Electromagnetism - Important Terms In Magnetism

To describe the magnetic properties of materials, we define the following few terms which should be clearly understood:
    
Magnetic permeability 

It is the ability of a material to permit the passage of magnetic lines of force through it the degree of extent to which magnetic field can penetrate or permeate a material is called relative magnetic permeability of the material. It is represented by μr.

Relative magnetic permeability fo a material is defined as the ratio of the number of lines of magnetic induction per unit area (flux density B) in that material to the number of magnetic lines per unit area that would be present if the medium were replaced by vacuum (flux density B₀)

μ_r = B / B₀

μr has no dimension its value foe vacuum is one.

Relative magnetic permeability of a material may also be defined as the ratio of magnetic permeability of the material (μ) and magnetic permeability to free space (μo)

μ_r = μ / μ₀

∴ μ  = μ_rμ₀

We know that μ₀ =4π  x 10^-7 Weber/amp metre (Wb A ^-1 m ^{– 1})   or Henry/metre (Hm^-1)     

∴  S.I units of permeability (μ) are 

Hm^-1 = Wb A^-1 m^-1 = Tm² A^-1 M^-1 = TmA^-1                                                                                                          
                                                                          
Magnetic induction (or magnetic flux density B

To understand this term we make use of Lorentz force equation.

When a positive test charge qo is fired with a velocity v through a point P and the moving charge experiences a sideways force F we assert that a magnetic field is present at P. the magnetic induction B of this field is a vector satisfying Lorentz force equation

F = q₀ (v X B)

Magnitude of this force is 

F = q₀ v B sin θ

Where θ is angle between v and B. 

We may define magnetic induction or flux density of a magnetic field being equal to the force experienced by a unit positive charge moving with unit velocity in a direction perpendicular to the magnetic field. 

S.I unit of B is Weber/metre² (Wb m^-2) or tesla (T)   

Magnetizing force or magnetizing intensity (H)

The degree to which a magnetic field can magnetize a material is represented in terms of magnetizing force or magnetizing intensity (H) let us conside4r a steroidal solenoid with n turns per unit length carrying a current I wound round a ring of a magnetic material. The magnetic induction of the field produced in the material of the steroidal solenoid is 

B = μ_nL

The product n L is called magnetizing force or magnetizing intensity H 

H = n L.

So that B = μ H

Hence the magnitude of magnetizing force may be defined as the number of ampere turns flowing round unit length of toroid solenoid to produce the magnetic induction B in the solenoid.

If inside the steroidal solenoid there is free space then magnetic induction

B₀ = μ₀ H

Where μ₀ is permeability of free space

The S. l units of H are ampere turn/ metre Am^-1 from 

H = B₀/ μ₀ = F/ q₀v / μ₀ = F / q₀ v μ₀

H = N/C(ms -1) TmA-1 = Nm-2 T-1

Also H = N / Tm² = N / Wb = N Wb^-1 = m Jm ^-1 Wb^-1

(c) Intensity of magnetization it represents the extent to which a specimen is magnetized when placed in a magnetizing field.

Quantitatively the intensity of magnetization of a magnetic material is defined as the magnetic moment per unit volume of the material. 

I = magnetic moment / volume = M / V

If a = uniform area of cross-section of the magnetized specimen (a rectangular bar)

2l = magnetic length of the specimen.

M = strength of each pole of the specimen, 

∴ from (8)

L = m x 2l / a x 2l = m / a 

Hence intensity of magnetization of a magnetic material is also defined as the pole strength per unit area of cross- section of the material.

As l = magnetic moment / volume

∴ l = Amp metre² / metre³ = Am^-1

These are Si unit of I which are same as SI unties of H. 

(d) Magnetic susceptibility it is a property which determines how easily a specimen can be magnetized.

Quantitatively susceptibility of a magnetic material is defined as the ratio of the intensity of magnetization induced in the material to the magnetizing force (H) applied on it. Magnetic susceptibility is represented by 

Ym = I / H

Since by definition, I is magnetic moment per unit volume y_m is usually called volume susceptibility of the material. 


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