1. Generation of Magnetic Field
iron core I
air gap with constant B field N S 1

2. Equivalent of a Magnetic DipoleS
Magnetic dipole can be viewed as a pair of magnetic charges by analogy with electric dipole. I 2

3. Forces Exerted on a Magnetic Dipole in a Magnetic FieldB 3

4. Current Loops (Magnetic Dipoles) in Atoms
Electron orbiting nucleus
Electron spin
Nuclear spin
negligible
 A complete understanding of these atomic mechanisms requires application of quantum mechanics. 4

5. Current Loops (Magnetic Dipoles) in Atoms (Cont’d)
In the absence of an applied magnetic field, the infinitesimal magnetic dipoles in most materials are randomly oriented, giving a net macroscopic magnetization of zero.
When an external magnetic field is applied, the magnetic dipoles have a tendency to align themselves with the applied magnetic field. 5

6. Magnetized Materials
A material is said to be magnetized when induced magnetic dipoles are present.
The presence of the induced magnetic dipoles modifies the magnetic field both inside and outside of the magnetized material. 6

7. Permanent Magnets
Most materials lose their magnetization when the external magnetic field is removed.
A material that remains magnetized in the absence of an applied magnetic field is called a permanent magnet. 7

8. Magnetization Vector
The magnetization or net magnetic dipole moment per unit volume is given by
average magnetic dipole moment [Am2]
Number of dipoles per unit volume [m-3]
[A/m] 8

9. Magnetic Materials
The effect of an applied electric field on a magnetic material is to create a net magnetic dipole moment per unit volume M.
The dipole moment distribution sets up induced secondary fields:
Field due to induced magnetic dipoles
Total field
Field in free space due to sources 9

10. Volume and Surface Magnetization Currents
A magnetized material may be represented as an equivalent volume (Jm) and surface (Jsm) magnetization currents.
These charge distributions are related to the magnetization vector by 10

11. Volume and Surface Magnetization Currents (Cont’d)
Magnetization currents are equivalent currents that account for the effect of the magnetized material, and are analogous to equivalent volume and surface polarization charge densities in a polarized dielectric.
If the magnetization vector is constant throughout a magnetized material, then the volume magnetization current density is zero, but the surface magnetization current is nonzero. 11

12. Ampere’s Law in Magnetic Media
Ampere’s law in differential form in free space:
Ampere’s law in differential form in a magnetized material: 12

13. Magnetic Field Intensity
define the magnetic field intensity as 13

14. General Forms of Ampere’s Law
The general form of Ampere’s law in differential form becomes
The general form of Ampere’s law in integral form becomes 14

15. Permeability Concept
For some materials, the net magnetic dipole moment per unit volume is proportional to the H field
the units of both M and H are A/m.
magnetic
susceptibility
(dimensionless) 15

16. Permeability Concept (Cont’d)
Assuming that
we have
The parameter m is the permeability of the material. 16

17. Permeability Concept (Cont’d)
The concepts of magnetization and magnetic dipole moment distribution are introduced to relate microscopic phenomena to the macroscopic fields.
The introduction of permeability eliminates the need for us to explicitly consider microscopic effects.
Knowing the permeability of a magnetic material tells us all we need to know from the point of view of macroscopic electromagnetics. 17

18. Relative Permeability
The relative permeability of a magnetic material is the ratio of the permeability of the magnetic material to the permeability of free space 18

19. Diamagnetic Materials
In the absence of applied magnetic field, each atom has net zero magnetic dipole moment.
In the presence of an applied magnetic field, the angular velocities of the electronic orbits are changed.
These induced magnetic dipole moments align themselves opposite to the applied field.
Thus, m < 0 and mr < 1. 19

20. Diamagnetic Materials (Cont’d)
Usually, diamagnetism is a very miniscule effect in natural materials - that is mr  1.
Diamagnetism can be a big effect in superconductors and in artificial materials.
Diamagnetic materials are repelled from either pole of a magnet. 20

21. Paramagnetic Materials
In the absence of applied magnetic field, each atom has net non-zero (but weak) magnetic dipole moment. These magnetic dipoles moments are randomly oriented so that the net macroscopic magnetization is zero.
In the presence of an applied magnetic field, the magnetic dipoles align themselves with the applied field so that m > 0 and mr > 1. 21