For Engineering Physics Students

1. MODULE 4
CHAPTER 1
MAGNETISM

2. SYLLABUS
• Magnetic field and Magnetic flux density
• Gauss’s law for Magnetic flux density
• Ampere’s Circuital law
• Faraday’s law in terms of EMF produced by
changing magnetic flux
• Magnetic permeability and susceptibility
• Classification of magnetic materials-para, dia
and ferromagnetic materials

3. Magnetic field and Magnetic flux
density
• Magnetic field /Magnetic field intensity ( H )
A field of electromagnetic energy
which transfers the forces of a
magnet is known as magnetic
field.
Magnetic field strength or
Magnetic field intensity. It is
denoted by the letter H. Unit is
amperes per meter, A/m.
Magnetic flux density is defined
as the amount of magnetic flux
passing through a unit area at
right angles to the magnetic field
lines. It is denoted by the letter
B. It is a vector quantity and unit
is Tesla (T).

4. Gauss’s law for Magnetic flux density
• Gauss’s law for magnetism states that the net
magnetic flux throughout any closed surface is
zero.
∅ 𝐵 = 𝐵 . 𝑑𝑠 = 0
• The magnetic flux entering a
surface is equal to the
magnetic flux leaving a
surface.
• Magnetic field lines always
form closed loops.
• No monopoles exist
CONCLUSIONS

5. Ampere’s Circuital law
• The line integral of magnetic field B around
any closed loop is equal to µ˳ times the
current enclosed by the loop
𝑩. 𝒅𝒍 = µ˳ 𝑰
• Where µ˳ the permeability of free space, its
value is given by 𝟒𝝅 × 𝟏𝟎−𝟕
H/m.

6. Proof of Ampere’s circuital law
By Biot–savart’s law, the magnitude of B at a
point O at a distance r from center C is given by
𝑩 =
µ˳
𝟒𝝅
𝟐𝑰
𝒓
Now, the magnetic field throughout the loop is,
𝐵 . 𝑑𝑙 = 𝐵 𝑑𝑙 𝐶𝑜𝑠𝜃
= 𝐵 𝑑𝑙 =
µ˳
𝟒𝝅
𝟐𝑰
𝒓
𝒅𝒍 =
µ˳
𝟒𝝅
𝟐𝑰
𝒓
𝟐𝝅𝒓
= µ˳ 𝑰
Consider a long straight conductor
carrying a current I. Consider a closed
loop around this conductor having
radius r and each point of this loop
experiences a magnetic field B due to
the current. Let r be the radius of the
loop.

7. Faraday’s law in terms of EMF produced by
changing magnetic flux
STATEMENT: Whenever the magnetic flux associated with a circuit
changes an emf is induced and the induced emf in a closed loop is
equal to the rate of change of magnetic flux through the loop
i.e. Ԑ = −
𝑑∅ 𝐵
𝑑𝑡
where Ԑ is the induced emf and ∅ 𝐵 is the magnetic flux.
The magnetic flux over a small area 𝒅𝑨 in a magnetic field 𝑩 is
given by
𝑑∅ 𝐵 = 𝐵. 𝑑𝐴
When a magnet is moved away or towards the coil,
galvanometer detects some current, this current is called
induced current and the corresponding emf is called induced
emf. This induced emf is due to the change in magnetic flux from
the magnet. Faradays law relates this induced emf to change in
magnetic flux in any loop.

8. Lenz’s law:
Lenz’s law gives the direction of induced emf. It
states that the direction of induced emf is
opposite to the direction of change in magnetic
flux, ∅ 𝐵 .
The negative sign in the equation indicates that
directions are opposite.
Ԑ = −
𝑑∅ 𝐵
𝑑𝑡
change in
magnetic
flux
induced
emf

9. Magnetic permeability and
susceptibility
The magnetic permeability is defined as the property by which a
material allows the magnetic line of force to pass through it. It is
denoted by µ . SI unit is Henry per meter (H/m). It is the ratio of
magnetic induction to the magnetic field strength. i.e. µ =
𝐵
𝐻
.
The relative permeability is the ratio of the permeability of any
medium to the permeability of air or vacuum. It is expressed as
µ 𝒓 =
µ
µ˳
𝒐𝒓 µ = µ˳ µ 𝒓
• Magnetization (M)
The magnetic dipole moment acquired per unit volume is known
as magnetization. It is denoted by the letter M. unit is amperes
per meter (A/m).

10. • Susceptibility is the ratio
of magnetization M (magnetic moment per
unit volume) to the applied magnetizing field
intensity H. It is a dimensionless quantity.
𝝌 𝒎 =
𝑴
𝑯
• Relation among B, H &
𝑩 = µ˳ 𝑯
• Relation between H and M
𝑴 = 𝝌 𝒎 𝑯
The total magnetic field inside a material is given by
𝑩 = µ˳ (𝑯 + 𝑴)

11. 𝑩 = µ˳ (𝑯 + 𝑴)
= µ˳ 𝑯 + 𝝌 𝒎 𝑯
= µ˳ 𝑯 𝟏 + 𝝌 𝒎
= µ˳ 𝑯 µ 𝒓
Where,
𝟏 + 𝝌 𝒎 = µ 𝒓
Now, µ = µ˳ µ 𝒓
Therefore, B=µH

12. Classification of magnetic materials-para,
dia and ferromagnetic materials
Diamagnetic Para magnetic ferromagnetic
The individual atoms or
molecules have no net
magnetic dipole moment
in the absence of external
magnetic field
The individual atoms or
molecules have a net
magnetic dipole moment
in the absence of external
magnetic field
The individual atoms or
molecules have a net
magnetic dipole moment
in the absence of external
magnetic field
They are weakly repelled
by a magnet
They are weakly attracted
by a magnet
They are strongly attracted
by a magnet
Susceptibility is negative Susceptibility is small and
positive
Susceptibility is large and
positive
Susceptibility is
independent of
temperature
Susceptibility varies
inversely with
temperature
Susceptibility varies
inversely with temperature

13. Substances do not obey
Curie’s law
Substances obey Curie’s
law;
Curie’s law is 𝜒 =
𝐶
𝑇
χ is Susceptibility,
C is Curie’s constant &
T is temperature in
Kelvin.
Above Curie temperature
ferromagnetic materials
becomes paramagnetic
and they obey Curie-Weiss
law , that is 𝜒 =
𝐶
𝑇−𝑇 𝐶
Where Tc is Curie
temperature.
Relative permeability is
less than unity
Relative permeability is
slightly greater than unity
Relative permeability is
greater than unity
Do not exhibit Hysteresis
phenomenon
Do not exhibit Hysteresis
phenomenon
Exhibits Hysteresis
Examples: water, air, gold,
copper, lead, quartz,
sodium chloride,
hydrogen etc.
Examples: platinum,
aluminium, magnesium,
chromium etc.
Examples: iron, nickel,
cobalt, steel etc.

14. Some applications of ferromagnetic materials
Ferromagnetic materials are widely used
• for making Electromagnets
• for making permanent magnets
• as core of transformers, motors & generators
• magnetic tapes and devices for storing
memory