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Magnetism
Magnetic materials have the ability to attract or repel other types of magnetic
materials.
But not all materials
are magnetic
The origin of magnetism is moving electrical charge. Electrons move around
the nucleus in electrons clouds, but they also spin around their own axis.
Atoms of non-magnetic materials have a
balance of electrons that spin clockwise
and counterclockwise.
Atoms of magnetic materials have an
imbalance of spinning electrons – more
electrons spinning one way versus the
other.
These atoms cluster together to
form magnetic domains.
Having domains only gives a
material the ability to become a
magnet.
In order for a material with domains
to become magnetic, the domains
have to be aligned by an external
magnetic field.
If enough of a materials domains
become aligned, the material forms
a magnetic dipole and becomes a
permanent magnet.
A magnetic dipole is made up of
two poles – a north pole and a
south pole.
Poles cannot be isolated – a
magnet cannot be broken to
get a separate north and
south pole. Instead, it creates
two magnets, each with a
north and south pole.
Rules of Interaction
Like poles repel
Opposite poles attract
Magnets can exert forces on each other without making contact, proving
that there are magnetic fields that surround them.
Magnetic field lines always project externally out of the north pole of a
magnet and are directed into a south pole.
The field is stronger in areas where the field lines are closer together.
Other magnets align themselves along the tangents of a magnet’s field
lines
Magnetic and Electric Fields Interactions
When a current-carrying wire is placed in a magnetic field the magnetic field
exerts a force on the wire.
Assuming the wire is perpendicular to the field lines, the force is always
perpendicular to both (utilizing x, y, and z axes)
To determine the direction that the force exerts on the wire, use the right-hand
rule.
First…find your RIGHT hand
Thumb points in direction of electric
current
(flows + to -)
Fingers point in direction of magnetic
field lines
(project from N to S)
Palm points in direction of force
When something is perpendicular to
paper, use following symbols
-- into paper
-- out of paper
The magnitude of the force is determined by the amount of current in the wire,
the length of the wire in the field, and the strength of the magnetic field/
F = BIlsinθ
F = force (N)
B = magnetic field (Tesla)
I = current (A)
l = length of wire in field (m)
θ = angle between field lines and
wire
The magnitude of the force is determined by the component of the current that
is perpendicular to the field.
If the wire was parallel, there would be NO force on it.
A rectangular loop of wire hangs
vertically in a horizontal magnetic field.
The uniform magnetic field points out
of the page. If the current is 0.245 A
and the magnetic field is 1.42 T, what
is the net force acting on the loop?
The same phenomenon shows up when a single charge moves through a
magnetic field. Single positive charges obey the right hand rule
F = qvBsinθ
F = force (N)
B = magnetic field (Tesla)
q = charge (C)
v = speed of particle (m/s)
θ = angle between field lines and
path of charge
If a negative charge moves through a field, the force is in the opposite direction
of the force for a positive charge.
An electron travels at 2.0 x 107 m/s in
a plane perpendicular to a uniform
0.010-T magnetic field. What is the
radius of its path?
This spiral path is what is responsible for the aurora borealis at the Earth’s
poles.
Charged particles from the solar wind interact with the magnetic field of the
Earth which forces their trajectory into a circular motion.
We know that when current is placed in
a magnetic field, the magnetic field
exerts a force on the wire.
A wire also has its own magnetic field
that can apply a force on objects that
are placed in the field.
Right-hand Rule #2
Thumb points in direction of electric
current
(flows + to -)
Fingers curl in direction of magnetic
field lines
There is NO external magnet present. Magnetic field caused by moving
charge in wire.
To find the magnitude of the magnetic field, use
the following formula:
B = μ0I/2πr
B = magnetic field (T)
I = current (A)
μ0 = permeability constant (4π x 10-7 Tm/A)
r = distance to wire
A magnetic field is a vector product like an
electric field – direction maters.
Two parallel wires 10.0 cm apart carry currents in opposite directions. Current
I1 = 5.0 A is out of the page and I2 = 7.0 A is into the page. What is the
magnitude and direction of the magnetic field halfway between the two wires.
Electromagnetic Induction
We have observed how a current-carrying wire in a magnetic field produces a
force on the wire.
Can the opposite be true? Can a moving magnetic field around a wire produce
a current?
This phenomenon is called electromagnetic induction.
In the 1830’s, Michael Faraday created an
apparatus in which an insulated wire is
wrapped around a ring. The ring was also
attached to a galvanometer, which
measures very small current.
Faraday noticed that a constant current did
not produce a current in the galvanometer.
But at the instant he turned it on or off, the
needle moved.
It wasn’t a constant current that induced
another current. It was a changing current.
English chemist and
physicist
1791 - 1867
Furthermore, what was important was not the changing current, but the
changing magnetic field in the ring.
As the current was increasing, it was increasing the magnetic flux in the ring
Magnetic flux –the number of magnetic field lines that passes through a
given area
Magnetic Flux
ФB = BAcosθ
ФB = magnetic flux (Weber)
B = magnetic field (T)
A = area bound by wire (m2)
θ = angle between magnetic field lines
and perpendicular to plane of area
The only part of the magnetic field
that contributes to magnetic flux is
the component that is perpendicular
to area bound by the wire.
A square loop of wire with sides 10.0 cm long is turning in a 1.25-T magnetic
field. What is the change in flux between when the loop is perpendicular to the
field lines and when the loop is at a 35° angle to the field lines?
Faraday’s Law of Induction
Faraday proposed that current is
produced because of a changing
magnetic flux in the iron ring.
He theorized Faraday’s Law, which
states that a changing magnetic flux
over time creates electromotive force
and subsequent induced current in
the other wire.
E = - N∆ФB / ∆t
N = number of loops
E = electromotive force (V)
∆ФB = change in magnetic flux (Wb)
∆t = time interval (s)
There are many ways to
change the magnetic flux
inducing a current. Again, if
the number of field lines in
the loop changes, the flux
changes.
How is the flux changed in
each situation?
A square coil of wire with 5.00-cm
sides contains 100 loops and is
positioned perpendicular to a uniform
0.600-T field. It is quickly pulled from
field at a constant speed to a region
where there is no magnetic field. If
the right edge of the coil is at the edge
of the field, it takes 0.100 s for the
whole coil to reach the field-free
region. Assuming the coil has a
resistance of 100 Ω, find the following:
a) the change in flux through the coil
a) the emf and current induced
Lenz’ Law
Obvious question – Why is the
emf negative?
E = - N∆ФB / ∆t
The current produced by an induced emf moves in a direction so that its
magnetic field opposes the original change in flux.
This is known as Lenz’s Law.
Flux decrease 
current moves so
magnetic field
coincides
Flux increase 
current moves so
magnetic field
counteracts
A 30.0-cm conducting rod with a
resistance of 2.5 Ω moves on a
U-shaped conductor with a
speed of 1.6 m/s. The resistance
of the U-shaped conductor is
25.0 Ω and it is in a uniform
magnetic field of 0.35 T.
Calculate the induced emf over a
0.5-s time interval.
Calculate the current (magnitude
and direction) in the conductor.