MAGNETIC SUSCEPTIBILITY (k)

Magnetic Susceptibility (k) : The Ratio between the intensity of magnetization produced in a substance and the magnetizing force producing it, is called the magnetic susceptibility of the substance, and is denoted by k.

i.e.

UNIFORM MAGNETIC FIELD

Uniform Magnetic Field: An Uniform Magnetic Field is one in which a pole of say unit strength experiences the same force, is the same.

The lines of force are parallel and straight in an uniform field.

A well known example of an uniform field is magnetic field due to the earth.

MAGNETIC FLUX

Magnetic Flux (𝜙):

In the case of a point pole of strength m webers, the flux density B at distance r is

B=m4πr2   webers/sq meter

∴ Total flux 𝜙 emanating out of strength m webers is

ϕ=flux density×surface area  =B×A

 =m4πr2×4πr2=m webers

ABSOLUTE PERMEABILITY

Definition: The Absolute Permeability (𝜇ₐ) is the ratio of the flux density B (in webers/sq meter) in a substance to the field intensity or magnetizing force H (in newtons/weber of ampere turns/meter) which produces that flux density B.

i.e.,                                                     μa=BH

The Absolute Permeability  𝜇ₐ is also related to the 𝜇₀ (free space) and 𝜇ᵣ (relative permeability) as:

μa=μ0×μr

MAGNETIC FLUX DENSITY (B)

A magnetic pole placed in free space, gives out lines of force in all directions.

The force experienced by a north pole of one weber when placed at P, at a distance r meters from a point pole of m webers, or the field intensity at P, is given by

H=m4π⋅μ0⋅μr⋅r2   N/Wb

The magnitude of field intensity at all points at a distance r from the point pole will be the same, but its direction will be different at different points; but in each case it will be right angles to the surface containing the point.

Now, let us consider a piece of soft iron is placed in a magnetic field H. Let B lines of magnetic induction per square meter of a surface be imagined at right angles to the flux direction.

The magnitude of B is known as the flux density. In  other words, flux density per unit area of a surface at right angles to the flux direction.

Now B will be proportional to H

i.e.,     B∝H      or        B=μ0⋅μr⋅H

Substituting the value of H from above, we have

B=μ0⋅μr⋅m4π⋅μ0⋅μr⋅r2=m4πr2Wb/m2

[Since 𝘮 is in webers and 4𝜋r² is the surface area of a sphere of radius r in meter, therefore B, the flux density is in webers per square meter].