The Field Of a Magnetized Object

INTRODUCTION TO ELECTRODYNAMICS

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

CONTENTS: Magnetization Dia-magnetism Para-magnetism Fero-magnetismThe Field Of A Magnetized Object

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.

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)

Cont…

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.

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

Cont…

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.

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.

Cont…

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.

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’ :

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.

Cont…• First , we use the formula :

• So potential becomes:

Cont…• Now we can use a vector product rule:

• By using f = 1/(r-r’) and V = M we get equation as:

Cont…• The first integral looks like the potential of a volume

current density :

• So equation no.7 becomes:

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:

Cont…

Thus,

Cont…• So , equation 9 becomes :

• If we now define a surface current :

• where nˆ is the unit normal to the surface.

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.

Bibliography:• http://

unlcms.unl.edu/cas/physics/tsymbal/teaching/EM-913/section6-Magnetostatics.pdf

• http://www.physicspages.com/2013/06/29/magnetization-bound-currents/

• http://www.slideshare.net/9998366697/diamagnetismparamagnetismferromagnetismantiferromagnetism-and-ferrimagnetismmagnetic-materials-ppt?qid=05467164-ae00-48fa-bf8c-595ea584a4be&v=&b=&from_search=4