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EMF 4.pdf
1. Origin of Magnetic Moment
Magnetism arises from the Magnetic Moment or Magnetic dipole of
Magnetic Materials.
When the electrons revolves around the nucleus Orbital magnetic
moment arises, similarly when the electron spins, spin Magnetic
moment arises.
The permanent Magnetic Moments can arise due to the
1.The orbital magnetic moment of the electrons
2.The spin magnetic moment of the electrons, and
3.The spin magnetic moment of the nucleus
2. Origin of magnetic dipoles
β’ The spin of the electron produces a magnetic field with a
direction dependent on the quantum number ml.
3. The spin of the electron produces a magnetic field with
a direction dependent on the quantum number ms.
Origin of magnetic dipoles
5. β’ Materials can be classified based on their magnetic property or behavior
β’ magnetic susceptibility ππ
β’ relative permeability ππ
β’ A material is said to be nonmagnetic if ππ = 0 or ππ = 1; it is magnetic
otherwise.
β’ Free space, air, and materials with ππ = 0 or ππ β 1 are regarded as
nonmagnetic.
β’ Materials may be grouped into three major classes:
β’ diamagnetic
β’ paramagnetic and
β’ ferromagnetic
6.
7. Diamagnetic Materials
β’ It is a weak form of magnetism
β’ Diamagnetism is because of orbital magnetic moment.
β’ No permanent dipoles are present so net magnetic moment is zero.
β’ Persists only when external field is applied.
β’ Dipoles are induced by change in orbital motion of electrons due to applied magnetic field.
β’ Diamagnetic susceptibility is independent of temperature and applied magnetic field strength.
β’ Susceptibility is of the order of -10-5.
β’ Relative permeability is less than one.
β’ It is present in all materials, but since it is so weak it can be observed only when other types of
magnetism are totally absent.
β’ Examples: Bi, Zn, gold, H2O, alkali earth elements (Be, Mg, Ca, Sr), superconducting
elements in superconducting state.
9. Paramagnetic Materials
β’ Possess permanent dipoles.
β’ If the orbital's are not completely filled or spins not balanced, an overall small magnetic
moment may exist. (i.e.) paramagnetism is because of orbital and spin magnetic
moments of the electron.
β’ In the absence of external magnetic field
β’ all dipoles are randomly oriented
β’ so net magnetic moment is zero.
β’ In presence of magnetic field the material gets feebly magnetized i.e. the material allows
few magnetic lines of force to pass through it.
β’ Relative permeability Β΅r >1 (barely, β 1.00001 to 1.01).
β’ The orientation of magnetic dipoles depends on temperature and applied field.
β’ Susceptibility is independent of applied mag. field & depends on temperature
β’ Susceptibility is small and positive.
β’ The susceptibility range from 10-5 to 10-2.
β’ Examples: alkali metals (Li, Na, K, Rb), transition metals, Al, Pt, Mn, Cr etc.
11. Ferromagnetic Materials
β’ Permanent dipoles are present so possess net magnetic moment
β’ Origin for magnetism in Ferro mag. Materials is due to Spin magnetic moment of
electrons.
β’ Material shows magnetic properties even in the absence of external magnetic field.
β’ Possess spontaneous magnetization.
β’ Spontaneous magnetization is because of interaction between dipoles called
EXCHANGE COUPLING.
β’ When placed in external mag. field it strongly attracts magnetic lines of force.
β’ All spins are aligned parallel & in same direction.
β’ Susceptibility is large and positive, it is given by Curie Weiss Law
β’ Material gets divided into small regions called domains.
β’ They possess the property of HYSTERESIS.
β’ Examples: Fe, Co, Ni.
15. MAGNETIC BOUNDARY CONDITIONS
β’ We define magnetic boundary conditions as the conditions that H (or B) field must satisfy
at the boundary between two different media.
β’ By Gaussβs law for magnetic fields
β 1
16. β’ Consider the boundary between two magnetic media 1 and 2, characterized, respectively,
by and π1 and π2 as in Figure.
17.
18. β’ Applying eq. 1 to the pillbox (Gaussian surface) for the above Figure and allowing
Ξβ β 0, we obtain
π = π π
19.
20. β’ If the boundary is free of current or the media are not conductors (for K is free current
density), K = 0 and eq. 3 becomes
β’ Thus the tangential component of H is continuous while that of B is discontinuous at the
β’ boundary.
β’ If the fields make an angle π with the normal to the interface, we get,
πΆππ π1 =
B1π
B1
βΉ B1 πΆππ π1 = B1π
Similarly πΆππ π2 =
B2π
B2
βΉ B2 πΆππ π2 = B2π
1
21. and ππππ1 =
H1π‘
H1
βΉ H1 ππππ1 = H1π‘
βΉ
π΅1
π1
ππππ1 = H1π‘
and ππππ2 =
H2π‘
H2
βΉ H2 ππππ2 = H2π‘
βΉ
π΅2
π2
ππππ2 = H2π‘
βΉ
π΅1
π1
ππππ1 = H1π‘
2
Dividing equ. 2 by equ. 1 we get
βΉ
tan π1
tan π2
=
π1
π2
tan π1
π1
=
tan π2
π2
