of the magnet
  become, each piece will have a North pole and a
  South pole. 

S
N
S
N
S
N
7
Like poles repel Unlike poles attract
Like repels like
Opposites attract!
8
The Earth is like a giant magnet!

• The nickel iron core of the earth gives the earth
  a magnetic field much like a bar magnet.
• The north pole of the compass magnet is attracted
  to the magnetic south pole of the Earth.

9
Magnetic Field Lines

• Michael Faraday realized that a magnet has a
  magnetic field distributed throughout the
  surrounding space
• Magnetic field lines describe the structure of
  magnetic fields in three dimensions. They are
  defined as follows If at any point on such a
  line we place an ideal compass needle, free to
  turn in any direction (unlike the usual compass
  needle, which stays horizontal) then the needle
  will always point along the field line.
• Field lines converge where the magnetic force is
  strong, and spread out where it is weak.
• By convention, we say that the magnetic field
  lines leave the North end of a magnet and enter
  the South end of a magnet. 
• Small pieces of iron or small compasses can be
  used to visualize the magnetic field

Field Lines Around a Magnetic Sphere
10
Magnetic Fields

• A stationary charge has an electric field around
  it a moving charge has an electric and a
  magnetic field around it and exerts a force on
  any other charge moving through the magnetic
  field.
• Magnetic fields are vector quantities.that is,
  they have a magnitude and a direction.
• Magnetic Field vectors as written as B or B
• Direction of magnetic field at any point is
  defined as the direction of motion of a charged
  particle on which the magnetic field would not
  exert a force.
• Magnitude of the B-vector is proportional to the
  force acting on the moving charge, magnitude of
  the moving charge, the magnitude of its velocity,
  and the angle between v and the B-field.
• Unit is the Tesla or the Gauss (1 T 10,000 G).

11
Magnetic Domains

• Understanding source of the magnetic field
  generated by bar magnet lies in understanding
  currents at atomic level within bulk matter.

Intrinsic spin of electrons (more important
effect)
12
Magnetic Domains

• Magnetic substances like iron, cobalt, and nickel
  have unpaired spins, in these substances there
  can be small areas where the groups of atoms are
  aligned (unpaired spins pointing in the same
  direction). These regions of aligned atoms are
  called domains.
• All of the domains of a magnetic substance tend
  to align themselves in the same direction when
  placed in a magnetic field. These domains are
  typically composed of billions of atoms.

13
Magnetic Materials

• Materials can be classified by how they respond
  to an applied magnetic field, Bapp.
• Paramagnetic (aluminum, tungsten, oxygen,)
• Atomic magnetic dipoles (atomic bar magnets)
  tend to line up with the field, increasing it.
  But thermal motion randomizes their directions,
  so only a small effect persists.
• Diamagnetic (gold, copper, water,)
• The applied field induces an opposing field
  again, this is usually very weak. Exception
  Superconductors exhibit perfect diamagnetism ?
  they exclude all magnetic fields
• Ferromagnetic (iron, cobalt, nickel,)
• Somewhat like paramagnetic, the dipoles prefer to
  line up with the applied field. But there is a
  complicated collective effect due to strong
  interactions between neighboring dipoles ? they
  tend to all line up the same way.

14
Ferromagnets

• Even in the absence of an applied B, the dipoles
  tend to strongly align over small patches
  domains. Applying an external field, the
  domains align to produce a large net
  magnetization.
• Soft ferromagnets
• The domains re-randomize when the field is
  removed
• Hard ferromagnets
• The domains persist even when the field is
  removed
• Permanent magnets
• Domains may be aligned in a different direction
  by applying a new field
• Domains may be re-randomized by sudden physical
  shock
• If the temperature is raised above the Curie
  point (770 for iron), the domains will also
  randomize ? paramagnet

15
How does a magnet attract screws, paper clips,
refrigerators, etc., when they are not magnetic?

• The materials are all soft ferromagnets. The
  external field temporarily aligns the domains so
  there is a net dipole, which is then attracted to
  the bar magnet.
• - The effect vanishes with no applied B field
• - It does not matter which pole is used.

16
Electromagnetism

• When an electric current passes through a wire a
  magnetic field is formed.
• When an electric current is passed through a coil
  of wire wrapped around a metal core, a very
  strong magnetic field is produced. This is called
  an electromagnet.

17
Indicating Direction of Magnetic Field
x x x x x x x x x x x x x
x x x x x x x x x x x

• If B is directed into the page we use crosses
  representing the tail of arrows indicating the
  direction of the field,
• If B is directed out of the page, we use dots.
• If B is in the page, we use lines with arrow
  heads.

. . . . . . . . . . . . .
. . . . . . . . . . .
18
Magnetic Field near a current-carrying wire

• In this diagram, the solid teal circle in the
  center represents a cross-section of a
  current-carrying wire in which the current is
  coming out of the plane of the paper.
• The concentric circles surrounding the wire's
  cross-section represent magnetic field lines.
• The rule to determine the direction of the
  magnetic field lines is called the right hand
  curl rule.  In this rule, your thumb points in
  the direction of the current fingers curl in the
  direction of B
• The equation to calculate the strength of the
  magnetic field around a current-carrying wire is
  B perpendicular µoI / (2pr) where
• µo, permeability of free space  4p x 10-7 Tm/A
• I, current flowing through the wire, measured
  in amps
• B, magnetic field strength, measured in Tesla
• r, distance from the wire, measured in meters

19
Ampere's law

• Ampere's law allows the calculation of magnetic
  fields.
• Consider the circular path around the current
  shown below. The path is divided into small
  elements of length (? l). Note the component of B
  that is parallel to ? l and take the product of
  the two to be B?? l. Ampere's law states that the
  sum of these products over the closed path equals
  the product of the current and µ
  or
• For a long straight wire

I
r
B
Dl
20
Magnetic Field near a coil
When a current carrying conductor is formed into
a loop or several loops to form a coil, a
magnetic field develops that flows through the
center of the loop or coil along its longitudinal
axis and circles back around the outside of the
loop or coil. The magnetic field circling each
loop of wire combines with the fields from the
other loops to produce a concentrated field down
the center of the coil.
The strength of a coil's magnetic field increases
not only with increasing current but also with
each loop that is added to the coil. A long,
straight coil of wire is called a solenoid and
can be used to generate a nearly uniform magnetic
field similar to that of a bar magnet.
21
Direction of Magnetic Field near a coil
Second right hand rule Imagine holding an
insulated coil with your right hand. Curl your
fingers around the loops in the direction of the
conventional current. Your thumb points toward
the N-pole of the electromagnet.
22
Force on a current carrying wire

• Moving charges experience a force in a magnetic
  field, so a current-carrying wire will experience
  such a force, since a current consists of moving
  charges.
• The interaction between the magnetic field of the
  wire and the external magnetic field is exhibited
  by a force which is calculated with the formula
  Fmax BIL where B is the external,
  perpendicular magnetic field measured in Tesla, I
  is the current measured in amps, and L is the
  length of the current segment (in meters) that
  lies in the external magnetic field, B.

23
General Case field at angle q relative to
current.
B
B sin q
q
I
24
Force on a wire carrying current in a magnetic
field
Bin
x x x x x x x x x x x x x
x x x x x x x x x x x
x x x x x x x x x x x x x
x x x x x x x x x x x
x x x x x x x x x x x x x
x x x x x x x x x x x
Bin
Bin
I
I 0
I
25
Force on two current carrying wire
Force from other (blue) wire is shown In red below

• If two parallel wires have currents traveling in
  the same direction, the magnetic fields generated
  by those currents between the wires will both
  point in opposite directions resulting in the
  wires attracting each other.
• if two parallel wires have currents traveling in
  opposite directions, the magnetic fields
  generated by those currents between the wires
  will both point in the same direction, in this
  case, into the plane of the page. These wires
  would repel each other.

Force from other (teal) wire is shown In red above
26
Force on a single charged particle

• Another right hand rule! This one provides a
  convenient trick to remember the spatial
  relationship between F, v, and B.
• If the moving charge is negative instead of
  positive, the direction of the force is opposite
  to that predicted by the right hand rule.
• The direction of the magnetic force is always at
  right angle to the plane formed by the velocity
  vector v and the magnetic field B.

F
B
F qvBsin?
q
B F/qvsin?
v
27
Right Hand Rule
28
Magnetic Fields Direction and Magnitude

• Direction of magnetic field at any point is
  defined as the direction of motion of a charged
  particle on which the magnetic field would not
  exert a force. F qvBsin?
• ? is the angle between the field and the
  velocity. If the angle is zero, sin ? is zero and
  there is no force. The component of velocity of
  the charged particle that is parallel to the
  magnetic field is unaffected, i.e. the charge
  moves at a constant speed along the direction of
  the magnetic field.
• Magnitude of the B-vector is proportional to the
  force acting on the moving charge, magnitude of
  the moving charge, the magnitude of its velocity,
  and the angle between v and the B-field.
  B F/qvsin?

q
B
v
B
v
q
29
Motion of Charged Particle in magnetic field

• Consider positively charge particle moving in a
  uniform magnetic field.
• Suppose the initial velocity of the particle is
  perpendicular to the direction of the field.
• Then a magnetic force will be exerted on the
  particle and make follow a circular path.
• The magnetic force produces a centripetal
  acceleration
• The particle travels on a circular trajectory
  with a radius
• Magnetic forces do NOT do any work on moving
  charges since F and v are perpendicular.

r
Bin
30
Thomsons Experiments

• The discovery of the electron. Near the end of
  the nineteenth century scientists suspected that
  electrical phenomena were produced by tiny
  charged particles. J. J. Thomson (1856-1940)
  proved this fact with an experiment on cathode
  rays.
• He called these particles ELECTRONS and made the
  first step in determining their physical
  properties by measuring their charge-mass ratio
  (q/m). To do this, he built a special and
  completely evacuated tube like the one below

31
Thomsons Experiments

• Thomson knew that electrons could be deflected by
  a magnetic field.
• And by balancing the magnetic and electric
  forces, kept the electron beam flowing along the
  original direction
• This relationship let him to compute the velocity
  of each electron through the ratio of the two
  balanced fields

32
Thomsons Experiments

• If the electric field is turned off, on the force
  due to the magnetic field remains.
• The magnetic force is perpendicular to the
  direction of motion and the electrons follow a
  circular path with radius R.
• The magnetic force is a centripetal force so
• Solving for q/m results in the charge to mass
  ratio for an electron
• Thomson was also able to find the q/m for a
  positive ions and determine the mass of a proton.

33
Electric Motor

• An electric motor, is a machine which converts
  electrical energy into mechanical (rotational or
  kinetic) energy.  

34
Electric Motor

• A current is passed through a loop which is
  immersed in a magnetic field. A force exists on
  the top leg of the loop which pulls the loop out
  of the paper, while a force on the bottom leg of
  the loop pushes the loop into the paper

The net effect of these forces is to rotate the
loop.
35
Electric Motor - Torque on a Current Loop

• Imagine a current loop in a magnetic field as
  follows

36
Electric Motor - Torque on a Current Loop

• In a motor, one has N loops of current
• ? is the angle between normal to the plane of the
  loop and the direction of the magnetic field and
  A is the area of the loop

37
Electric Motor
38
Brushes on the DC motor
To keep the torque on a DC motor from reversing
every time the coil moves through the plane
perpendicular to the magnetic field, a split-ring
device called a commutator is used to reverse the
current at that point. The electrical contacts to
the rotating ring are called "brushes" since
copper brush contacts were used in early motors.
39
Galvanometer

• A galvanometer is an electromagnet that interacts
  with a permanent magnet. The stronger the
  electric current passing through the
  electromagnet, the more is interacts with the
  permanent magnet.

Galvanometers are used as gauges in cars and many
other applications.
The greater the current passing through the
wires, the stronger the galvanometer interacts
with the permanent magnet.
40
Northern Lights

• The solar wind is constantly bombarding the
  Earths magnetic field. Sometimes these charged
  particles penetrate that field. These particles
  are found in two large regions known as the Van
  Allen Belts.

41
Northern Lights

• The Earths magnetic field extends far into
  space. It is called the magnetosphere. When
  the magnetic particles from the sun, called
  solar wind, strike this magnetosphere, we see a
  phenomenon called ..

Northern Lights.
42
Electric Field vs. Magnetic Field
Electric Magnetic Source Charges Moving
Charges Acts on Charges Moving
Charges Force F Eq F q v B
sin(q) Direction Parallel
E Perpendicular to v,B
43
Sources

• http//www.physics.wayne.edu/apetrov/PHY2140/lec
  tures
• Physics by Zitzewitz
• http//dev.physicslab.org/Document.aspx?doctype3
  filenameMagnetism_CurrentCarryingWires.xml
• http//www.cliffsnotes.com/WileyCDA/CliffsReviewTo
  pic/Electromagnetic-Forces-and-Fields.topicArticle
  Id-10453,articleId-10435.html
• http//digilander.libero.it/mfinotes/VEuropeo/Phys
  ics/thomson.htm