theory mahnetism

1. 18 January 2024 M.A. Khatik 1
Subject: Engineering Physics
Zeal college of Engineering and Research Narhe ,Pune.
By M.A. Khatik
AssistantProfessorin Departmentof EngineeringSciences

2. 18 January 2024 M.A. Khatik 2
The magnetism originates from the spin and
orbital magnetic moment of an electron.
And magnetic moment is produced by rotation of electron around the
nucleus which produces a current which is given by 𝑴 = 𝑰. 𝑨--(1)
but current is given by 𝑰 =
𝒆
𝑻
and
Area of the orbit A= 𝝅𝒓𝟐
∴ 𝒆𝒒𝒂𝒖𝒕𝒊𝒐𝒏 𝟏 𝒃 𝒆𝒄𝒐𝒎𝒆𝒔
M =
𝒆
𝑻
𝝅𝒓𝟐-------------------------(2)
But 𝑻 =
𝟐𝝅𝒓
𝒗
∴ 𝒆𝒒𝒂𝒖𝒕𝒊𝒐𝒏 𝟐 𝒃 𝒆𝒄𝒐𝒎𝒆𝒔
M =
𝒆𝒗
𝟐𝝅𝒓
𝝅𝒓𝟐
M =
𝒆𝒗𝒓
𝟐
this is magnetic moment----------------------(3)
Multiplying and dividing by “m” on RHS we get
Q- On the basis of spin motion of electron and orbital motion of
electron and spin motion of nucleus explain the origin of
Magnetism

3. 18 January 2024 M.A. Khatik 3
M =
𝒎𝒓𝒗𝒆
𝟐𝒎
-------------------------------------------(4)
But from Bohr’s second postulate of atomic theory
Angular momentum = L= mrv = 𝒏ℏ
Where ℏ =
𝒉
𝟐𝝅
𝒆𝒒𝒖𝒂𝒕𝒊𝒐𝒏 𝟒 𝒃𝒆𝒄𝒐𝒎𝒆𝒔
∴ 𝑴𝑳 = 𝒏
𝒆ℏ
𝟐𝒎
-----(5) for orbital motion of electron
∴ 𝑴𝒔 = 𝒔
𝒆ℏ
𝟐𝒎
--------(6) for spin motion of electron
∴ 𝑴𝑵 = 𝑵
𝒆ℏ
𝟐𝒎
----(7) for spin motion of nucleus
Where
𝒆ℏ
𝟐𝒎
is called Bohr’s Magneton.

4. 18 January 2024 M.A. Khatik 4
Define the following terms:
(1) Intensity of Magnetization (𝑴𝒛) :
“ The ratio of magnetic moment (𝑴) to volume of
specimen (V) is called intensity of magnetization.” unit is C/m
(2) Magnetic Susceptibility (𝝌):
“The ratio of intensity of magnetization (I) to
magnetizing field strength (H) is called magnetic Susceptibility ”.
(3) Magnetic Permeability (𝝁):
“The ratio of magnetic induction (B) to Magnetizing
field strength (H) is called Magnetic Permeability”.
(4) Relative Permeability (𝝁𝒓):
“The ratio of Permeability of medium (𝝁) to Permeability
of free space (𝝁𝒐) is called Relative Permeability ”.
(5) Magnetic filed induction (B):” magnetic flux perunit area is called
magnetic filed induction”.
𝑴𝒛 =
𝑴
𝑽
𝝌 =
𝑴𝒛
𝑯
𝝁 =
𝑩
𝑯
𝝁𝒓 =
𝝁
𝝁𝒐
𝑩 =
∅
𝑨

5. Relation between magnetic permeability
𝝁 and magnetic susceptibility (𝝌)
Consider a magnetic material is placed in uniform magnetic field of
strength (H) then total induction (B) passes through it, is the sum of
induction due to H and 𝑴𝒛
𝑩 = 𝝁𝒐𝑯 + 𝝁𝒐𝑴𝒛
𝑩 = 𝝁𝒐(𝑯 + 𝑴𝒛) -------------(2)
But 𝑩 = 𝝁𝑯 𝒂𝒏𝒅 𝑴𝒛=𝝌𝑯
∴equation (2) becomes
𝝁𝑯 = 𝝁𝒐(𝑯 + 𝝌𝑯)
𝝁 = 𝝁𝒐(𝟏 + 𝝌)
𝝁
𝝁𝒐
= (𝟏 + 𝝌)
𝝁𝒓 = (𝟏 + 𝝌)
S
N

6. Diamagnetic Paramagnetic Ferromagnetic
1- All the electrons are
revolving around the
nucleus in different
direction but net magnetic
moment is zero. Because
all electrons are in
paired.
∴ 𝑴 = 𝟎
All the electrons are
revolving around the
nucleus in different
direction but net
magnetic moment is not
zero. Because very few
electrons are unpaired. ∴
𝑴 ≠ 𝟎
All the electrons are
revolving around the
nucleus in different domain
in same direction but net
magnetic moment is zero. ∴
𝑴 = 𝟎
2- when these materials
are placed in a magnetic
field then these materials
weekly repel the magnetic
fields .
2- when these materials
are placed in a magnetic
field then these
materials weekly attract
the magnetic fields .
2- when these materials are
placed in a magnetic field
then these materials
strongly attract the
magnetic fields .

7. 18 January 2024 M.A. Khatik 7
Diamagnetic Paramagnetic Ferromagnetic
4- magnetic properties of
these materials 𝝌 do not
depend on temperature.
4- magnetic properties of
these materials 𝝌 is
inversely proportional
temperature(T)
4- magnetic properties of
these materials 𝝌 is
inversely proportional
temperature(T) but after
specific temperature called
Curi temperature (Tc).
5- hence these materials
do not obey Curi law.
i.e. 𝝌 ∝
𝟏
𝑻
Graph:-
5- hence these materials
obey Curi law.
i.e. 𝝌 ∝
𝟏
𝑻
Graph:-
5- hence these materials
obey Curi law after Curi
temperature.
i.e. 𝝌 ∝
𝟏
𝑻
Graph:-
6- Examples:
Water, Quartz, CuCl2
Examples:
Gold, silver, Cu Al , etc
Examples:
Fe , Ni, Co only

8. 18 January 2024 M.A. Khatik 8
2- in Magnetic storage devices:
Now a days audio video or any information is stored
semiconductors memories. But semiconductors are volatile
where as magnetic storage is permanent and non volatile.
Computer hard disk is a suitable example of magnetic
storage device.
Applications of magnetism

9. 18 January 2024 M.A. Khatik 9
3- in Magneto optical recordings:
CD or DVD writing and reading is a best example of
magneto optical recording in which a LASER beam is used
to write or to read a data on the surface of CD or DVD which
coated with magnetic material iron oxide. This data is stored in
the pits on the surface of CD or DVD.

10. 18 January 2024 M.A. Khatik 10
Subject: Engineering Physics
Zeal college of Engineering and Research Narhe ,Pune.
By M.A. Khatik
AssistantProfessorin Departmentof EngineeringSciences

11. 18 January 2024 M.A. Khatik 11
“In case of metals, as the temperature decreases resistivity
also decreases but in case of some metals at particular
temperature resistivity reduces to zero and thus conductivity
become infinity. Such temperature is called as “Critical
Temperature” or “Transition temperature” , and this
phenomenon is known as superconductivity. And the
materials which exhibit this phenomenon are called
superconductors. As shwon in fig.

12. Properties of Superconductors
(1)- Zero Electrical Resistance (𝝆 = 0 and σ = ∞)
(4)- Meissner Effect ( Susceptibility = χ = M/H = -1)
(2)- Critical Magnetic Field
(3)- Persistence Current

13. 18 January 2024 M.A. Khatik 13
At normal conducting State
1. At room temperature i.e.
above critical temperature
( T >Tc ).It is impossible to
determine the zero electrical
resistance.
2. Because voltage drop is
observed across the ends of
superconductor is not zero.
As V ≠ 0 ∴ R=
𝑽
𝑰
≠ 𝟎
3. Thus electrical resistance is
not equal to zero.
At superconducting State
1. But At below critical
temperature ( T <Tc ). It is
possible to determine the
zero electrical resistance.
2. Because voltage drop is not
observed across the ends of
superconductor.
As V = 𝟎 ∴ R=
𝑽
𝑰
= 𝟎.
3. Thus electrical resistance is
zero.

14. Explanation from the graph :
Thus from graph we conclude
that material becomes normal
conductor from superconductor
either increase in applied
magnetic field (Hc) or critical
temperature. Hence graph is
parabolic in nature.
Statement: “Minimum applied magnetic field required to
destroy the superconductivity and restore the normal
resistivity of specimen is called critical magnetic field.(Hc )”.

15. 15
2
0 1
C
C
T
H H
T
 
 
 
  
 
 
 
Where; H0 – Critical field at 0K
T - Temperature below TC
TC - Transition Temperature
Hc – Critical field below TC
For example : for Mercury (Hg)
Critical magnetic field (Hc) = 0.04 T at T= 0 Kelvin. Where as
Critical magnetic field (Hc) = 0.02T at T= 3 K
This relation plays an important role in the study of properties of
superconductors.
The relation between critical temperature and critical magnetic filed
is given by

16. 1. When a superconducting ring placed in magnetic field
and it is cooled below its critical temperature, then
magnetic flux gets trapped in it.
2. Due to this trapped flux an induced current circulates
on the surface of the ring even magnetic field is
switched off.
3. And it does not decrease, because superconductors has
zero electrical resistance.
4. 𝑰 = 𝑰𝒐𝒆
−𝑹𝒕
𝑳 where R=0 ∴ 𝑰 = 𝑰𝒐
5. Such current is called persistence current”.
6. As R=0 hence there will not be any power loss ( P = I2 R)
.

17. 18 January 2024 M.A. Khatik 17

18. Statement : “When the superconducting material is placed in
a magnetic field starts to cool it, equal to or less than its
critical temperature (T≤TC) then magnetic flux is trapped
in it and a magnetic field is developed inside the
superconducting material which opposes the magnetic
flux lines of external applied magnetic filed” hence it
behaves like a diamagnetic material. This is phenomenon
is called Meissner Effect”.
Figure
SC push out
Magnetic Flux
At T > Tc
magnetic flux
passes through SC
At T < Tc

19. 1. When a superconducting material is placed in a
magnetic field , then due to this magnetic field a
current is induced in the superconductor and this
current circulates on the surface of the
superconductor.
2. Due to this circulating current a self magnetic filed
creates every where equal and opposite to applied
magnetic filed.
3. This induced magnetic filed on the surface of
superconductor opposes the applied magnetic filed .
4. Hence all flux excluded from the specimen.
5. Thus Meissner concluded that a superconductor acts
as a perfectly diamagnetic at superconducting state.

20. At Normal conducting State ( at T> 𝑻𝒄)
Then Magnetic flux passes through it is given by
B = μo (H +M) ------(1)
Where , H = External applied magnetic filed
M = Magnetization produced within specimen
B = Magnetic flux passes through specimen
At superconducting State ( at T< 𝑻𝒄)
no magnetic flux passes through the specimen, then B = 0 ,
∴equation (1) becomes
0 = μo (H +M) --------(2)
∴ M = -H
∴ M/H = -1 = χ = susceptibility of material ---------(3)
susceptibility negative means superconductor behaves as a
perfectly diamagnetic below critical temperature.

21. Types of Superconductors
Type I
1. Soft superconductor
2. Because made up from pure
superconducting materials
3. Sudden loss of magnetization
4. Exhibit compete Meissner Effect
5. One HC = 0.1 tesla
6. Hence they have very less technical
applications
7. No mixed state
8. Eg. – Pb, Sn, Hg
Type II
1. Hard superconductor
2. Because made up of alloy
superconducting materials
3. Gradual loss of magnetization
4. Does not exhibit complete Meissner
Effect
5. Two HC1 & HC2 (≈30 tesla)
6. Hence they have very large technical
applications.
7. Mixed state present
8. Eg. –alloy of Nb-Sn, Nb-Ti, Ba-Bi
Superconducting
-M
Normal
Mixed
HC1 HC
HC2
H
-M
H
HC
Superconducting
Normal

22. Principle: it works on the principle of persistent current
Explanation: D.C. Josephson’s effect
1. When two superconductors are
connected by an insulator .
2. And no external voltage is applied
across the superconductors.
3. Then very small amount of current
flows through the insulator due to
tunneling of Cooper’s pair of electrons
through the junction.
4. This junction is called Josephson’s
junction and this effect is called D.C.
Josephson’s effect
Explanation: D.C. Josephson’s effect
1. When two superconductors are
connected by an insulator .
2. And D.C external voltage is applied
across the superconductors.
3. Then a sinusoidal electrical current
flows through the junction due to
force fully tunneling of Cooper’s
pair of electrons through the
junction.
4. Such effect is called A.C.
Josephson’s effect

23. Uses of Josephson devices
• Magnetic Sensors
• Gradiometers
• Oscilloscopes
• Decoders
• Analogue to Digital converters
• Oscillators
• Microwave amplifiers
• Sensors for biomedical, scientific and defense purposes
• Digital circuit development for Integrated circuits
• Microprocessors
• Random Access Memories (RAMs)

24. Principle :
Small change in magnetic field, produces variation in the flux
quantum.
Construction:
(SQUID) consists of two superconductors separated by thin
insulating layers to form two parallel Josephson junctions.
Explanation :
• When the magnetic field is applied perpendicular to the ring
current is induced at the two junctions.
• Induced current flows around the ring due to which magnetic
flux produces in the ring this creates a quantum field applied.
• And it is used to detect the variation of very minute magnetic
signals ( magnetic field).
SQUID
( superconducting Quantum Interface Device)

25. Uses of SQUID
• Storage device for magnetic flux
• Study of earthquakes
• Removing paramagnetic impurities
• Detection of magnetic signals from brain,
heart etc.

26. Construction :
Consists of
superconducting ring
having magnetic fields
of quantum
values(1,2,3..)
Placed in between the
two josephson
junctions

27. 1- Applications of Meissner Effect
Meissner's effect of superconductors is used in magnetic levitation
trains because of Repulsion of external magnets helps to creates the
air cushion between train wheels and its track due to which train
levitates on the tracks and its speed increases to 500 km/hr which is
too much high as compare to normal trains.
Yamanashi MLX01 Maglev train

28. 1) Large distance power transmission because resistivity
(ρ = 0) is zero and hence conductivity is infinite.
2) Superfast switching device (because R=0)
3) Memory / Storage element (because of persistent
current)
4) Highly efficient small sized electrical generator and
transformer ( because of very high critical magnetic
field ).
5) Nuclear Magnetic Resonance (NMR) to scan the brain
wave activity, and to diagnosis of brain tumor.
(because of very high magnetic field below Tc).
6) Separate damaged cells and healthy cells.
Applications of superconductivity