The magnetic field is weak above the top wire of the current loop because the top and bottom lengths of wire produce magnetic fields in opposite directions (one into the page and one out of the page), which cancel each other out. So at a point directly above the wire, the net magnetic field is small.

1. MAGNETISM
• History of Magnetism • Sources of Magnetism
• Bar Magnets • Spin & Orbital Dipole
Moments
• Magnetic Dipoles
• Permanent Magnets
• Magnetic Fields
• Earth’s Magnetic Field
• Magnetic Forces on
Moving Charges and Wires • Magnetic Flux
• Electric Motors • Induced Emf and Current
• Current Loops and • Generators
Electromagnets
• Crossed Fields
• Solenoids

2. History of Magnetism
• The first known magnets were naturally occurring lodestones, a type
of iron ore called magnetite (Fe3O4). People of ancient Greece and
China discovered that a lodestone would always align itself in a
longitudinal direction if it was allowed to rotate freely. This property
of lodestones allowed for the creation of compasses two thousand
years ago, which was the first known use of the magnet.
• In 1263 Pierre de Maricourt mapped the magnetic field of a lodestone
with a compass. He discovered that a magnet had two magnetic poles
North and South poles.
• In the 1600's William Gilbert, physician of Queen Elizabeth I,
concluded that Earth itself is a giant magnet.
• In 1820 the Danish physicist Hans Christian Ørsted discovered an
electric current flowing through a wire can cause a compass needle to
deflect, showing that magnetism and electricity were related.

3. History (cont.)
• In 1830 Michael Faraday (British) and Joseph Henry (American)
independently discovered that a changing magnetic field produced a current
in a coil of wire. Faraday, who was perhaps the greatest experimentalist of
all time, came up with the idea of electric and magnetic “fields.” He also
invented the dynamo (a generator), made major contributions to chemistry,
and invented one of the first electric motors
• In the 19th century James Clerk Maxwell, a Scottish physicist and one of
the great theoreticians of all times, mathematically unified the electric and
magnetic forces. He also proposed that light was electromagnetic radiation.
• In the late 19th century Pierre Curie discovered that magnets loose their
magnetism above a certain temperature that later became known as the
Curie point.
• In the 1900's scientists discover superconductivity. Superconductors are
materials that have a zero resistance to a current flowing through them
when they are a very low temperature. They also exclude magnetic field

4. Magnetic Dipoles
Recall that an electric dipole consists
of two equal but opposite charges - +
separated by some distance, such as in
_
a polar molecule. Every magnet is a
magnetic dipole. A bar magnet is a
simple example. Note how the E field Electric dipole and E field
due an electric dipole is just like the
magnetic field (B field) of a bar
magnet. Field lines emanate from the
+ or N pole and reenter the - or S
pole. Although they look the same,
they are different kinds of fields. E S N
fields affect any charge in the
vicinity, but a B field only affects
moving charges. As with charges,
opposite poles attract and like poles Magnetic dipole and B field

5. Magnetic Monopole Don’ t Exist
We have studied electric fields to due isolated + or - charges, but as
far as we know, magnetic monopole do not exist, meaning it is
impossible to isolate a N or S pole. The bar magnet on the left is
surrounded by iron filings, which orient themselves according to the
magnetic field they are in. When we try to separate the two poles by
breaking the magnet, we only succeed in producing two distinct
dipoles (pic on right). Bar magnet demo

6. Magnetic Fields
You have seen that electric fields and be uniform, nonuniform and
symmetric, or nonuniform and asymmetric. The same is true for
magnetic fields. (Later we’ll see how to produce uniform
magnetic fields with a current flowing through a coil called a
solenoid.) Regardless of symmetry or complexity, the SI unit for
any E field is the N/C, since by definition an electric field is force
per unit charge. Because there are no magnetic monopoles, there
is no analogous definition for B. However, regardless of
symmetry or complexity, there is only one SI unit for a B field. It
is called a tesla and its symbol is T. The coming slides will show
how to write a tesla in terms of other SI units. The magnetic field
vector is always tangent to the magnetic field. Unlike E fields, all
magnetic field lines that come from the N pole must land on the S
pole--no field lines go to or come from infinity.

7. Force Due to Magnetic Field
The force exerted on a charged particle by a magnetic field is given
by the vector cross product:
F = qv ×B
F = force (vector)
q = charge on the particle (scalar)
v = velocity of the particle relative to field (vector)
B = magnetic field (vector)
Recall that the magnitude of a cross is the product of the
magnitudes of the vectors times the sine of the angle between
them. So, the magnitude of the magnetic force is given by
F = q v B sinθ
where θ is angle between q v and B vectors.

8. Cross Product Review
Let v1 = 〈 x1, y1, z1 〉 and v2 = 〈 x2, y2, z2 〉 .
By definition, the cross product of these vectors (pronounced “v1
cross v2”) is given by the following determinant.
i j k
v1 × v2 = x1 y1 z1
x2 y2 z2
= (y1 z2 - y2 z1) i - (x1 z2 - x2 z1) j + (x1 y2 - x2 y1) k
Note that the cross product of two vectors is a vector itself that is
⊥ to each of the original vectors. i, j, and k are the unit vectors
pointing, along the positive x, y, and z axes, respectively. (See the
vector presentation for a review of determinants.)

9. Right Hand Rule Review
A quick way to determine the direction of a cross product is to
use the right hand rule. To find a × b, place the knife edge of
your right hand (pinky side) along a and curl your hand toward
b, making a fist. Your thumb then points in the direction ofa × b.
a× b
It can be proven that the magnitude of
a × b is given by:
|a× b|= a b sinθ b
where θ is the angle between φ
a and b. a

10. Magnetic Field Units
F = q v B sinθ
1 N = 1 C (m / s) (T)
From the formula for magnetic force we can find a relationship
between the tesla and other SI units. The sine of an angle has no
units, so
1N 1N
1T = =
C (m / s) Am
A magnetic field of one tesla is very powerful magnetic field.
Sometimes it may be convenient to use the gauss, which is
equal to 1/10,000 of a tesla. Earth’s magnetic field, at the
surface, varies but has the strength of about one gauss.

11. Direction of Magnetic Field & Force
Near the poles, where the field lines are close together, the field is very strong (so
the field vector are drawn longer). Anywhere in the field the mag. field vector is
always tangent to the mag. field line there. The + charge in the pic in moving into
the page. Since q is +, the q v vector is also into the page. The - charge
is moving to the right, so the q v vector is to the left. The mag. force vector is
always ⊥ to plane formed by the q v vector and the B vector.
B
The force on the - charge is into F
the page. If a charge is motionless
relative to the field, there is no
magnetic force on it, but if either a + - v
magnet is moving or a charge is
moving, there could a force on the
B
charge. If a charge moves parallel
to a magnetic field, there is no
magnetic force on it, since
sin 0° = 0.

12. Magnetic Field & Force Practice
Find the direction of the magnetic force or velocity:
1. A + charge at P is moving out of the page.
2. A - charge at Q is moving out of the page.
3. A - charge at Q is moving to the right.
4. A + charge at Q is moving up.
5. A - charge at R is
moving up and to the left.
6. A + charge at R is moving
down and to the right. P
7. A - charge at R feels a
force into the page.
8. A + charge at P feels a
force out of the page.
R
9. A - charge at Q feels an Q
upward force.

13. Magnetic Force Sample Problem
This magnet is similar to a parallel plate capacitor in that there is a strong uniform
field between its poles with some fringing on the sides. Suppose the magnetic field
strength inside is 0.07 T and a 4.3 mC charge is moving through the field at right
angle to the field lines. How strong and which way is the magnetic force on the
charge? Answer:
F = qv ×B ⇒ F = q v B
since sin 90° = 1.
S
5 m/s
+
N N So, F = 0.0015 N
directed out of the page.

14. Motion of a Charge in a Magnetic Field
The ×’s represent field lines pointing into the page. A positively charged
particle of mass m and charge q is shot to the right with speed v. By the
right hand rule the magnetic force on it is up. Since v is ⊥ to B,
F = FB = q v B. Because F is ⊥ to v, it has no tangential component; it is
entirely centripetal. Thus F causes a centripetal acceleration. As the particle
turns so do v and F, and if B is uniform the particle moves in a circle. This
is the basic idea behind a particle accelerator like Fermilab. Since F is a
centripetal force, F = FC = m v2 / R. Let’s see how speed, mass, charge,
× × × × × × × × × × × × × field strength, and radius of
curvature are related:
× × × × × × × × × × × × ×
R
× × × × × × × × × × × × × FB = FC
× × × × × × × × × × × × ×
× × × × × F
× × × × × × × × ⇒ q v B = m v2 / R
× × × × × × × × × × × × × mv
B
× × × × × ×+ × × × × × × × ⇒ R=
q, m v qB
× × × × × × × × × × × × ×

15. Magnetic Force on a Current Carrying Wire
A section of wire carrying current to the right is shown in a uniform magnetic
field. We can imagine positive charges moving to right, each feeling a magnetic
force out of the page. This will cause the wire to bow outwards. Shown on the
right is the view as seen when looking at the N pole from above. The dots
represent a uniform mag. field coming out of the
page. The mag. force on the
wire is proportional to the
field strength, the current,
S and the length of the wire.
I ............
............
............
............
. .I . . . . . . . . . .
............
N B
Continued…

16. Magnetic Force on a Wire (cont.)
Current is the flow of positive charge. As a certain amount of
charge, q, moves with speed v through a wire of length L, the force
of this quantity of charge is:
F = qv × B
Over the time period t required for the charge to traverse the length
of the wire, we have:
............
F = (q / t ) v t × B ............
............
............
Since q / t = I and v t = L, we can . .I . . . . . . . . . .
write: ............
F = IL × B B
where L is a vector of magnitude L pointing in the direction of I.

17. Electric Motor I
F
I }d
I
I B
Current along with a magnetic field can produce torque. This is the basic idea behind
an electric motor. Above is a wire loop (purple) carrying a current provided by some
power source like a battery. The current loop is submerged in an external field. From
F = I L × B, the force vectors in black are perpendicular to their wire segments. The
net force on the loop is zero, but the net torque about the center is nonzero. The forces
on the left and right wires produce no torque since the moment arm is zero for each
(they point right at the center). However, the force F on the top wire (in the
background) has a moment arm d, so it produces a torque F d. The bottom wire (in
the foreground) produces the same torque. These torques work together to rotate the
loop, converting electrical energy into mechanical energy. Continued…

18. Electric Motor (cont.)
As the loop turns it eventually reaches a vertical position (the plane of
the loop parallel to the field). This is when the moment arms of the
forces on the top and bottom wires are the longest, so this is where
the torque is at a max. 90° later the loop will be perpendicular to the
field. Here all moment arms and all torques are zero. This is the
equilibrium point. The angular momentum of the loop, however, will
allow it to swing right through this position.
Now is when the current must change direction, otherwise the torques
will attempt to bring the loop back to the equilibrium. This would
amount to simple harmonic motion of the loop, which is not
particularly useful. If the current changes direction every time the
loop reach equilibrium, the loop will spin around in the same
direction indefinitely. Although a battery only pumps current in one
direction, the change in direction of current can be accomplished with
help of a commutator, as can be seen with these animations:
Animation 1 Animation 2

19. Electromagnets: Straight Wire
Permanent magnets aren’t the only things that produce magnetic fields. Moving
charges themselves produce magnetic fields. We just saw that a current carrying
wire feels a force when inside an external magnetic field. It also produces its own
mag-netic field. A long straight wire produces circular field lines centered on the
wire. To find the direction of the field, we use another right hand rule: point your
thumb in the direction of the current; the way your fingers of your right hand wrap is
the direction of the magnetic field. B diminishes with distance from the wire. The
pics at the right
I show cross sections of a current carrying
wire.
I out of page, I into page,
B counterclockwise B clockwise
B ×

20. Straight Wire Practice
Draw some magnetic field lines (loops in this case) along the wire.
I
Using x’s and dots to represent vectors out of and into the page,
show the magnetic field for the same wire. Note B diminishes with
distance from the wire.
. . . . . . . . . . . .
B out of page
. . . . . . . . . . . .
. . . . . . . . . . . . I
× × × × × × × × × × ×
B into page × × × × × × × × × × ×
× × × × × × × × × × ×

21. Current Loops and Magnetic Fields
The magnetic field inside a current loop tends to be strong; outside, it tends to be
weak. Here’s why: Using the right hand rule we see that each length of wire
contributes to a B field into the page (all lengths reinforcing one another). Outside
the loop, say at P, the field is weak since the left side of the wire produces a field
out of the page, but the right side produces a field into the page. Explain why the
field is weak above the top wire. The situation is the same with a circular loop. The
effect is magnified with multiple turns of wire. Yet another right hand rule helps
with current loops: Wrap your right hand in the direction of the loop and your
thumb points in the direction of B inside. This is reminiscent of angular momentum
for a spinning body.
I I
strong field I
I strong field
P inside loop,
into page
weak field directed into
outside page
weak field
I

22. Current Loops and Bar Magnets
Notice how similar the magnetic field of a
current loop is to that of a simple bar magnet.
Wrap your right hand along the loop in the
direction of the current and your thumb points in
the direction of the north pole of your electro-
magnet. Note also how the field lines are very
close together inside the loop, just as they are
when they thread through a bar magnet.
I

23. Solenoids
• Solenoids are one of the most common
electromagnets.
• Solenoids consist of a tightly wrapped
coil of wire, sometimes around an iron
core. The multiple loops and the iron
magnify the effect of the single loop
electromagnet.
• A solenoid behaves as just like a simple
bar magnet but only when current is
flowing.
• The greater the current and the more
turns per unit length, the greater the
field inside.
• An ideal solenoid has a perfectly uniform
magnetic field inside and zero field
outside.

24. Wire Direction
How Solenoids Work Sections of B
The cross section of a solenoid is shown.
At point P inside the solenoid, the B field 1-3 Up & Right
is a vector sum of the fields due to each 4 Right
section of wire. Note from the table that 5-8 Down & Right
each section of wire produce a field vector
with a component to the right, resulting in 9-11 Down & Right
a strong field inside. In the ideal case the 12 Right
magnetic field would be uniform inside
13-16 Up & Right
and zero outside.
B=0
1 2 3 4 5 6 7 8
I out of the page
B P
x x x x x x x x I into the page
9 10 11 12 13 14 15 16

25. Solenoids and Bar Magnets
A solenoid produces a magnetic field just like a simple bar magnet.
Since it consists of many current loops, the resemblance to a bar
magnet’s field is much better than that of a single current loop.

26. Sources of Magnetism
We have seen charges in motion (as in a current) produce magnetic
fields. This is one source of magnetism.
Another source is the electron itself. Electrons behave as if they were
tiny magnets. Quantum mechanics is required to explain fully the
magnetic properties of electrons, but it is helpful to relate these
properties back to the motion of charges. Every electron in an atom
behaves as a magnet in two ways, each having two magnetic dipole
moments:
Spin magnetic dipole moment - due to the “rotation” of an electron.
Orbital magnetic dipole moment - due to the “revolution” of an
electron about the nucleus.
Note: Electrons are not actually little balls that rotate and revolve like
planets, but imagining them this way is useful when explaining
magnetism without quantum mechanics.

27. Spin Magnetic Dipole Moment
Just as electrons have the intrinsic properties of mass and charge, they have an intrinsic
property called spin. This means that electrons, by their very nature, possess these three
attributes. You’re already comfortable with the notions of charge and mass. To
understand spin it will be helpful to think of an electron as a rotating sphere or planet.
However, this is no more than a helpful visual tool.
Imagine an electron as a soccer ball smeared with negative charge rotating about an axis.
By the right hand rule, the angular momentum of the ball due to its rotation points down.
But since its charge is negative, the spinning ball is like a little current loop flowing in
the direction opposite its rotation, and the ball becomes an electromagnet with the N
pole up. For an electron we would say its spin magnetic dipole moment vector, μs,
points up. Because of its spin, an electron is like a little bar magnet.
μs
- -- -
N
-- I S
- -

28. Orbital Magnetic Dipole Moment
Imagine now a planet that not only rotates but also revolves around its star. If the
planet had a net charge, its rotation would give it a spin magnetic dipole moment,
and its revolution would give it an orbital magnetic dipole moment. Charge in
motion once again produces a magnetic field.
Since an electron’s charge is negative, its orbit is like a current loop in the opposite
direction. By the right hand rule, the angular momentum vector in the pic below
would point down and the orbital magnetic dipole moment, μorb, points up. An
orbiting electron behaves like a tiny electromagnet with its N pole in the direction of
μorb. Remember, though, that in reality electrons are not like little planets. In
quantum mechanics, instead of circular orbits we speak of electrons behaving like
waves and we can only talk of their positions in terms of
probabilities.
μorb N
S
- I

29. Materials and Magnetism
• Each electron in an atom has two magnetic dipole moments associated with it,
one for spin, and one for orbit. Each is a vector.
• These two dipole moments combine vectorially for each electron.
• The resultant vectors from each electron then combine for the whole atom,
often canceling each other out.
• For most materials the net dipole moment for each atom is about zero.
• For some materials each atom has a nonzero dipole moment, but because the
atoms have all different orientations, the material as a whole remains
nonmagnetic.
• Ferromagnetic materials, like iron, are comprised of atoms that each have net
dipole moment. Furthermore, all the atoms have the same alignment, at least
within very tiny regions called domains. The domains can have different
orientations, though, leaving the iron nonmagnetic except when placed in an
external field.
• Permanent magnets are produced when the domains in a ferromagnetic
material are aligned.

30. Permanent Magnets
Each atom in a ferromagnetic material Lets melt the iron, and
like iron is like a little magnet, and bring in a magnetic field. Temp
these magnets are all aligned in tiny
regions called domains. At high temps Now, when we let the solid
Melting
these domains can align in the cool down, and take away
point
presence of an external field (like the external magnetic field,
Earth’s) leaving a permanent magnet. we have formed a perma-
This happens at the Mid-Atlantic nent magnet in the same
Ridge beneath the Atlantic Ocean. direction as external field.
Domains
Bar Magnet

31. Earth’s Magnetic
Earth’s field looks similar to what we’d
Field expect if there were a giant bar magnet
imbedded inside it, but the dipole axis of this
11.5°
magnet is offset from the axis of rotation by
11.5°. Also, the south pole of this magnet is
near the geographic north pole, NG. A
compass points in the direction of the
NM NG magnetic north pole, NM, around which the
field lines reenter Earth’s surface. (Magnetic
north is actually the south pole of Earth’s
S magnetic dipole.) NM, which is currently
located in Greenland, drifts about over the
centuries. About every million years Earth’s
field reverses entirely, as we know from the
N orientations of magnetic fields near the Mid-
Atlantic Ridge. The field is likely due to the
μorb motion of charged particles in the fluid outer
core, and it protects us from an otherwise

32. Magnetic Fields: Overview
Although the magnetic properties of electrons must ultimately be
explained with quantum mechanics, we can think of magnetism
arising whenever we have charge in motion. This motion can be that
of an electron (either spinning or orbiting) or it can be in the form of
a current. Remember: moving charges produce magnetic fields, and
external magnetic fields exert a magnetic force on moving charges
(at least if the charge has a component of its velocity perpendicular
to the field).

33. Magnetic Flux
Magnetic flux, informally speaking, is a measure of the amount of magnetic field
lines going through an area. If the field is uniform, flux is given by:
ФB = B · A = B A cosθ
The area vector in the dot product is a vector that points A
perpendicular to the surface and has a magnitude equal θ
to the area of the surface.
Imagine you’re trying to orient a window so as to allow
the maximum amount of light to pass through it. To do
this you would, of course, align A with the light rays.
With θ = 0, cosθ = 1, and the number of light rays
passing through the window (the flux) is a max. Note:
with the window oriented parallel to the rays, θ = 90°
and ФB = 0 (no light enters the window).
The SI unit for magnetic flux is the tesla-square meter:
T m2. This is also know as a weber (Wb).

34. Changing Magnetic Flux
• A changing magnetic flux in a wire loop induces an electric current.
• The induced current is always in a direction that opposes the change
in flux.
These facts were discovered by Michael Faraday and represent a key connection
between electricity and magnetism. One simple example of this is a magnet
moving in and out of a wire loop. As a bar magnet approaches a wire loop along a
line perpendicular to the loop, more and more field lines poke through the loop and
the flux increases. To oppose this change in flux a current is induced in the
direction shown. Note that the induced
current produces its own
magnetic field pointing to the
right. Also note that there is no
battery in the loop! This current
N S will only exist when the flux
inside the loop changes. When
the magnet is withdrawn the flux
v decreases and current is induced
I
in the other direction. There is no
Java script current when the magnet is still.

35. Induced emf’s and Currents
The current induced in a loop come not from a battery but from a changing
magnetic flux. We can think of the loop containing an imaginary battery that
gets turned on whenever flux in the loop changes. The strength of this
battery is called the emf (electromotive force); it’s symbol is a script E: ,
and it’s measured in volts. The induced current is given by:
I =  /R where R is the internal resistance in the loop.
 itself depends on the rate at which the flux inside the loop is changing. If
the flux is changing at a constant rate,
This Faraday’s law. The negative sign here
 = - ∆ФB / ∆t indicates the emf opposes the change in flux.
The greater the change in flux the greater, the greater the induced emf, and
greater the induced current.

36. Electromagnetic Induction: Practice
For each scenario determine the direction of the induced emf and current.
wire loop
.... × × × ........
.... ........
.... × × ×
× × × ×
........
B very large
B increasing B decreasing
but constant
× × ×
× × ×
× × × ×
B increasing B decreasing B increasing

37. Induction: Nonuniform, Static Fields
y B is static (constant in time). It is uniform in
×
×
×
×
× × × × ×
× × × × ×
space in the y and z directions but not in the
×
×
×
×
×
x direction. B decreases as x increases. As
the rectangular loop is moved in the following
×
×
×
×
×
directions, determine the direction of the
×
×
×
×
×
induced emf and current as well as the direction
×
×
×
×
×
×
of the net force on the loop by the field.
x
Loop motion: 1. Left 2. Right 3. Up 4. Down 5. In 6. Out
. . . . . . B is uniform here but only in the region
. . . . . . shown. Beyond this region B is
. . . . . . approximately zero. As the loop is pulled
. . . . . . out of the field determine the direction of
. . . . . . the induced emf and current as well as the
. . . . . . direction of the net force on the loop. Do
the same as the loop is pushed into the field.

38. Electric Generators
In a motor we have seen that a current loop in an external magnetic field produces
a torque on the loop. In a generator we’ll see that a torque on a current loop inside
a magnetic field produces a current. In summary:
Motor: Current + Magnetic field → Torque
Generator: Torque + Magnetic field → Current
Turbines in a power plant are usually rotated either by a waterfall or by steam
created heat produced from nuclear power or the burning of coal. As the turbines
rotate, current loops turn through a magnetic field to generate electricity. This
process converts mechanical energy into electrical energy.
The simplest form of an electric generator is called an alternating current
(AC) generator. The current produced by an AC generator switches directions
every time the wire inside of it is rotated through a half turn. In the United
States, generator generally have a frequency of 60 Hz, which means the
current switches direction 120 times every second! A graph of the current
output from an AC generator produces a sinusoidal curve due to the periodic
nature of the generator’s rotation. Continued…

39. Electric
Generator
(cont.)
Animation
B
Iinduced
As a turbine turns (due to some power source like coal) a current loop (purple) is
rotated inside a magnetic field. The field is static but as the loop turns as the
number of field lines poking through it changes. Thus we have a changing flux and
a corresponding induced emf and current. The pic shows a loop just after it was
horizontal (perpendicular to the field). The flux is decreasing since the loop is
becoming more vertical. Since fewer field lines are entering the loop, the induced
current is in a direction to produce more field lines downward. Just prior to this, as
the loop was approaching horizontal, the number of field lines inside it was
increasing, so the current was in the other direction to oppose this change. The
current changes direction twice with each turn--whenever the loop is horizontal.
The result here is AC, but (direct current) DC motors exist as well in which current
only flows in one direction.

40. Electric & Magnetic Fields
Picture tubes in standard televisions are basically cathode ray tubes (CRT’s). In a
CRT electrons are shot from a hot filament into a region of “crossed fields” in
which a magnetic field is perpendicular to an electric field. On the other side of
the crossed fields is a fluorescent screen (not shown) where electrons produce
spots of light when they make contact with it. J. J. Thompson used a CRT to
discover the electron in 1897. When the charge
enters the fields, FE is up and FB + + + + + + + + + +
is down. By adjusting B and × × × × × × ×
measuring the deflection of the B× × × × × ×
electrons, Thompson determined
that they were negatively charged × × × × × × ×
and calculated their mass to charge
ratio. Let’s find a relationship × × × × × × ×
between q, B, and E v × × × × × ×
if there is no deflection - × × × × × × ×
at all: q, m
× × × × × × E
Fnet = 0 ⇒ FB = FE ×
× × × × × × ×
E
⇒ qvB = qE ⇒ v = - - - - - - - - - - -
B

41. Credits
How speakers work http://www.geo.umn.edu/orgs/irm/bestiary/index.html
Bestiary of magnetic minerals http://sprott.physics.wisc.edu/demobook/chapter5.htm
History of magnets http://www.webmineral.com/data/Magnetite.shtml
Magnetite http://pupgg.princeton.edu/~phys104/2000/lectures/lecture4/sld001.htm
Slide show http://www.physics.umd.edu/deptinfo/facilities/lecdem/demolst.htm
Best ever site for pictures, simple explanations, etc. http://www.trifield.com/magnetic_fields.htm
Another good site for how magnets work http://bell.mma.edu/~mdickins/TechPhys2/lectures3.html
Equations and such http://schools.moe.edu.sg/xinmin/lessons/physics/default.htm
See also:
http://www.micro.magnet.fsu.edu/electromag/java/index.html
http://www.micro.magnet.fsu.edu/electromag/java/detector/
How a metal detector works http://www.micro.magnet.fsu.edu/electromag/java/compass/
How a compass is oriented magnetically http://www.micro.magnet.fsu.edu/electromag/java/faraday2/
How Faraday did his current experiment http://www.micro.magnet.fsu.edu/electromag/java/harddrive/
How a hard drive works http://www.micro.magnet.fsu.edu/electromag/java/magneticlines/
How magnet lines is working http://www.micro.magnet.fsu.edu/electromag/java/magneticlines2/
How two magnets repel and attract
http://www.micro.magnet.fsu.edu/electromag/java/nmr/populations/index.html
Nuclear spin up/down http://www.micro.magnet.fsu.edu/electromag/java/pulsedmagnet/
Pulsed magnets http://www.micro.magnet.fsu.edu/electromag/java/speaker/
http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/elemag.html http://library.thinkquest.org/16600/intermediate/magnetism.shtml
http://www-geology.ucdavis.edu/~gel161/sp98_burgmann/magnetics/magnetics.html
http://www.micro.magnet.fsu.edu/electromag/java/index.html http://webphysics.davidson.edu/Applets/BField/Solenoid.html
http://www.ameslab.gov/News/Inquiry/spring96/spin.html http://cfi.lbl.gov/~budinger/medTechdocs/MRI.html
http://www.wondermagnet.com/dev/images/dipole1.jpg