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Magnetic Fields and
Electromagnetism
Chapter 24 and 26
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 direction—it detects
the earth’s magnetic field
• Use of magnets to aid in navigation can be traced back to at
least the eleventh century
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.
All magnetic
phenomena result
from forces between
electric charges in
motion.
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
S
N
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
monopoles—No 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
Like poles repel; Unlike poles attract
Like repels like…
Opposites attract!
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.
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
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).
Magnetic Domains
• Understanding
source of the
magnetic field
generated by bar
magnet lies in
understanding
currents at atomic
level within bulk
matter.
Orbits of electrons about nuclei
Intrinsic “spin” of
electrons (more
important effect)
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.
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.
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.
Magnetic
Domains
• “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
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.
S
N
End of paper clip
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.
Indicating Direction of Magnetic Field
• 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.
x x x x
x x x x x
x x x x x x
x x x x x
x x x x
. . . .
. . . . .
. . . . . .
. . . . .
. . . .
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 / (2πr)
where
–
–
–
–
µo, permeability of free space = 4π 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
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 (Δ l).
Note the component of B that
is parallel to Δ l and take the
product of the two to be B∥Δ 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
Dl
B
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.
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.
Force on a current carrying wire
• Moving charges experience a force in a magnetic field, so a currentcarrying 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.
General Case: field at angle q relative to current.
Fmax  BIl sin q
B
B sin q
q
I
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
I=0
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
I
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
I
Force on two current carrying wire
• 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.
•
Force from other
(teal) wire is shown
if two parallel wires have
currents traveling in opposite In red above
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
(blue) wire is shown
In red below
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 = qvBsinq
+q
v
B= F/qvsinq
Right Hand Rule
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 = qvBsinq
– q is the angle between the field and the velocity. If the angle is zero, sin q 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.
+q
v
B
v
B
+q
• 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/qvsinq
Motion of Charged Particle in magnetic field
• Consider positively charge particle
moving in a uniform magnetic field.
mv 2
• Suppose the initial velocity of the ´ ´ ´F  ´qvB ´ ´ ´
r
particle is perpendicular to the
q
direction of the field.
v
r
• Then a magnetic force will be
´
´ ´ F´
´ ´ ´
exerted on the particle and make
follow a circular path.
´
´ ´
´
´ ´ ´
• The magnetic force produces a
centripetal acceleration
Bin
• The particle travels on a circular mv
´
´ ´
´
´ ´ ´
r
trajectory with a radius:
qB
• Magnetic forces do NOT do any work
on moving charges since F and v are
perpendicular.
Thomson’s 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:
Thomson’s 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:
Thomson’s 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.
Electric Motor
• An electric motor, is a machine which converts electrical
energy into mechanical (rotational or kinetic) energy.
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.
Electric Motor - Torque on a Current Loop
• Imagine a current loop in a magnetic field as follows:
I
B
B
F
F
a/2
b
F
F
a
F1  F2  BIb
 max  F1 a2  F2 a2   BIb  a2   BIb  a2
 max  BIba  BIA
  BIAsin q
Electric Motor - Torque on a Current Loop
  NBIAsin q
• In a motor, one has “N” loops of current
q 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”
Electric Motor
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.
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.
Northern Lights
• The solar wind is constantly bombarding the Earth’s
magnetic field. Sometimes these charged particles
penetrate that field. These particles are found in two
large regions known as the Van Allen Belts.
Northern Lights
• The Earth’s 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.
Electric Field vs. Magnetic Field
Source
Acts on
Force
Direction
Electric
Magnetic
Charges
Charges
F = Eq
Parallel E
Moving Charges
Moving Charges
F = q v B sin(q)
Perpendicular to v,B
Sources
• http://www.physics.wayne.edu/~apetrov/PHY2140/#
lectures
• Physics by Zitzewitz
• http://dev.physicslab.org/Document.aspx?doctype=3
&filename=Magnetism_CurrentCarryingWires.xml
• http://www.cliffsnotes.com/WileyCDA/CliffsReviewT
opic/Electromagnetic-Forces-andFields.topicArticleId-10453,articleId-10435.html
• http://digilander.libero.it/mfinotes/VEuropeo/Physic
s/thomson.htm