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Magnetism
Magnets
You have likely played
with magnets in the past.
But probably not very
formally.
Magnets are interesting
Origin:
• Magnetite is a naturally occurring
magnetic mineral
• First record of discovery of
properties from 2600 years ago
• Named after region where it was
discovered: the Greek island of
Magnesia
Magnets are interesting
Properties:
Magnets exert force on other magnets
from a distance:
1
𝐹𝑚𝑎𝑔𝑛𝑒𝑡𝑖𝑐 ∝
𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 2
~ Coulomb’s Law, but for magnets
The connection is closer than you think!
Thanks, Einstein (and Derek Muller for
explaining it so lucidly)
Magnets are interesting
Properties:
All magnets have north and south pole:
likes repel; opposites attract
If you were to split a magnet in two, you
would end with two magnets, each with a
north and south pole.
True even to the atomic level!
Magnetic field
The force exerted on other
objects can be described
with a ‘magnetic field’.
• Like the electric field,
imaginary but useful for
describing interactions
Magnetic field
Conventions
• Points away from north pole,
towards south pole
• Lines never cross
• Tighter lines = more intense
field
• “Flux”, 
Greek letter phi
• Pronounced ‘fee’
• Measures magnetic field strength per area
Magnets and currents
Magnetism is connected
to electricity
• In 1820, Danish scientist
Hans Christian Oersted
noticed deflection of
compass needle in
presence of electric
current.
• Laid the foundation for
Henry, Faraday, Maxwell,
Tesla, and Einstein.
A long wire carrying
current creates a circular
magnetic field
A loop of wire carrying
current creates a linear
magnetic field
See more: Magnetic Field Demonstrations Simple Wire Coils
Right-hand rule #1
1. Point your thumb in the direction
of the flow of current
1. by convention, from positive
terminal to negative terminal
2. Imagine curling the fingers of your
right-hand around the wire.
3. The circular magnetic field around
a long current-carrying wire goes
in the same direction as your
fingers.
Magnetic forces on moving charged
particles
Positively charged particles move
into page.
Passing through a magnetic field
goes from north to south (here:
right to left)
Moving particles experience
upward force.
Magnetic forces on moving charged
particles
Positively charged particles move
into page.
Passing through a magnetic field
goes from north to south (here:
left to right)
Moving particles experience
downward force.
Magnetic forces on moving charged
particles
Positively charged particles come
out of the page.
Passing through a magnetic field
goes from north to south (here:
right to left)
Moving particles experience
downward force.
Right-hand rule #2
1. Point your right forefinger in the
same direction as the movement
of charge.
2. Point your middle finger in
direction of magnetic field.
3. Your thumb points in the
direction of the force
POSITIVELY-charged moving
particles will experience.
In real life…
Walter Lewin ~10:00 – 11:50
Try it!
Positively charged particle come
out of page
Passing through a magnetic field
goes from north to south (here:
left to right)
In what direction will the
particles feel a force?
Try it
Negatively charged particles
move into page.
Passing through a magnetic field
goes from north to south (here:
right to left)
In what direction will the
particles feel a force?
Think about it…
Is this drawing accurate?
Applications
Televisions and mass
spectrometers use
precisely this physical
principal to work.
Mathematical model
Increase current  increase
force I  F
Increase length of wire exposed
to field  increase force
𝑙  F
Increase strength of magnetic
field  increase force
B  F
F = I 𝑙 B sinθ
Mathematical model
Force is greatest when  = 90.
Current running
perpendicular to magnetic
field experiences force.
Force is zero when  = 0
Current running parallel to
magnetic field experiences no
force.
F = I 𝑙 B sinθ
Quantifying magnetic field strength
𝐹𝑚𝑎𝑥 = I 𝑙 B
so, 𝐵 =
𝐹𝑚𝑎𝑥
𝐼𝑙
1.000 tesla is defined as the strength of the magnetic field that will
exert 1.000 N of force on 1.000 m of wire carrying 1.000 A.
𝒏𝒆𝒘𝒕𝒐𝒏
𝒕𝒆𝒔𝒍𝒂 =
𝒂𝒎𝒑𝒆𝒓𝒆 𝒎𝒆𝒕𝒆𝒓
𝑵
𝑻=
𝑨𝒎
How big is a tesla?
Factor
Example
10-12
Primates’ brains
10-9
Magnetic strength of heliosphere
10-6
Strength of magnetic tape near tape head
10-5
Strength of Earth’s magnetic field 31 T near
equator; 58 T @ 50
10-3
Strength of typical refrigerator magnet
100
Typical coil gap of typical loudspeaker
Strength of coin-sized neodymium magnet
101
Strength used to levitate frog
102
Strongest pulsed magnet produced in lab
106
Strength of neutron star
Example
A loop of wire (30 cm long and 10 cm
wide) is partially suspended in a
magnetic field and hangs from a scale
that reads zero when the current is
zero. If the scale reads 3.48 x 10-2 N
when current of 0.245 A passes
through the wires, calculate the
strength of the magnetic field. The
magnetic field points into the page.
Solution
Use the right-hand rule to compare
the direction of the force on the
downward portion of the loop with
the direction of the force on upward
portion of the loop.
Use the right-hand rule to determine
the direction of the force experienced
by the bottom portion of the loop.
Example
Try it first. Then delete this box.
F = I 𝑙 B sinθ
So B =
F
Try it first. Then delete this box.
I 𝑙 sinθ
3.45 x 10−2 𝑁
Try it first. Then delete this box.
B=
(02.45 A)(0.1 m)(sin 90°)
N
Try it first. Then delete this box.
B = 1.42
= 1.42 T
Am
This process is used to
precisely calculate the
strength of electric
fields.
Solution
What would the force on the coil be if
it were entirely inside the magnetic
field?
Mathematical model v2
𝐹𝑚𝑎𝑥 = I 𝑙 B
where I = Nq/t
l = vt
So, 𝐹𝑚𝑎𝑥 = NqvB
So, the force on each particle,
𝐹𝑚𝑎𝑥 = qvB
or
𝐹 = qvB sinθ
Example
A negative charge –Q is placed at rest near a magnet. In what direction
will it move?
In what direction would a positively charged particle +Q move?
@ v = 0 m/s, F = 0 N
It won’t move at all!
Try it first. Then delete this box.
Example
A proton moving vertically upward at a
speed of 5.0 x 106 m/s passes through a
magnetic field. When it passes through the
field, it experiences a 8.0 x 10-14 N push to
the west. If a northward-moving proton
experiences 0 N,
a) In what direction is the magnetic field in
this area?
b) How strong is the field in this area?
Solution - a
A proton moving vertically upward
passes through a magnetic field.
When it passes through the field, it
experiences a push to the west. A
magnetic field exerts a force
towards the west on a proton
moving vertically upward If a
northward-moving proton
experiences 0 N, in what direction
is the magnetic field in this area?
Experiences force to the west
By right-hand rule, upward
traveling positive charge
Try it first. westward
Then delete thisforce
box.
experiencing
must
be traveling through field pointing
north.
Solution - b
A proton moving at a speed of 5.0 x 106 m/s
experiences a 8.0 x 10-14 N push to the west. How
strong is the field in this area?
𝐹=
F
it first. Thenso,
delete𝐵
this=
box.
qvB Try
sinθ
q v sinθ
−14
𝐵=
8.0 x 10
N
Try it first. Then delete this box.
1.6 x
10−19 C
5.0 x
m
6
10
s
B=0.10 TTry it first. Then delete this box.
(sin90°)
This process is used to
precisely calculate the
charge and mass of
particles.
There’s more!
• Walter Lewin