this is awsome one

2. The Field Of a
Magnetized Object
INTRODUCTION TO
ELECTRODYNAMICS

3. Submitted to : Ma’am Ammara
Submitted by : Group-3
B.S Physics (5th Semester)
Section (A)
GCWU Sialkot
Group Members:
• Bisma Shakir 14020210-018
• Faiqa Barkat 14020210-027
• Maria Kousar 14020210-005
•Maham Idrees 14020210-010
•Warda Jabbar 14020210-048
•Ishrat Fardoos 14020210-012
•Nimra Asmat 14020210-021

4. CONTENTS:
 Magnetization
 Dia-magnetism
 Para-magnetism
 Fero-magnetism
The Field Of A Magnetized Object

5. Magnetization:
Definition:
“The process of making a substance
temporarily or permanently magnetic, as by
insertion in a magnetic field.”
“OR”
“The extent to which an object is magnetized”
M = magnetic dipole moment per unit
volume.

6. Dia-magnetism:
“ Diamagnetic materials acquire a very
weak magnetization opposite an external applied
magnetic field, and lose their alignment when the field
is removed. ”
Examples:
Bi, Zn, Gold, H2O, Alkali Earth elements (Be,
Mg, Ca, Sr)

7. Cont…

8. Properties of dia-magnetism:
• They are repelled by the external applied magnetic field.
• The permanent dipoles are absent in diamagnetic
materials.
• In a non-uniform magnetic field, they are repelled away
from the stronger parts of the field.
• The relative permeability ( µr ) is always less than one.

9. Paramagnetism:
“ Paramagnetic materials acquire a weak
magnetization aligned with an external applied
magnetic field , and also lose their magnetization
when the field is removed.”
Examples:
Alkali Metals ( Li, Na, K,Rb ) , Transition
Metals , Al , Pt , Mn , Cr etc

10. Cont…

11. Properties of paramagnetism:
• Paramagnetic materials experience a feeble
attractive force when brought near the pole of a
magnet.
• There materials possess some permanent dipole
moment which arise due to some unpaired
electrons.
• The magnetic susceptibility is small and +ve.

12. Ferromagnetism:
“ They have dipoles which can align with an
external magnetic field to produce a much
stronger magnetization, and also they retain the
magnetization after the field is removed. ”
Examples:
Fe , Co , Ni etc.

13. Cont…

14. Properties of ferromagnetism:
• The direction in which the material gets magnetised is
the same as that of the external field.
• These materials exhibits magnetization even in the
absence of an external magnetic field . This property is
called spontaneous magnetization.
• Ferromagnetic materials experience a very strong
attractive force when brought near the pole of a magnet.
• Permeability is very much greater than one.
• Susceptibility is +ve and high.

15. Field Of A Magnetized Object:
Bound Currents:
• Suppose we have a piece of magnetized material ; the
magnetic dipole moment per unit volume , M is given.
• Starting with the vector potential of an ideal dipole at the
origin:
• we can write this more generally as the potential when the
dipole is at position r’ :

17. Cont…
• Then if m= M(r’) we can get the potential due to a
distribution of magnetic dipoles as :
• For pretty well any configuration, this integral is difficult or
impossible to calculate analytically, but we can transform it
into a different form, in a similar way to that used in the
electrostatic case for polarization.

18. Cont…
• First , we use the formula :
• So potential becomes:

19. Cont…
• Now we can use a vector product rule:
• By using f = 1/(r-r’) and V = M we get equation as:

20. Cont…
• The first integral looks like the potential of a volume
current density :
• So equation no.7 becomes:

21. Cont…
• The second integral can be transformed into a surface
integral by using the divergence theorem.
• For a general vector field “V” and a constant vector
field “C” we have, using a vector identity in the first line:

22. Cont…
Thus,

23. Cont…
• So , equation 9 becomes :
• If we now define a surface current :
• where nˆ is the unit normal to the surface.

24. Cont…
• So, with these functions , we have the final relation:
• This means that the potential of a magnetized object is the same as
would be produced by a volume current throughout
the material, plus a surface current on the boundary.

25. Bibliography:
• http://unlcms.unl.edu/cas/physics/tsymbal/teaching/E
M-913/section6-Magnetostatics.pdf
• http://www.physicspages.com/2013/06/29/magnetizati
on-bound-currents/
• http://www.slideshare.net/9998366697/diamagnetism
paramagnetismferromagnetismantiferromagnetism-
and-ferrimagnetismmagnetic-materials-
ppt?qid=05467164-ae00-48fa-bf8c-
595ea584a4be&v=&b=&from_search=4