Lecture Notes 20
Magnetic Forces Goals
■ To observe and visualize magnetic fields and forces.
■ To study the motion of a charged particle in a magnetic
■ To evaluate the magnetic force on a current-carrying
■ To determine the force and torque produced with a magnet
and current-carrying loop of wire (the DC motor).
■ To study the fields generated by long, straight conductors.
■ To observe the changes in the field with the conductor in
loops (forming the solenoid).
■ To calculate the magnetic field at selected points in space.
■ To understand magnetism via magnetic moments. Historical Notes - Lodestone (magnetite mineral):
The name "magnet" comes from lodestones found in a place called Magnesia.
A piece of intensely magnetic magnetite that was used as an early form of
Only magnetite with a particular crystalline structure,
lodestone, can act as a natural magnet and attract and
magnetize ironn China, the earliest literary reference
to magnetism lies in a 4ry BC book called
Book of the Devil Valley Master: "The lodestone makes
iron come or it attracts it." The earliest mention of the
attraction of a needle appears in a work composed
between 20 and 100AD.
From amusement and magic-like to application −
“leading stone” (lodestone) –
compasths and navigation
By the 12 century the Chinese were known to use
the lodestone compass for navigation.
Today’s powerful lodestones − and
magnetic materials are ubiquitous. What if no lodestones existed?
► The Chinese would certainly not have invented the
magnetic compass. ► Magnetism would have been
discovered much later, and one wonders how. ► Lacking the
compass, the great voyages of discovery could hardly have
taken place--Columbus, De Gama, Magellan and the rest. ►
The history of the world might have been quite different!
• Magnetic energy is the strongest natural force in the universe and
the power of magnets is one of the most basic powers of nature.
• The use of magnet therapy for health and well-being has an
ancient history dating back thousands of years.
• Ancient Egyptians used loadstones to prolong life and improve health. It is said that Cleopatra wore a
polished lodestone on her third eye, in the belief that it helped maintain her youth and beauty.
• In more recent times, Paracelsus (1493-1541) considered to be the father of modern medicine, believed
that the "life force' of the body was most influenced by the force found in magnets.
• In Europe, Russia, China, Japan and many other countries, convinced of the benefits, millions of
people continue to use magnet therapy.
• Today, we are experiencing an exciting revival of this ancient therapy. Resulting from the impact of
more and more clinical studies and anecdotal evidence, 120 million people worldwide spend over $1.5
billion globally on the therapeutic benefits of magnets. Two experiments, different scale: Although the magnet on the left is an
electromagnet (huge) and the one on the right is a permanent magnet
(small), the idea is the same. Observations:
► Youget a hint of magnetic field whenever you attach a note to a refrigerator
door with a small magnet.
► Accidentally erase a computer disk by bringing it near a magnet.
► Creditcards, VCRs,…etc
► A familiar type of magnet: “electromagnets”. A wire coil is wound around an iron
core and a current is sent through the coil. The strength of the magnetic field is
determined by the size of the current.industry, such magnets are used for
sorting scrap iron among many other things.
► Youare probably more familiar with “permanent magnets” (like the refrigerator-
door type). They do not need current to have a magnetic field.
► Magnets: A magnet is an object made of certain materials which create a
From these modest origins, the sciences of electricity and magnetism developed
separately for centuriestil 1820AD.
In 1820, Oersted found a connection between them: an electric current in a wire
can deflect a magnetic compass needle.
The new science of “electromagnetism”was developed by Faraday, Henry, and
Maxwell (who, in the mid-19th century put electromagnetism on a sound
theoretical basis)… 20.1 Magnetism
The behavior of bar magnets
■ Notice the general behavior trends of attraction and repulsion,
dipole or monopole. The simplest magnetic structure that can exist is a magnetic dipole.
Magnetic monopoles do not exist (as far as we know)
∴We cannot define the magnetic field as we do for the electric field (E=F /q.)
Magnetic properties of materials can be traced back
to their atoms and electrons.
The clustering of the lines (of e.g. iron filings) at the ends of a magnet
suggests that one end is a “source” of the lines (the field diverges from it) and
the other end is a “sink” of the lines (the field converges toward it).
By convention: north pole and south pole, respectively.
The magnet with its two poles is an example of a “magnetic dipole”.
Note:A magnetized bar is
magnetically weak in the middle
Determine which of the two
bars is magnetized
(without using any other material.) A compass will align with fields
The compass will align with
whatever average field is
strongest. As shown in
figure, the field caused by
the current in the wire is
stronger than that any
background field from the
Absent the current-carrying
wire, the compass would
align with the earth’s
magnetic field. This allows
a consistent direction to be
determined by someone with
the need for navigation. Iron filings will align as a compass does
Each small filing lines up tangent to the field lines
allowing a visual demonstration The magnetic field lines and pattern of iron filings in the
vicinity of a bar magnet and the magnetic field lines in the gap
of a horseshoe magnet. “Earth is a huge magnet”
● It can be represented by a huge bar magneo (a magnetic dipole.) (William Gilbert 1540-1603)
● The dipole axis makes an angle about 11.5 with the rotation axis.
● It intersects Earth’s surface at the “geomagnetic north poand the“geomagnetic south pole”.
● The “north magnetic pole” is really the south pole of Earth’s magnetic dipole.
■ Our Earth
itself has a
This field is not
very strong but it
is consistent. o
● The “field declination” is the angle (left or right) between geographic north (which is toward 90
latitude) and the horizontal component of the field. The “field inclination” is the angle (up or down)
between a horizontal plane and the field’s direction.
● We can use a “compass” and a “dip meter” to determine these two angles.
● The field observed at any location on the surface of Earth varies with time. In fact, Earth’s field has
reversed its polarity about every million years. Examples of Magnetic Fields
Fields are created in a variety of ways and observed in a variety of places. 20.2 Magnetic Field and Magnetic Force
Frictional Forces Newton’s
Tension Force Second Law
Restoring Force of a Spring ΣF = m a
The magnetic force, like the other forces we have encountered,
may contribute to the net force that acts on an object Review: When a charge is placed in an electric field, it
experiences a force, according to
F = qE Definition of the magnetic field
The “magnetic field B” at a point is along the tangent to a field
line. Its direction is that of the force on the north pole of a bar magnet, or
the direction in which a compass needle points. The strength of the field is
proportional to the number of lines passing through a unit area normal to
the field . Therefore , B is also called the “magnetic flux density” .
Thereare two ways to set up a magnetic field:
(1)Moving electrically charged particles.
(2)Elementary particles such as electrons have an intrinsic magnetic field around
them; that is these fields are a basic characteristic of the particle, just as are their
mass and electric charge (or lack of charge).
The magnetic fields of the electrons in certain materials add together to give a
net magnetic field around the material. This is true for the material in permanent
magnets (which is good, because they can then hold notes to a refrigerator door). In
other materials, the magnetic fields of all the electrons cancel out, giving
magnetic fieldsurrounding the material. This is true for the material in your body
(which is also good, because otherwise you might be slammed up against a
refrigerator door every time you passed by). The force that a magnetic field exerts on a moving charge
Experimentally, we find that when a charged particle
(either alone or part of a current)moves through a magnetic field,
a force due to the field can act on the particle.
The following conditions must be met for a charge to experience a magnetic
force when placed in a magnetic field:
1. The charge must be moving.
2. The velocity of the charge must have a component that is perpendicular to
the direction of the magnetic field. The effect of an existing magnetic field on a
charge depends on the charges direction of motion
relative to the field.
The magnetic force F on a particle with
charge q and velocity v in a magnetic field B is
perpendicular to both v and B and given by :
F = q v × B (0 ≤≤φ 180 )
Its magnitude iF = q vB sinφ ,
where φ is the angle betweev and B .
The SI unit of the magnetic field is thetesla ( T )
•Note that 1 T≡ N.s/(C.m), and since C/s = 1A,
1 T≡ 1 N/(A.m).
•Since the tesla is a large unit, a (cgs) unit called
the gauss ( G ) is often used where 1 T = 10
Some approximate magnetic fields
At the surface of a neutron star 10
At Earth’s surface 10−10,
In interstellar space 10T Example 1 Magnetic Forces on Charged Particles
Aproton in a particle accelerator has a speed of 5.0x10 6m/s. The proton
encounters a magnetic field whose magnitude is 0.40 T and whose direction
makes and angle of 30.0 degrees with respect to the proton’s velocity
(see part (c) of the figure). Find (a) the magnitude and direction of the
force on the proton and (b) the acceleration of the proton. (c) What would
be the force and acceleration of the particle were an electron? (a) ( −19)( 6 ) ) ( )
F = qovBsinθ = 1.60×10 C 5.0 1× m s 0.40T sin30.0
= 1.× 10 N3
(b) F 1.6×10 N 13 2
a= m = 1.67×10−27kg =9.6×10 m s
(c) Magnitude is the same, but direction is opposite.
F 1.6×10 −1N 17 2
a = = −31 =1.8×10 m s
me 9.11×10 kg The Right Hand Rule
Right Hand Rule No. 1.
Extend the right hand so the fingers point along the direction of the magnetic field
and the thumb points along the velocity of the charge. The palm of the hand then
faces in the direction of the magnetic force that acts on a positive charge.
If the moving charge is negative, the direction of the force is opposite to that
predicted by RHR-1. Using the right hand rule, one may
determine the direction of the field
produced by a moving positive charge. The effect of the sign of a moving charge The effect of the sign of a moving charge
Positive and negative charges will feel opposite effects from a magnetic field. Motion of a charge
in an electric field
Motion of a charge
in a magnetic field Concepts at a glance
Test Field Moving Field
When a particle is subject to both electric and magnetic fields, the total force on it is:
F = q ( E + v × B )
It is convenient to symbolize the direction of B as:
× × × × × × × × ● ● ● ● ● ● ● ● ●
× × × × × × × × ● ● ● ● ● ● ● ● ●
× × × × × × × × ● ● ● ● ● ● ● ● ●
× × × × × × × × ● ● ● ● ● ● ● ● ●
B is into the page B is out of the page velocity selector
Magnetic fields can alter
A velocity selector is a
device for measuring the
velocity of a charged particle.
It consists of a tube in which
an electric field