Permeability

Permeability

AU : Dec.-10

• The flow of flux produced by the magnet not only depends on the magnetic field strength but also on one important property of the magnetic material called permeability. It is related to the medium in which magnet is placed. The force exerted by one magnetic pole on other depends on the medium in which magnets are placed.

Key Point : The permeability is defined as the ability or ease with which the magnetic material forces the magnetic flux through a given medium.

For any magnetic material, there are two permeabilities        

i) Absolute permeability ii) Relative permeability.

1. Absolute Permeability (µ)

• The magnetic field strength (H) decides the flux density (B) to be produced by the magnet around it, in a given medium. The ratio of magnetic flux density B in a particular medium (other than vacuum or air) to the magnetic field strength H producing that flux density is called absolute permeability of that medium.                 

• It is denoted by u and mathematically can be expressed as,

i.e        µ = B/H    i.e   B = µH

The permeability is measured in units henries per metre denoted as H/m.

2. Permeability of Free Space or Vacuum (µ₀)

• If the magnet is placed in a free space or vacuum or in air then the ratio of flux density B and magnetic field strength H is called Permeability of free space or Vacuum or air.

• It is denoted as µ₀ and measured in H/m. It denotes the ease with which the magnetic flux permeates the free space or vacuum or air.

• It is experimentally found that this u, i.e. ratio of B and H in vacuum remains constant every where in the vacuum and its value is 4π × 10^-7 H/m.

∴ µ_{0  =} B/H in vacuum = 4π×10^-7 H/m

Key Point : For a magnetic material, the absolute permeability u is not constant. This is because B and H bears a nonlinear relation in case of magnetic materials. If magnetic field strength is increased, there is change in flux density B but not exactly proportional to the increase in H.The ratio B to H is constant only for free space, vacuum or air which is µ₀=4π×10^-7 H/m

3. Relative Permeability (µ_r)

• Generally the permeability of different magnetic materials is defined relative to the permeability of free space (u o). The relative permeability is defined as the ratio of flux density produced in a medium (other than free space) to the flux density produced in free space, under the influence of same magnetic field strength and under identical conditions.

• Thus if the magnetic field strength is H which is producing flux density B in the medium while flux density B. in free space then the relative permeability is defined as

∴  µ_{r =} B/B₀  where H is same.

It is dimensionless and has no units.

For free space, vacuum or air, µ_r= 1

According to definition of absolute permeability we can write for given H,

µ - B/H in medium   ... (1.8.1)

µ₀ = B₀/H in free space ... (1.8.2)

Dividing equation (1.8.1) and equation (1.8.2),

µ/ µ₀=B/B₀

But B/B₀ = µ_r hence µ/ µ₀ = µ_r

µ  = µ₀ µ_r   H/M

The relative permeability of metals like iron, steel varies from 100 to 100,000

Key Point : If we require maximum flux production for the lesser magnetic field strength then the value of the relative permeability of the core material should be as high as possible.

For example if relative permeability of the iron is 1000 means it is 1000 times more magnetic than the free space or air.

• The factors affecting the permeability of a magnetic TIONS. material are temperature, alloying elements, heat treatment of the material and intrinsic material properties such as magnetic moment, domain magnetization etc.

Review Question

1. Define permeability of a magnetic material and the factors on which it depends. AU : Dec.-10, Marks 4