RELATIVE PERMEABILITY

If a piece of soft iron is placed between the pole pieces of a magnet (as shown in below figure), it is observed that the lines of force will be concentrated into it, as if it is easier for them to pass through the soft iron piece than through the surrounding air.

In scientific language this fact is expressed by saying that iron is more permeable or has greater permeability than air. 

It means that magnetic resistance of air is more than iron.

The fact that iron is more permeable than air leads us to another definition of relative permeability, "the conducting power of a substance for lines of magnetic force as compared with air."

MAGNETIC LINES OF INDUCTION

The lines of force travel externally in the magnet, i.e., they pass from north pole through the field to south pole. 

But these lines of force, as soon as they reach south pole, are not supposed to end there; they are imagined to continue through the magnet, finally reaching that point on the north pole from where they started, thus forming closed curves.

These lines of force imagined existing inside the magnetic material are known as Lines of Induction.

MAGNETIC LINES OF FORCE

Definition: A line of force, may be defined as the continuous curve in a magnetic field, the tangent drawn at any point of which gives the direction of resultant intensity at that point.

Mapping of lines of force

These lines of force may in practice be drawn by plotting successive directions pointed out by a small compass needle moving in the field.

Although the magnetic influence itself is entirely invisible, its existence and strength can be judged by such lines of force, which indicate the direction in which the magnetic influence is acting, and the density of which gives the intensity of the field at any point.

MAGNETIC FIELD INTENSITY (H)

When two magnetic poles of strengths 𝑚₁ and 𝑚₂ webers are placed at a distance r meters in a medium of relative permeability 𝜇ᵣ , they experience a force 𝑭 of attraction or repulsion, given by

F=m1×m24π⋅μ0⋅μr⋅r2  N

Since the force exerted on a unit north pole (of strength 1 weber) placed at a point in a magnetic field would be the measure of the intensity of the magnetic field. The "field strength" at that point therefore is the formula for magnetic force. 

If we put 𝑚 = 1 weber and 𝑚₂ = 𝑚 weber (say), then we shall get the field strength 𝑭 as

F=m4π⋅μ0⋅μr⋅r2  N/Wb

This force F experienced by a unit pole, i.e., the field strength, is also denoted by H, and its measure not only newtons/weber but also ampere turns/m.

i.e.,                  H=m4π⋅μ0⋅μr⋅r2  N/Wb


or                      H=m4π⋅μ0⋅μr⋅r2  ampere−turns/meter (AT/m)

By definition the field intensity or magnetic field strength 𝐻 at any point in magnetic field is the force experienced by a unit north pole (1 weber) placed at that point.

Field strength 𝐻, involves the idea of the force, which has both magnitude and a direction, is a vector quantity.

UNIT OF MAGNETIC POLE STRENGTH

The force between two point poles 𝐦₁ and 𝐦₂ held at a distance 𝐫 apart, in any medium is given by

F=m1×m24π⋅μ0⋅μr⋅r2N

If in the above relation we put

𝑚₁ = 𝑚₂ = 1   (say)
r = 1  m

𝜇ᵣ = 1   (say in vaccum)
𝜇₀ = 4𝜋⨯ 10⁻⁷   H/m

then

F=1×14π(4π×10−7)1×1=116π2×10−7

From the above, we may derive the definition of a unit pole as that pole which when placed one meter away in free space (vacuum) from an equal and similar pole experiences repulsive force of
116π2×10−7  newtons    or   14πμ0  newtons.

This unit of pole strength is called Weber.