Download III-1

III. Magnetism
Fields produced mostly by moving
charges acting on moving charges.
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III–1 Magnetic Fields
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Main Topics
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Introduction into Magnetism.
Permanent Magnets and Magnetic Fields.
Magnetic Induction.
Electric Currents Produce Magnetic Fields.
Forces on Electric Currents.
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Introduction into Magnetism
• Magnetic and electric effects are known for
many thousands years. But only in 19th
century a close relation between them was
found. Deeper understanding was reached
only after the development of the special
theory of relativity in 20th century.
• Studying of magnetic properties of
materials has been up to now a field of
active research.
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Permanent Magnets I
• The mathematical description of magnetic
fields is considerably more complicated
then it is for the electric fields.
• It is worth to begin with good qualitative
understanding of simple magnetic effects.
• It has been known for a long time that
certain materials are capable of interacting
by another long-distance force which is not
electrostatic.
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Permanent Magnets II
• This force had been named magnetic.
• This force can be either attractive or
repulsive.
• The magnitude of this force decreases with
distance.
• There had been a suspicion that electric and
magnetic forces were the same thing. They
are not! But they are related.
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Permanent Magnets III
• The reason: magnets don’t influence
charges at rest but they do influence moving
charges.
• At first, the magnetic properties were
attributed to some “magnetic charges”.
• Since both attractive and repulsive forces exist
there must be two kinds of these “charges”.
• But it was found that these magnetic ”charges”
can’t be separated!
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Permanent Magnets IV
• If you separate a piece of any size and shape
from a permanent magnet, it will always
contain both “charges”. So they are called
more appropriately – magnetic poles.
• Unlike poles attract and like poles repel.
• We expect that poles don’t switch without
external influence and the interactions are
stable.
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A Simple Experiment
• The fact that unlike poles attract and like
poles repel can be proved by a simple
experiment using three magnets:
• Let’s mark one pole on each of the magnets.
• At least two of the magnets must have the mark
on the same pole. We can find them using the
interaction with the third magnet.
• We readily see e.g. that marked poles repel.
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Permanent Magnets V
• Around any magnet there is magnetic field
which can interact with other magnets.
• In pre-physics ages it was found that the
Earth is a source of a magnetic field. It is a
large permanent magnet.
• A magnetic needle would always point in
the North-South direction.
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Permanent Magnets VI
• This is a principle of compass, used by the
Chinese thousands years ago for navigation.
• A convention has been accepted:
• the pole of a magnet pointing to the North
geographic pole is called the north and the other
one the south.
• the magnetic field has the direction from the
north to the south. i.e. in the direction a
compass would point, which enables a simple
calibration of magnets.
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Permanent Magnets VII
• From this it is clear that the south magnetic pole of
the Earth is near to the North geographical pole.
• A compass doesn’t point exactly to the north. It
has a declination which depends on the particular
location since magnetic and geographic poles dont
coincide. The field is even not horizontal.
• Magnets can be imagined consisting of smaller
magnets so the convention works even inside
them.
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Magnetic Fields I
• Similarly as in the case of electric fields, we
accept an idea that magnetic interactions are
mediated by magnetic fields.
• Every source of magnetic field e.g. magnet
spreads (by the speed of light) around an
information on its position, orientation and
strength. This information can be received
by another source. The results is that a force
between those sources appears.
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Magnetic Fields II
• As can be easily proved by a magnetic
needle, magnetic fields generally change
directions and therefore must be described
in every point by some vector quantity.
Magnetic fields are vector fields.
• Magnetic fields are usually described
 by the
vector of the magnetic induction B .
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Magnetic Fields III
• The magnetic field lines are:
• lines tangential to the magnetic induction
in every point.
• closed lines which pass through the space
as well as through the magnets in the
same direction as a north pole of a
magnetic needle would point – from
north to south.
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Magnetic Fields IV
• Since magnetic monopoles don’t exist, the
magnetic field lines are closed lines and outside
the magnets they resemble the electric field lines
of an electric dipole.
• Although it is in principle possible to study
directly the forces between sources of magnetic
fields, it is usual to separate problems to
• how fields are produced
• how they interact with other sources.
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Electric Currents Produce
Magnetic Fields I
• First important step to find relations
between electric and magnetic fields was
the discovery done by Hans Christian
Oersted (1777-1851, Danish) in 1820. He
found that electric currents are sources of
magnetic fields.
• A long straight wire produces magnetic
field whose field lines are circles centered
on it.
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Electric Currents Produce
Magnetic Fields II
• It is interesting that these closed field lines exist as
if they were produced by some invisible magnets!
• Magnetic field due to a circular loop of wire is
torroidal (doughnut).
• The direction of the field lines can be found using
a right-hand rule.
• Later we shall see where this rule comes from and
how these and other fields look in more detail and
quantitatively.
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Forces on Electric Currents I
• When it was found that electric currents are
sources of magnetic fields it could have
been expected that magnetic fields also
exert force on currents-carrying wires.
• The interaction was also proved by Oersted

and a formula for a force on a wire of dl
carrying the current I was found:
 

dF  I (dl  B) (cross product)
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Forces on Electric Currents II
• For a long straight wire which
can be

described by the vector l carrying the
current I the integral formula is valid:
 

F  I (l  B)
• If currents produce magnetic fields and they
are also affected by them it logically means
that currents act on currents by magnetic
forces.
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Forces on Electric Currents III
• Now, we can qualitatively show that two
parallel currents will attract them selves and
the force will be in the straight line which
connect these currents.
• This seems to be similar to a force between
two point charges but now the force is the
result of a double vector product as we shall
see soon.
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Forces on Electric Currents IV
• From the formula describing force on
electric currents the units can be derived.
• The SI unit for the magnetic induction B is
1 Tesla, abbreviated as T, 1T = 1 N/Am
• Some older are units still commonly used
for instance 1 Gauss: 1G = 10-4 T
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Homework
• Chapter 27 – 1, 2, 6, 10, 14, 15, 19, 20
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Things to read and learn
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This Lecture Covers :
Chapter 27 – 1, 2, 3
Advance Reading :
Chapter 28 – 1, 2, 3, 4, 6
Try to understand all the details of the
vector product of two vectors!
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The vector or cross product I
  
Let c  a  b
Definition (components)
ci   ijk a j bk

The magnitude of the vector c

 
c  a b sin 
 
Is the surface of a parallelepiped made by a , b.
The vector
or
cross
product
II

The vector c is perpendicular
to the
plane

  

made by the vectors a and b and a , b , c
must form a right-turning system.



ux
uy
uz

c  ax
ay
az
bx
by
bz
ijk = {1 (even permutation), -1 (odd), 0 (eq.)}
^