Magnetism of Matter

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Chapter 32

• Magnetism of Matter
• Maxwells Equations

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Chapter 32
-Magnets
- Gauss Law for Magnetic Fields
- The Magnetism of the Earth
- Magnetism and Electrons
-Magnetic Materials
- Diamagnetism
- Paramagnetism
- Ferromagnetism
- Induced Magnetic Fields
- Displacement Current
-Maxwells Equations
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Magnet
Magnetic monopole do not exist.
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GaussLaw for Magnetic Fields
For the Magnetic Flux through the closed surface
Since the magnetic monopole do not exist. Apply
Gauss law for magnetic field we get
.(GaussLaw for Magnetic Fields)
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Compare the GaussLaw for Electric Fields
We have
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The Magnetism of the Earth
The earth is a huge magnet.
The magnetic pole that is in the Earths
northern hemisphere known as a north magnetic
pole is really the south pole of the earths
magnetic dipole.
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Magnetic dipole
The magnetic dipole moment of a current loopµ
and the magnetic field at point P a distance z
from the loop on its axis.
In an external magnetic field, a magnetic dipole
moment experiences a torque that rotates into
alignment with .
And the potential energy as
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Magnetism and electrons
Magnetic materials are magnetic
because of the electrons with them can generate
a magnetic field. There are two more ways, each
involving a magnetic dipole moment that produces
a magnetic field in the surrounding space.

• Spin Magnetic Dipole Moment ( )
• - Orbital Magnetic Dipole Moment ( )

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Spin Magnetic Dipole Moment ( )
An e- has an intrinsic angular momentum (spin
angular momentum)
by
.
Here is the magnitude of the measured z component
of
The definition of Bohr magnetron,
As the potential energy is always produced as
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Orbital Magnetic Dipole Moment
The e- in an atom has orbital angular momentum

by

And the potential energy is
? Bohr magnetron ,
Note
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3 Types of Magnetic Materials
1. Diamagnetism
Diamagnetism Diamagnetic substances such as
Bismuth, Copper, Zinc, were repelled by a strong
magnet. In contrast, paramagnetic substances are
always attracted by a magnet. Such materials
might be those having atomic magnetic dipole
moment of zero, perhaps originating from atoms
having several electrons with their orbital and
spin magnetic dipole moments adding vectorially
to zero.
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2. Paramagnetism Paramagnetism occurs in
materials whose atoms have permanent magnetic
dipole moments it makes no difference whether
these dipole moments are of the orbital or spin
types.
The paramagnetic materials at room temperature
are Chromium, Tungsten, Aluminium, and Magnesium.
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2. Paramagnetism
The thermal motion of the atoms tends to disturb
the alignment of the dipoles, and consequently
the magnetization (M) decreases with increasing
temperature following Curies law
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For a paramagnetic material
The figure shows the ratio M/Mmax as a function
of Bext /T. It is a magnetization curve.
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3.Ferromagnetism (permanent magnetism)
Iron, Cobalt, Nickel, Gadolinium, Dysprosium, and
alloys containing these elements.
If the temperature of a ferromagnetic material is
raisen to the critical value (called Curie
temperature), the exchange coupling cease to be
effective. The ferromagnetism in the material
becomes the paramagnetism at the Curie
temperature.
For example, the curie temp of an iron is 1043K
( 770oC)
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Hysteresis loop
This is the magnetization curve of the
ferromagnetic material. The path bcdeb can be
repeatedly as the loop during the operation with
changing the current in the solenoid effectively
to Bo.
It means that the iron remembers how it became
magnetized, a negative current producing a
magnetization different from a positive one.
This memory is essential to the operation of
magnetic storage of information, such as on
cassette tapes or computer disks.
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Induced Magnetic Fields
1.Faradays law of induction
2. A changing magnetic field B produces an
electric field E
This equation is still called Faradays law of
induction.
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Induced Magnetic Fields
Furthermore, the equation governing the induction
of a magnetic field .

• The figure is a circular
• parallel-plate capacitor
• the side view ,
• the top view, from with in the capacitor.

is uniform and grows in magnitude as the charge
on the cap increases.
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Induced Magnetic Fields
Faradays law of induction..(a)
Maxwells law of induction(b)
There are 2 different things in (a) and (b) which
look similar
1. (b) has 2 extra symbols ( ).
2. (b) lacks of the minus sign (-) meaning that
the induced and the induced have
opposite directions when they produced in
otherwise similar situation.
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Ampare-Maxwell Law
Recall Ampares law
And Maxwells law of induction
Combine these equations into single equation
named it Ampare-Maxwell law
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Displacement Current
From the previous equation,
It shows that the product of must
have the dimension of a current.
displacement current
Ampare-Maxwell law
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Displacement Current

• An Amperian loop encloses a surface through which
  passes a wire carrying a current

(b) The same Amperian loop encloses a surface
that passes between the capacitor plates. No
conduction current passes through the surface.
So the Ampare-Maxwell law could be written for
(a) as
And for (b) the inside, between the capacitor
plates the Ampare-Maxwell law could be written as
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Maxwells Equations
The four fundamental equations of
electromagnetism, called Maxwells equation.
Name
Equation
Gauss law for electricity
Gauss law for magnetism
Faradays law
Ampare-Maxwell law
These equations are the basis of many of the
equations we see in charge particle to optics.