# Relative permeability

If the magnetic field exists in a material other than a vacuum, the permeability in the equation is that of the material and not a vacuum. The permeability of a material is written as m but it is usual to speak of the relative permeability of the material. This is the ratio of the permeability of the material to that of a vacuum, and is written as mr (note that mr is a pure number with no units or dimensions).

Therefore:   m = mrmo

Some values for relative permeabilities are given below. The value for iron is many thousands of times that of air; this is why the introduction of an iron core into a solenoid produces a very large increase in the field within it.

 Material Realative permeability Mild steel 2000 Silicon-iron (4.25% Si) 9000 Supermalloy (Fe 16%,Ni 79%,Mo 5%) 1 000 000

Student investigation
Use a Hall probe to investigate the variation of magnetic field of a magnadur magnet with the distance from the magnet.

Repeat the experiment using the other side of the magnet