Physics of Magnetism

76 CHAPTER 8. SOME BASIC CONCEPTS AND UNITS

conductors a force equal to newton per meter of length. This definition implies,

using Eq. (8.5), that the permeability in vacuum takes the value

We define the unit of magnetic field strength in terms of the base unit ampere of electric

current. For an infinitely long solenoid with n windings per length of solenoid, one finds

inside the solenoid, by applying Ampere’s law,

As n is expressed in and the electric current I in A, the magnetic field H has the unit

ampere per meter or Consequently, a magnetic field of is the magnetic

field in an infinitely long solenoid consisting of n turns per meter of coil and carrying an

electric current of

The unit of the magnetic induction or magnetic flux density B can be defined by

rewriting Eq. (8.4) as

This equation defines the magnetic induction B for any medium such that the force exerted

on a current element is equal to the vector product of this element and the mag-

which is called tesla, that
is,

magnetic induction is newton per ampere meter or

So the magnetic induction is equal to 1 T if a current element

of 1 A experiences a force of 1 N. As the magnetic permeability in vacuum

netic induction. As the current element is expressed in Am and the force in N, the unit of

equals

a magnetic field strength of in free space corresponds to a mag­

netic induction of or , equivalently, a magnetic induction of 1 T corresponds

to a magnetic field of approximately

The magnetic flux t through a surface element is the scalar product of the

magnetic flux density and this surface element:

The unit of magnetic flux density B is tesla and so the unit of magnetic flux is equal to tesla

square meter or which is called weber (Wb), that is or

also

Another definition of the magnetic flux comes from the phenomenon of induction: its

rate of change generates an electromotive force in a closed conductor. If the current

passes through n turns of the conductor, the e.m.f. is given by:

This equation can also be used to define the unit of flux. As the electromagnetic force is

expressed in volt and n is a pure number, the unit of magnetic flux becomes volt second or

we see that the unit of magnetic flux can be transformed into

again equal to 1 Wb.

Vs. Remembering that the unit of energy, joule, can be written as 1 J = 1 V A s = 1 N m,

which is