Page 69 - Basic Electrical Engineering

material, or air as the core, the inductance will increase many times. The
(permcability), μ is expressed as

μ = μ μ r
o

where μ is the relative permeability and μ is the permeability of free space.
r
o
The relative permeability of iron may be as high as 2000 times than that of
air. Hence, an iron core coil may have an inductance value 2000 times more

than that of an air-core one, other dimensions remaining the same. Again,
inductance, L is inversely proportional to the length of the flux path and

directly proportional to the area of the core material or the coil. Inductance is
proportional to the square of the number of turns. To have an inductance of a

large value, the number of turns should be high.
The inductance, L can be expressed in terms of the rate of change of the

flux with respect to current flowing in the coil as

For a small increment of di, let the increase of flux be dϕ. Therefore,

If ϕ and i have a linear relationship,