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Chapter 20
Magnetism
20.1 Magnets and Magnetic Fields
Magnets have two ends – poles – called
north and south.
Like poles repel; unlike poles attract.
20.1 Magnets and Magnetic Fields
However, if you cut a magnet in half, you don’t
get a north pole and a south pole – you get two
smaller magnets.
Ferromagnetism
• Ferromagnetism is the basic mechanism by
which certain materials (such as iron) form
permanent magnets, or are attracted to
magnets.
• The spin of an electron, creates a small
magnetic field. Electrons have either “up” or
“down” spins and are often paired up with
down. Atoms with unpaired electron spins can
have a net magnetic effect.
• Iron, Nickel, Cobalt and their alloys are most
notable ferromagnetic
materials
Ferromagnetism: Domains
When the material is
unmagnetized, the domains
are randomly oriented.
They can be partially or
fully aligned by placing the
material in a strong
external magnetic field.
Domains are formed by
small regions where atoms
are aligned such that their
individual electron spins
are in the same direction.
20.1 Magnets and Magnetic Fields
Magnets cause space to be modified in their vicinity,
forming a “magnetic field”.
The magnetic field caused by magnetic “poles” is
analogous to the electric field caused by electric
“poles” or “charges”.
Magnetic field lines differ from
electric field lines in that they are
continuous loops with no
beginning or end.
20.1 Magnets and Magnetic Fields
The Earth’s magnetic field is similar to that of a
bar magnet.
Note that the Earth’s
“North Pole” is really
a south magnetic
pole, as the north
ends of magnets are
attracted to it.
Units of Magnetic Field
Tesla (SI)
– N/(C m/s)
– N/(A m)
Gauss
– 1 Tesla = 104 gauss
Magnetic Force on Particles
Magnetic fields cause the existence of
magnetic forces.
A magnetic force is exerted on a particle
within a magnetic field only if
– the particle has a charge.
– the charged particle is moving
with at least a portion of its velocity
perpendicular to the magnetic field.
Magnetic Force on a Charged Particle
(Lorentz Force)
• magnitude: F = qvBsinθ
– q: charge in Coulombs
– v: speed in meters/second
– B: magnetic field in Tesla
– θ: angle between v and B
• direction: Right Hand Rule
• FB = q v x B (This is a “vector cross product”)
Magnetism
 Magnetic
force (Lorentz force)
Magnetic Force
Sample Problem: Calculate the magnitude and
direction of the force exerted on a 3.0 μC charge
moving north at 300,000 m/s in a magnetic field
of 200 mT if the field is directed
a) North.
b) South.
c) East.
d) West.
Magnetic forces…
• are always orthogonal (at right angles) to the
plane established by the velocity and
magnetic field vectors.
• can accelerate charged particles by changing
their direction.
• can cause charged particles to move in
circular or helical paths.
Magnetic forces cannot...
• change the speed or kinetic energy of
• charged particles do work on charged particles.
Magnetic Forces…
…are centripetal.
• Remember that centripetal
acceleration is v2/r.
• Remember centripetal force is
therefore mv2/r.
20.4 Force on Electric Charge Moving in a
Magnetic Field
If a charged particle is
moving perpendicular
to a uniform magnetic
field, its path will be a
circle.
Motion of Charged Particles in a Magnetic Field
 Case
1: Velocity perpendicular to magnetic field
Movement of charged particles
in B Field
http://wps.aw.com/aw_young_physics_11/13
/3510/898593.cw/index.html
http://video.mit.edu/watch/cloud-chamber-4058/
Sample Problem:
An electric field of 2000 N/C is directed to the
south. A proton is traveling at 300,000 m/s to the
west. What is the magnitude and direction of the
force on the proton? Describe the path of the
proton? Ignore gravitational effects.
Sample Problem:
A magnetic field of 2000 mT is directed to
the south. A proton is traveling at 300,000
m/s to the west. What is the magnitude and
direction of the force on the proton?
Describe the path of the proton? Ignore
gravitational effects.
Sample Problem:
How would you arrange a magnetic field and an
electric field so that a charged particle of
velocity v would pass straight through without
deflection?
Motion of Charged Particles in a Magnetic Field
Velocity selector
Mass
Spectrometer
Motion of Charged Particles in a Magnetic Field
Mass spectrometer
Motion of Charged Particles in a Magnetic Field
Mass spectrometer
Force on an Electric Current in a
Magnetic Field
A magnet exerts a force on a current-carrying wire. The
direction of the force is given by the right-hand rule.
Video: wire in B field
Fingers: direction of conv. current, I
Curl fingers: dir. of magnetic field, B
thumb: direction of force, F
Magnetic Force on a Current-Carrying
Conductor
 Magnetic
force on a current (in a straight wire)
Sample Problem: What is the force on a
100 m long wire bearing a 30 A current
flowing north if the wire is in a downwarddirected magnetic field of 400 mT?
After ½ turn:
To summarize:
Magnetic Fields…
Affect moving charge
– F = qvBsinθ
– F = ILBsinθ
– Right Hand Rule is used to determine
direction of this force.
Magnetic fields are also caused by moving
charge…
Electric Currents Produce Magnetic Fields
Experiment shows that an electric current produces
a magnetic field. When brought into the field, a
magnet will experience a force due to the current, in
the same way as iron filings close by a bar magnet
experience a force causing them to align to the
magnetic field.
Magnetic fields produced by straight currents:
Magnitude of Magnetic Field
produced by straight currents
μo: 4π × 10-7 T m / A
(called magnetic permeability of free space)
I: current (A)
r: radial distance from center of wire (m)
Sample Problem: What is the magnitude
and direction of the magnetic field at point
P, which is 3.0 m away from a wire
bearing a 13.0 Amp current?
Sample problem: what is the magnitude and
direction of the force exerted on a 100 m long
wire that passes through point P which bears a
current of 50 amps in the same direction?
20.6 Force between Two Parallel Wires
The magnetic field produced
at the position of wire 2 due to
the current in wire 1 is:
The force this field exerts on
a length l2 of wire 2 is:
(20-7)
20.6 Force between Two Parallel Wires
Parallel currents attract; antiparallel currents
repel.
Principle of Superposition
When there are two or more currents
forming a magnetic field, calculate B
due to each current separately and then
add them together using vector addition.
Sample Problem:
What is the magnitude and direction of
the electric field at point P if there are
two wires producing a magnetic field at
this point?
Sample Problem: Where would the
magnetic field be zero?
Solenoid
• A solenoid is a coil of wire.
• When current runs through the wire, it
causes the coil to become an
“electromagnet”.
• Air-core solenoids have nothing inside
of them.
• Iron-core solenoids are filled with iron
to intensify the magnetic field.
Electric Currents Produce Magnetic Fields
RHR for direction of field
Thumb: direction of current
Fingers then wrap in
direction of field
magnetic field reversal
A geomagnetic reversal is a change in the Earth’s
magnetic field such that the positions of magnetic
north and magnetic south are interchanged. The
Earth’s field has alternated polarity, with the time
spans of reversal randomly distributed; most being
between 0.1 and 1 million years with an average of
450,000 years. Most reversals are estimated to take
between 1,000 and 10,000 years. The latest one,
occurred 780,000 years ago.
Earth’s Magnetosphere
A magnetosphere is formed when a stream of charged particles, such as the solar
wind, interacts with and is deflected by the magnetic field of a planet or similar
body
solar corona
aurora borealis
An aurora is a natural light display in the sky particularly in the
arctic and antarctic regions, caused by the collision of charged
particles with atoms in the upper atmosphere. The charged
particles originate in the magnetosphere and, on Earth, are
directed by the Earth’s Magnetic Field into the atmosphere.
The key ingredient in anything magnetic is
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the surrounding magnetic field
pairs of magnetic poles
moving electric charge
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Every spinning electron is a tiny magnet.
Since all atoms have spinning electrons, why
are not all atoms tiny magnets?
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2.
3.
Because the magnetic field
cancels out in most atoms
Because the electrons don’t
spin fast enough
They don’t align properly
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What is so special about iron that makes
each iron atom a tiny magnet?
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It is a metal
It has unpaired electrons
It has more electrons than
protons
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A magnetic field can be found
surrounding any
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Moving electric charge
Current carrying wire
Neither of these
Both of these
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