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 magwhich 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 magnetic 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
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 magwhich 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 magnetic 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