1
SPH 111
1.0 MAGNETISM
1.10 Magnetic Properties of Materials and Their Uses
We begin the discussion of magnetic materials by defining the different terms used. It is
necessary to investigate the magnetic properties of various materials because it leads us
to decide whether they are suitable for permanent magnets such as are used in
loudspeakers or temporary magnets as are used in transformers (as cores). The magnetic
properties of materials are attributed to the motion of electrons inside atoms.
1.11 Flux Density in the Magnetic material
The magnetic field intensity B
We define the space around a magnet or a current carrying conductor as the site of a
magnetic field. The magnetic field is represented by the field vector H characterizing the
force due to this field. Its direction at a point is the direction of the force experienced by
a north seeking pole at a point. The other basic magnetic field vector B, is called the
magnetic field induction or the magnetic flux density. It is represented by lines of
induction. The tangent to a line of induction at any point gives the direction of B at that
point.
The lines of induction are drawn so that the number of lines per unit cross-sectional area
is proportional to the magnitude of B. Where the lines are close together B is large and
where they are far apart then B is small.
In order to define B and its units consider a positive charge qo moving with velocity v
through a point and it experiences a force F due to the field. Then we say that the
magnetic field is present at the point, and B is the vector whose magnitude is given by the
relation
F = qovBsinθ
Where F is in a direction perpendicular to both v and B and θ is the angle between v and
B. The units for B from the above relation is thus Newton/(metre/second) which is
referred to as tesla, T. B may also be defined from this relation as the force per unit
current length and at right angles to the magnetic field.
Note: The product qv is a current so any assembly of moving charges or current
will experience a sideways force when in a magnetic field
In general B is proportional to H and the constant of proportionality µ (called the
permeability) depends on the medium of the space where H is present
, 2
Thus B = µH
In a vacuum µ = µo and is called the permeability of free space. The ratio of µ to µo is
called the relative permeability and is thus the ratio of the value of B when there is
material medium to the value when there is only vacuum i. e.
µ B
µr = =
µo Bo
Q: What is the relative permeability of vacuum
What are the units of µr
Magnetic flux φ
The product of intensity B normal to an area and the cross-sectional area A through
which B passes is called the flux. Flux is thus the number of field lines crossing an area
A and is usually denoted by φ and its SI unit is the Weber (Wb). Thus we can write
φ =Bacosθ
where θ is the angle between the lines and the area.
Magnetic moment
The orientation of a magnet is specified by means of a vector µ(called the magnetic
moment) along the axis of the magnet pointing in the direction from the south seeking
end toward the North seeking pole. The orientation of the magnetic moment due to a coil
is specified by the vector µ lying along the axis of the coil and pointing in the direction
related to the current by the right hand rule. The magnetic moment of a small plane coil
is a vector whose magnitude is the product of the number of turns, N, the current in each
turn, I, and the area A of the circuit. The direction of the vector is perpendicular to the
plane of the coil in the same sense given by the right hand rule, that is
µ = NAI
And is measured in Am2
A magnet in a uniform magnetic field experiences a couple which gives it an angular
acceleration and provided there is damping ultimately comes to rest with its axis parallel
to the field and so the magnetic moment vector and the field vector align. The direction
of the magnetic intensity at a point is the direction into which the magnetic moment
vector of either a small plane coil or a small magnet tends to turn when the small coil or
magnet is placed at that point in space.
1.12: Magnetization
In materials the electrons moving round the nucleus constitute current loops and so the
atoms may have resultant magnetic moments. This may happen in the presence or
absence of a magnetic field. The physical quantity used to describe the magnetic state of
a material is the magnetic moment per unit volume. This is called the magnetization M
i. e.
, 3
Total magnetic dipole moment
M =
Volume
Q: What are the units of M
Let us now evaluate the expressions for B and M and their relationship for a point in a
material placed in a magnetic field. Consider a toroid of length L, as shown:
Let the total number of turns = N, mean radius = r, and circumference = L. The total flux
density B depends on the following factors:
(i) the current flowing in the wire
(ii) the magnetization of the material.
Thus we have
B = Bo + Bm
where Bo is the flux density due to the current I in the wire, and Bm is the flux density due
to the magnetization of the material. Usually Bo>> Bm .
Magnetization is related to the average magnet dipole moment for many molecules. The
magnetization flux density Bm is produced by many small circulating currents inside the
magnetic material, due to the circulating and spinning electrons in the atoms. This is
shown in the diagram below:
In the same way, the small circulating currents inside the magnetic materials add up to a
single current Im flowing in the coil wound round the core. This current is called Surface
or Magnetization current, which adds up to the actual current I flowing in the coil. The
actual current produces a flux density Bo.
Let n be the turns per unit length (n = N/L), where L = 2πr. Then
µ NI N
Bo = µ o nI = o = µo L
2πr 2πr
Surface current Im produces a flux density Bm, which is given by the equation below
Bm = µo nI m
, 4
Therefore, the total flux density B is given by
B = Bo + Bm
B = µo n(I + I m )
1.13 Intensity of Magnetization
The magnetic moment of each current turn due to the surface current Im is given as
µ = A× Im
where A is the cross-sectional area of each turn. For the whole toroid, the magnetic moment
is given by
µ = nLAI m , nL = N
Magnetic moment per unit volume, i.e. intensity of magnetization M, is then
nLAI m nLAI m
M = = = nI m
V AL
⇒ Bm = µ o nI m = µ o M
Similarly, the magnetic field density or magnetic intensity due to the actual(applied) current
I is given by
B = µonI
Hence the total flux density B in the material is given by
B = Bo + Bm = µ o nI + µ o nI m = µo H + µo M
= µ o (H + M )
Q: 1. What are the units for H
2. What are the units for µ. Also find out the value for µo
1.14 Relative Permeability and magnetic susceptibility
From the foregoing discussion
B = µ o (H + M )
∴ µH = µ o (H + M )
And µr = µ H +M M
= = 1+
µo H H
SPH 111
1.0 MAGNETISM
1.10 Magnetic Properties of Materials and Their Uses
We begin the discussion of magnetic materials by defining the different terms used. It is
necessary to investigate the magnetic properties of various materials because it leads us
to decide whether they are suitable for permanent magnets such as are used in
loudspeakers or temporary magnets as are used in transformers (as cores). The magnetic
properties of materials are attributed to the motion of electrons inside atoms.
1.11 Flux Density in the Magnetic material
The magnetic field intensity B
We define the space around a magnet or a current carrying conductor as the site of a
magnetic field. The magnetic field is represented by the field vector H characterizing the
force due to this field. Its direction at a point is the direction of the force experienced by
a north seeking pole at a point. The other basic magnetic field vector B, is called the
magnetic field induction or the magnetic flux density. It is represented by lines of
induction. The tangent to a line of induction at any point gives the direction of B at that
point.
The lines of induction are drawn so that the number of lines per unit cross-sectional area
is proportional to the magnitude of B. Where the lines are close together B is large and
where they are far apart then B is small.
In order to define B and its units consider a positive charge qo moving with velocity v
through a point and it experiences a force F due to the field. Then we say that the
magnetic field is present at the point, and B is the vector whose magnitude is given by the
relation
F = qovBsinθ
Where F is in a direction perpendicular to both v and B and θ is the angle between v and
B. The units for B from the above relation is thus Newton/(metre/second) which is
referred to as tesla, T. B may also be defined from this relation as the force per unit
current length and at right angles to the magnetic field.
Note: The product qv is a current so any assembly of moving charges or current
will experience a sideways force when in a magnetic field
In general B is proportional to H and the constant of proportionality µ (called the
permeability) depends on the medium of the space where H is present
, 2
Thus B = µH
In a vacuum µ = µo and is called the permeability of free space. The ratio of µ to µo is
called the relative permeability and is thus the ratio of the value of B when there is
material medium to the value when there is only vacuum i. e.
µ B
µr = =
µo Bo
Q: What is the relative permeability of vacuum
What are the units of µr
Magnetic flux φ
The product of intensity B normal to an area and the cross-sectional area A through
which B passes is called the flux. Flux is thus the number of field lines crossing an area
A and is usually denoted by φ and its SI unit is the Weber (Wb). Thus we can write
φ =Bacosθ
where θ is the angle between the lines and the area.
Magnetic moment
The orientation of a magnet is specified by means of a vector µ(called the magnetic
moment) along the axis of the magnet pointing in the direction from the south seeking
end toward the North seeking pole. The orientation of the magnetic moment due to a coil
is specified by the vector µ lying along the axis of the coil and pointing in the direction
related to the current by the right hand rule. The magnetic moment of a small plane coil
is a vector whose magnitude is the product of the number of turns, N, the current in each
turn, I, and the area A of the circuit. The direction of the vector is perpendicular to the
plane of the coil in the same sense given by the right hand rule, that is
µ = NAI
And is measured in Am2
A magnet in a uniform magnetic field experiences a couple which gives it an angular
acceleration and provided there is damping ultimately comes to rest with its axis parallel
to the field and so the magnetic moment vector and the field vector align. The direction
of the magnetic intensity at a point is the direction into which the magnetic moment
vector of either a small plane coil or a small magnet tends to turn when the small coil or
magnet is placed at that point in space.
1.12: Magnetization
In materials the electrons moving round the nucleus constitute current loops and so the
atoms may have resultant magnetic moments. This may happen in the presence or
absence of a magnetic field. The physical quantity used to describe the magnetic state of
a material is the magnetic moment per unit volume. This is called the magnetization M
i. e.
, 3
Total magnetic dipole moment
M =
Volume
Q: What are the units of M
Let us now evaluate the expressions for B and M and their relationship for a point in a
material placed in a magnetic field. Consider a toroid of length L, as shown:
Let the total number of turns = N, mean radius = r, and circumference = L. The total flux
density B depends on the following factors:
(i) the current flowing in the wire
(ii) the magnetization of the material.
Thus we have
B = Bo + Bm
where Bo is the flux density due to the current I in the wire, and Bm is the flux density due
to the magnetization of the material. Usually Bo>> Bm .
Magnetization is related to the average magnet dipole moment for many molecules. The
magnetization flux density Bm is produced by many small circulating currents inside the
magnetic material, due to the circulating and spinning electrons in the atoms. This is
shown in the diagram below:
In the same way, the small circulating currents inside the magnetic materials add up to a
single current Im flowing in the coil wound round the core. This current is called Surface
or Magnetization current, which adds up to the actual current I flowing in the coil. The
actual current produces a flux density Bo.
Let n be the turns per unit length (n = N/L), where L = 2πr. Then
µ NI N
Bo = µ o nI = o = µo L
2πr 2πr
Surface current Im produces a flux density Bm, which is given by the equation below
Bm = µo nI m
, 4
Therefore, the total flux density B is given by
B = Bo + Bm
B = µo n(I + I m )
1.13 Intensity of Magnetization
The magnetic moment of each current turn due to the surface current Im is given as
µ = A× Im
where A is the cross-sectional area of each turn. For the whole toroid, the magnetic moment
is given by
µ = nLAI m , nL = N
Magnetic moment per unit volume, i.e. intensity of magnetization M, is then
nLAI m nLAI m
M = = = nI m
V AL
⇒ Bm = µ o nI m = µ o M
Similarly, the magnetic field density or magnetic intensity due to the actual(applied) current
I is given by
B = µonI
Hence the total flux density B in the material is given by
B = Bo + Bm = µ o nI + µ o nI m = µo H + µo M
= µ o (H + M )
Q: 1. What are the units for H
2. What are the units for µ. Also find out the value for µo
1.14 Relative Permeability and magnetic susceptibility
From the foregoing discussion
B = µ o (H + M )
∴ µH = µ o (H + M )
And µr = µ H +M M
= = 1+
µo H H
