O N PERMITTIVITY AND PERMEABILITY In the universal law of gravitation, we say that any two point masses exert a force on each other which is proportional to the product of the masses m , m and inversely proportional to the square of the distance r between them. We write it as F = Gm m / r where G is the universal constant of gravitation. Similarly in Coulomb’s law of electrostatics we write the force between two point charges q , q , separated by a distance r as F = kq q / r where k is a constant of proportionality. In SI units, k is taken as / πε where ε is the permittivity of the medium.
Also in magnetism, we get another constant, which in SI units, is taken as µ / π where µ is the permeability of the medium. Although G , ε and µ arise as proportionality constants, there is a difference between gravitational force and electromagnetic force. While the gravitational force does not depend on the intervening medium, the electromagnetic force depends on the medium between the two charges or magnets. Hence while G is a universal constant, ε and µ depend on the medium.
They have different values for different media. The product εµ turns out to be related to the speed v of electromagnetic radiation in the medium through εµ = / v . Electric permittivity ε is a physical quantity that describes how an electric field affects and is affected by a medium. It is determined by the ability of a material to polarise in response to an applied field, and thereby to cancel, partially, the field inside the material.
Similarly, magnetic permeability µ is the ability of a substance to acquire magnetisation in magnetic fields. It is a measure of the extent to which magnetic field can penetrate matter. Example . A straight wire of mass g and length .
m carries a current of A. It is suspended in mid-air by a uniform horizontal magnetic field B ( Fig. . ).
What is the magnitude of the magnetic field?