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Chapter 17 Lecture
Magnetism
Prepared by
Dedra Demaree,
Georgetown University
© 2014 Pearson Education, Inc.
Magnetism
• What causes the northern lights?
• How does Earth protect us from the solar wind and
cosmic rays?
• Are we really walking northward when we follow a
compass needle?
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Be sure you know how to:
• Use the electric field concept to explain how
electrically charged objects exert forces on each
other (Section 15.1).
• Find the direction of the electric current in a
circuit (Section 16.1).
• Apply Newton's second law to a particle moving
in a circle (Section 4.4).
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What's new in this chapter
• We learned that charged objects attract and
repel each other—similar to the way magnets
do.
– Electrically charged objects do not exhibit
magnetic properties.
– Are electricity and magnetism unrelated
phenomena, or are they connected in some
way?
• We will learn about the connections between
electricity and magnetism.
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Magnetic interaction
• If you bring the like poles of two magnets near
each other, they repel each other.
• If you bring opposite poles near each other, they
attract each other.
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Magnetic interaction
• Magnets always have two poles.
• If you break a magnet into two pieces, each
piece still has two poles—a north pole and a
south pole.
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Magnetic interaction
• A compass contains a
tiny magnet on a lowfriction pivot.
• The north pole of a
compass points toward
geographic north; the
south pole points toward
geographic south.
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Magnetic interaction
• Earth acts as a giant
magnet, with its magnetic
south pole close to its
geographic north pole
and its magnetic north
pole close to its
geographic south pole.
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Magnetic and electrical interactions
are different
• Electrically charged objects do not interact with
magnets in the same way that magnets interact
with magnets.
• Magnetic poles are not electric charges.
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Magnetic field
• Magnets interact without contact; we introduce
the magnetic field as the mechanism behind
magnetic interactions.
• We can assume that a magnet produces a
magnetic field—a magnetic disturbance with
which other objects with magnetic properties
(e.g., another magnet, anything made of iron)
interact.
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Direction of the magnetic field
• We can use a compass to detect the direction of
the magnetic field at a particular location.
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Direction of the magnetic field
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Representing the magnetic field: Field lines
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Tip
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Observational experiment
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Observational experiment
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Magnetic field produced by a current
• Charged objects in
motion produce a
magnetic field; stationary
charged objects do not.
• The method for
determining the shape of
the B field produced by
the electric current in a
wire is called the righthand rule.
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Right-hand rule for the B field
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Conceptual Exercise 17.1
• Draw the magnetic field lines of a solenoid
connected to a battery.
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Current loops and bar magnets
• The B field produced by the current in a loop or a coil
and that produced by a bar magnet are very similar.
• Wire coils with current are known as electromagnets.
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Magnetic force exerted by the magnetic field
on a current-carrying wire
• If a current-carrying wire is similar in some ways
to a magnet, then a magnetic field should exert a
magnetic force on a current-carrying wire similar
to the force it exerts on another magnet.
• A magnet sometimes pulls on a wire and
sometimes does not—the effect depends on the
relative directions of the B field and the current
in the wire.
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Magnetic field of a horseshoe magnet
• We use a horseshoe magnet to generate a
magnetic field with almost parallel field lines
between the poles.
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Observational experiment
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Observational experiment
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Observational experiment
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Right-hand rule for the magnetic force
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Tip
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Forces that current-carrying wires exert on
each other
• If a current-carrying straight wire produces a
magnetic field, the field should exert a force on a
second current-carrying straight wire placed
nearby.
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Testing experiment
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Testing experiment
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Interaction between two current carrying
coils
• We can predict what happens to two currentcarrying coils of wire when the current is as
shown in the figure.
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Tip
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Ampere
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Expression for the magnetic force that a
magnetic field exerts on a current-carrying
wire
• Knowing the spring
constant of the springs
and the mass of the wire,
we can use the stretch of
the springs to deduce the
magnitude of the
magnetic force exerted on
different-length wires
when different currents
are in them.
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Magnitude of the magnetic force
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Magnetic force exerted on a current
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Example 17.2
• Instead of supporting your clothesline with two poles,
could you replace the poles and the clothesline with a
current-carrying wire in Earth's B field, which near the
surface has magnitude 5 x 10–5 T and points north?
Assume that your house is located near the equator,
where the B field produced by Earth is approximately
parallel to Earth's surface. The clothesline is 10 m long;
the clothes and the line have a mass of 2.0 kg.
1. In which direction should you orient the clothesline
and which current is needed to support it?
2. Is this a promising way to support the clothesline?
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Summary of the differences between
gravitational, electric, and magnetic forces
• The gravitational and electric forces exerted on
objects do not depend on the direction of
motion of those objects, whereas the magnetic
force does.
• The forces exerted by the gravitational and
electric fields are always in the direction of the
g or E field, but the force exerted by the
magnetic field on a current-carrying wire is
perpendicular to both the B field and the
electric current.
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The direct current electric motor
• A motor is a device that converts electric energy
into mechanical energy.
• A simple motor consists of a rectangular currentcarrying coil placed between the poles of a large
electromagnet.
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The direct current electric motor
• A commutator causes the current to reverse
each time the coil passes the vertical orientation;
this is necessary for the net torque to always
remain clockwise.
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Torque exerted on a current-carrying loop
• The magnitude of the torque depends on how
far from the loop's rotation axis the magnetic
forces are exerted.
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Magnetic dipole moment
• The magnetic dipole
moment is the product of
the current I and area A.
• The direction of the dipole
moment vector is
perpendicular to the
surface of the loop and in
the direction of the B field
produced by the current at
the center of the loop.
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Using a coil in a magnetic field to measure
current: An ammeter
• We can use the following equation as the basis
for a method to measure the current through a
wire:
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Magnetic force exerted on a single moving
charged particle
• The magnetic field exerts a force on a
current-carrying wire, which is made of
moving electrons.
– The magnetic field also exerts a force on
each individual electron.
– The magnetic field also exerts a force on
other moving charged particles, such as
protons and helium nuclei.
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Direction of the force that the magnetic field
exerts on a moving charged particle
• We can use the right-hand rule for
the magnetic force to predict the
direction in which electrons in the
oscilloscope will be deflected.
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Magnitude of the force that a magnetic field
exerts on a moving charged particle
• We use the equation for the force a magnetic
field exerts on a current-carrying wire to
determine the force exerted on an individual
charge:
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Magnitude of the force that a magnetic field
exerts on a moving charged particle
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Right-hand rule for the direction of the
magnetic force exerted on a moving
charged particle
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Tip
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Quantitative Exercise 17.3
• Each of the lettered dots shown in the figure represents
a small object with an electric charge +2.0 x 10–6 C
moving at a speed 3.0 x 107 m/s in the directions shown.
Determine the magnetic force (magnitude and direction)
that a 0.10-T magnetic field exerts on each object.
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Circular motion in a magnetic field
• The force exerted by the
magnetic field always
points perpendicular to
the particle's velocity,
toward the center of the
particle's path.
– The particle will
move along a circular
path in a plane
perpendicular to the
field.
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Cosmic rays
• Cosmic rays are electrons, protons, and other
elementary particles produced by various astrophysical
processes, including those occurring in the Sun and
sources outside the solar system.
• Earth's magnetic field serves as a shield against harmful
cosmic rays, causing them to deflect from their original
trajectory toward Earth.
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Example 17.4
• Determine the path of a cosmic ray proton flying
into Earth's atmosphere above the equator at a
speed of 107 m/s and perpendicular to Earth's
magnetic field. The average magnitude of
Earth's magnetic field in this region is 5 x 10–5 T.
The mass m of a proton is 10–27 kg.
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Tip
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The auroras
• Charged particles moving in Earth's magnetic
field follow helical paths around the magnetic
field lines.
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The magnetic field produced by an electric
current in a long straight wire
• To determine the magnitude of the magnetic
field at various locations near the wire, we need
to place some kind of a detector of magnetic
fields at different locations.
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Observational experiment
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The magnetic field produced by an electric
current in a long straight wire
• The magnitude of the magnetic field at a
perpendicular distance r from a long straight
current-carrying wire is expressed as:
– The farther you move from the currentcarrying wire, the smaller the magnitude of
the magnetic field.
– The greater the current, the larger the
magnitude of the magnetic field.
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Magnetic permeability
• The constant μo is known as the magnetic
permeability. It is used when calculating the
magnetic field in a vacuum, although the value is
approximately the same for air.
• μ is the magnetic permeability of a substance
and replaces μo if the magnetic field is being
calculated inside a material.
– μ for iron is approximately 1000 times larger
than μo.
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Magnetic fields produced by different
shapes of current-carrying wires
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Magnetic field due to electron motion
in an atom
• In an early model of the hydrogen atom, electron
motion was depicted as a circular electric
current.
• The magnetic field at the center of a currentcarrying loop of radius r is:
– This motion also describes a magnetic dipole
moment for atoms, making this model
potentially useful for explaining magnetic
properties of materials.
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Example 17.5
• In the early 20th-century model of the hydrogen
atom, the electron was thought to move in a
circle of radius 0.53 x 10–10 m, orbiting once
around the nucleus every 1.5 x 10–16 s.
Determine the magnitude of the magnetic field
produced by the electron at the center of its
circular orbit and its dipole moment.
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Skills for analyzing magnetic processes
• Problems involving magnetic interactions are of
two main types:
– Determine the magnetic force exerted on a
current or on an individual moving charged
object by the magnetic field.
– Determine the magnetic field produced by a
known source such as an electric current.
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Skills for analyzing magnetic processes
• When solving problems:
– Sketch the direction of the magnetic field and
the current (or the velocity of a charged
particle) if known.
– Decide whether the magnetic field can be
considered uniform in the region of interest.
– Use the right-hand rule for the magnetic field
if the problem is about the field of a known
source.
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Example 17.6
• A horizontal metal wire of mass 5.0 g and length
0.20 m is supported at its ends by two very light
conducting threads. The wire hangs in a 49-mT
magnetic field, which points perpendicular to the
wire and out of the page. The maximum force
each thread can exert on the wire before
breaking is 39 mN. What is the minimum current
through the wire that will cause the threads to
break?
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Example 17.7
• Determine the magnetic field 5.0 cm from a long
straight wire that is connected in series with a
5.0-ohm resister and a 9.0-V battery.
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Intensity-modulated radiation therapy
(IMRT)
• An IMRT machine
accelerates electrons to
the desired kinetic
energy, then uses a
magnetic field to bend
them into a target,
resulting in the
production of X-rays.
Movable metal leaves
then shape the X-ray
beam to match the
shape of the tumor.
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Example 17.8
• Estimate the magnitude of the magnetic field
needed for an IMRT machine. For the estimate,
assume that the electrons are moving at a
speed of 2 x 108 m/s, the mass of the electrons
is 9 x 10–31 kg, and the radius of the turn is
5 cm.
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Flow speed, electric generator, and mass
spectrometer: Putting it all together
• We will examine some applications that involve
both magnetic and electric phenomena.
– These applications involve electrically
charged objects moving in a region that has
both nonzero magnetic field and electric fields
perpendicular to each other.
• We will also investigate how our knowledge of
magnetic fields helps us determine the masses
of ions using a mass spectrometer.
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Ions moving through a perpendicular
magnetic field and electric field
• This device separates positively and
negatively charged particles.
• When the electric and magnetic forces
exerted on the moving charged
particles balance, the ions travel with
constant velocity downward despite
the presence of both a magnetic field
and an electric field.
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Magnetohydrodynamic (MHD) generator
• An MHD generator converts the random kinetic energy
of high-temperature charged particles into electric
potential energy.
• MHD generators are used at some older coal-fired power
plants to improve the efficiency of power generation.
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Magnetic flow meter
• A magnetic flow meter works only for fluids with
moving ions, which includes most fluids.
• A magnetic field is oriented perpendicular to the
vessel through which the fluid flows. Oppositely
charged ions in the fluid are pushed by the
magnetic field to opposite walls, producing a
potential difference across the walls of the
vessel.
• With this information, we can determine the
fluid's volume flow rate.
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Quantitative Exercise 17.9
• Is the general magnetic flow meter idea feasible
for measuring blood speed in an artery?
Estimate the potential difference you would
expect to measure as blood in an artery passes
through a 0.10-T magnetic field region. Assume
the heart pumps 80 cm3 of blood each second
(the approximate volume for each heartbeat)
and the diameter of the artery is 1.0 cm.
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Mass spectrometer
• A mass spectrometer helps determine the masses of
ions, molecules, and even elementary particles such as
protons and electrons.
• It can also determine the relative concentrations of
atoms of the same chemical element that have slightly
different masses.
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Quantitative Exercise 17.10
• An atom or molecule with a single electron removed is traveling at
1.0 x 106 m/s when it enters a mass spectrometer's 0.50-T uniform
magnetic field region. Its electric charge is +1.6 x 10–19 C. It moves
in a circle of radius 0.20 m until it hits the detector.
1. Determine the magnitude of the magnetic force that the
magnetic field exerts on the ion.
2. Determine the mass of the ion.
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Magnetic properties of materials
• Materials, even among metals, have widely
varying magnetic properties.
– Magnets strongly attract objects made from
iron, such as paper clips, but do not exert an
observable magnetic force on objects made
from aluminum, such as soda cans.
– Iron has the ability to greatly amplify the
magnetic field surrounding it.
– How can we explain this?
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Observational experiment
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Observational experiment
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Magnetic properties of materials
• Materials that are repelled by magnets are
called diamagnetic (e.g., pyrolytic carbon or
water).
• Materials that are weakly attracted are called
paramagnetic (e.g., aluminum).
• Materials that are strongly attracted are called
ferromagnetic (e.g., iron).
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Magnetic properties of atoms
• Each electron has a
magnetic dipole moment
(an electron orbital
magnetic moment).
• The electron itself acts like
a tiny bar magnet, which
also contributes to the
total magnetic moment
produced by the atom.
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Diamagnetic materials
• In diamagnetic materials, the magnetic moments
produced by individual electrons in the atoms
cancel each other, making the total field
produced by the atom zero.
• In the presence of an external magnetic field, the
motion of the electrons in the individual atoms
changes slightly, and the net magnetic field in
the material is no longer zero, causing the
diamagnetic object to be repelled by the magnet.
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Paramagnetic materials
• If the orbital magnetic
moments of the electrons don't
cancel, an atom will have a
magnetic moment similar to
that of a small bar magnet.
• When a paramagnetic material
is placed in an external
magnetic field, the atoms
behave like tiny compasses
and tend to align with that
external magnetic field.
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Ferromagnetic materials
• Ferromagnetic materials have individual atoms with
magnetic moments, just like paramagnetic materials.
• The "magnetization" effect in an external magnetic field
is thousands of times stronger in ferromagnetic materials
than in paramagnetic materials.
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Summary
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Summary
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Summary
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