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Title: Magnetism and Superconductivity
Description: These notes are on the topic of Magnetism and Superconductivity. These notes are aimed at first-year students. I made these notes when I was in my first year of engineering and these help me get a 10/10 SGPA. And I'm sure this would help you too. Notes are organized properly and I've also put some questions for revision and tests. Notes also contain visuals and images to visualize the concepts.
Description: These notes are on the topic of Magnetism and Superconductivity. These notes are aimed at first-year students. I made these notes when I was in my first year of engineering and these help me get a 10/10 SGPA. And I'm sure this would help you too. Notes are organized properly and I've also put some questions for revision and tests. Notes also contain visuals and images to visualize the concepts.
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MMIT, Lohgaon, Pune // Engineering Physics [2019-20] // Unit 5 – Magnetism and Superconductivity
Unit 5: Magnetism and Superconductivity
Syllabus
Magnetism
- Origin of magnetism
- Classification of magnetism on the basis of permeability (qualitative)
- Applications of magnetic devices: transformer cores, magnetic storage, magneto-optical
recording
Superconductivity
- Introduction to superconductivity; Properties of superconductors: zero electrical
- resistance, critical magnetic field, persistent current, Meissner effect
- Type I and Type II superconductors
- Low and high temperature superconductors (introduction and qualitative)
- AC/DC Josephson effect; SQUID: basic construction and principle of working; Applications of
SQUID
- Applications of superconductors
Introduction
-
-
Magnetic materials play a prominent role in modern technology
...
Magnetic materials can broadly be classified into soft and hard materials
...
They are used in AC applications
...
Further, depending on their response to the external magnetic field, magnetic materials can
be broadly classified into three groups: diamagnetic, paramagnetic and ferromagnetic
materials
...
1
...
Magnetic dipole
- Magnetic dipole is generally a tiny magnet of microscopic to subatomic
dimensions generated due to current loop
...
- Magnetic dipole is referred to smallest magnetic unit having two poles
(north and south) that produces magnetic field and are inseparable from
each other
...
2
...
It is a measure of a dipole’s ability to align itself according to
direction of external magnetic field
...
- Magnetic dipole moment is defined as the maximum amount of torque caused by magnetic
force on a dipole that arises per unit value of surrounding magnetic field in vacuum
...
Magnetic field strength (H)
- The strength (or intensity) of magnetic field at any point in magnetic field is force
experienced by a unit north pole placed at that point
...
- The unit of H is ampere-turns per meter (A/m) in SI system
...
Magnetization (M)
- Magnetization (or intensity of magnetization) is the measure of magnetism of magnetic
materials
...
- The unit of magnetization in SI system is amperes per meter (A/m)
...
Thus, M H or M = H
Where, is called as magnetic susceptibility
...
Magnetic Susceptibility ()
- The magnetic susceptibility of a material is a measure of the ease with which the material
can be magnetized
...
- Hence, = M/H
- Materials having high susceptibility are easily magnetized
...
Magnetic flux ()
- Magnetic flux is a measurement of the total magnetic field which passes through a given
area
...
- The SI unit of magnetic flux is the Weber (Wb)
...
Magnetic Induction or magnetic flux density (B)
- A magnetic field is schematically represented by lines of magnetic induction or magnetic flux
density)
...
- Magnetic induction is the number of lines of force through a unit area of cross section
perpendicularly
...
- The SI unit of B is Weber per square meter (Wb/m2) and CGS unit is Tesla (T)
- 1 Gauss = 10-4 Tesla
8
...
The magnetic induction B produced
inside the material is given by
𝐵 = 𝜇0 (𝐻 + 𝑀)
Where, 0 is known as permeability of the free space
...
In free space, M=0, and 𝐵 = 𝜇0 𝐻
9
...
The absolute permeability of the
material is a measure of the degree of which the field lines penetrate (or permeate) the
material
...
𝐵
- Thus, 𝜇 = 𝐻
...
10
...
𝜇
- Thus, 𝜇𝑟 =
...
Its value for air or vacuum is one
...
Relation between r and
The magnetic induction
Or
Thus,
𝜇
As
𝜇𝑟 =
𝜇0
𝐵 = 𝜇0 1 + 𝐻
𝐵 = 𝜇𝐻
𝜇 = 𝜇0 1 +
𝜇𝑟 = 1 +
12
...
- It is the natural unit for the measurement of atomic magnetic moments
...
28 × 10−24 𝐴
...
1
...
These motions give rise to magnetic dipole moments
...
Each electron orbit is
equivalent to a tiny current loop
...
The sum of orbital magnetic moments of individual electrons generates the
total orbital magnetic moment of an atom
...
28 × 10−24 𝐴
...
It can be shown that spin magnetic moment is given by
𝑒
𝑠 = 𝑔
𝑆 = 𝛾𝑆
2𝑚
Where
𝑒
𝛾 = 𝑔 2𝑚 is called gyromagnetic ratio (g-factor) [For electron g=-2
...
- It can be shown that elementary nuclear magnetic moment is given by
𝑒ℎ
𝑁 =
= 5
...
𝑚2
4𝜋𝑚𝑝
- The magnetic moment of the nucleus is about 1/1837 of the magnetic moment of the
electron
...
Magnetization of atom and materials
(i) For a solid, the resultant magnetic moment of an atom is sum of the orbital and spin
magnetic moments of its electrons
...
Number of such magnetic moments aligns in different directions to and
it results into a net non-zero magnetic moment
...
(iv) In diamagnetic materials, atomic moments are weakly aligned along opposite direction of
external magnetic field
...
(vi) In ferromagnetic materials, atomic moments are strongly aligned along same direction of
external magnetic field
...
1
...
Diamagnetic Materials:
- Diamagnetic materials are substances which when placed in an
external magnetic field develop a weak magnetism in opposite
direction of the external magnetic field
...
- The examples are bismuth, silver, copper and hydrogen
...
e
...
00083, copper is 0
...
9999995
- The diamagnetic susceptibility is very small and negative i
...
<0
...
2
...
- The atoms are slightly oriented along the direction of the
external magnetic field
...
- The examples are aluminum, tin magnesium etc
...
e
...
00000065
- The paragmagnetic susceptibility is less than one but positive i
...
<1
...
3
...
These materials are strongly
attracted by a magnetic field
...
- They attract the lines of force strongly
...
- The relative permeabilities of these materials are much greater than one and dependent on
the field strengths i
...
r > 1
- For example, the purified iron and many magnetic alloys have relative permeabilities of iron
and many magnetic alloys is 100,000 or more
...
e
...
It is due to the
large attraction of magnetic field when placed in a magnetic field
...
Property
Diamagnetics
Paramagnetics
Ferromagnetics
1
Behavior in external
magnetic field
2
Alignment of
magnetic dipoles in
external magnetic
field
Develop a weak
magnetism in opposite
direction
Opposite and weak
Develop a weak
magnetism in the same
direction
Same direction and
weak
Develop a strong
magnetism in the same
direction
Same direction and
strong
3
Response to external
magnetic field
Relative permeability
(r)
Susceptibility ()
Slightly repelled by
external magnetic field
r < 1
(Bi: 0
...
e
...
00000065)
Less than one but
positive i
...
<1
1
Obeys Curie law ∝
Strongly attracted by
external magnetic field
r >> 1
(Fe: 1,00,000 or more)
Very high >>1
No Curie point
No Curie point
Susceptibility decrease
with temperature in
complex way
Have definite Curie point
Not exhibited
Not exhibited
Exhibited
Not exhibited
Not exhibited
Exhibited
Bismuth, silver, copper,
hydrogen, etc
Aluminum, tin
magnesium etc
Iron, steel, nickel, cobalt
etc
4
5
6
Effect of temperature
on susceptibility
7
Curie Point (above
which become
paramagnetic)
Hysterisis (Lag in
change on
magnetization)
Rententivity
(Residual magnetism)
Examples
8
9
10
𝑇
4
...
In the presence of the strong magnetic field,
antiferromagnetic materials are weakly magnetized in
the direction the field
...
The magnetic moments of atoms are aligned in opposite
directions and are equal in magnitude
...
Examples of antiferromagnetic substances: MnO, FeO,
CoO, NiO, Cr, Mn
This is the case below a particular temperature, called as Néel temperature (TN) above which
the material behaves as a paramagnet
...
Above TN, the susceptibility show
paramagnetic behavior
...
Ferrits and Ferrimagnetism [for reference]
-
Some ceramic materials exhibit net magnetization
...
These ceramics are
called ferrites, and the effect is known as ferri-magnetism
...
However, the spins do not cancel each other out, and a net spin
moment exists
...
These materials exhibit a large but field dependent magnetic susceptibility similar to ferromagnets
...
As these ceramics are good insulators, electrical losses
are minimal, and hence ferrites have lot of applications in devices such as high frequency
transformers
...
1
...
They have high initial permeability due to which they reach
saturation magnetization with a relatively low applied magnetic field
...
Susceptibility and permeability are high
...
They have high permeability and a high resistance to demagnetization
...
Susceptibility and
permeability are low
...
- The magnetic core confines and increases the magnetic
field of a coil by a factor of several thousands
...
Sr
...
Large eddy currents
produced by magnetic
fields
...
These eddy currents
produce heat at high
frequencies
...
These ceramic materials
serve as efficient
insulators, and help
decrease eddy currents
Can be operated at high
temperatures
...
It also has
high permeability and low
losses
...
Highly
responsive to magnetic
fields
...
These cores are used in
high frequency
applications
General domestic
applications
(b) Magnetic storage
Magnetic storage is one of the most widely used digital data storage using a magnetized medium
...
The basic approach to magnetic data storage is almost similar for the different
types of media
...
The storage media contains magnetic surface and it is divided into very small regions of
mostly uniform magnetization
...
e
...
Computer systems need to store data in digital format consists of binary information i
...
data in
the form of zero and ones
...
The
unmagnetized region is read as 0
...
The data is written and read using a small
device called heads
...
A read-write head moves very
close (few nanometer) to the magnetic surface
...
At the gap, the magnetic
flux forms a fringe pattern
...
The information is stored on the disk in the form of zero’s
(unmagnetized region) and ones (magnetized regions)
...
The information
stored on the magnetic devices i
...
the regions of magnetization and demagnetizations are detected
by the read head by detecting a varying magnetic field across the gap
...
A thin film of magnetic material (e
...
amorphous Terbium iron cobalt, TbFeCo)
magnetic film is coated on the substrate over
which the data is written
...
The magnetic layer side faces
towards the laser beam
...
A local magnetic field
determines the direction in which the spot is magnetized when it cools
...
The tiny
region that is magnetized is treated as 1 while the un-magnetized region is treated as 0
...
The laser
light is reflected from the surface of the media
...
When the laser beam is reflected from the regions that are magnetized it has certain
polarization
...
Thus, the change in direction of magnetization could be associated with numbers 0 or 1
...
Erasing the data
To erase the data, magnetic field is applied to the material in the opposite direction
...
The disk is again de-magnetized and data written on in the form of magnetization is erased
...
Magnetic dipole moment
2
...
Magnetization (M)
4
...
Magnetic Induction (B)
6
...
Relative Permeability (r)
8
...
Explain the origin of magnetism
...
Explain how materials are classified on the basis of permeability
...
Differentiate between paramagnetism, diamagnetism and ferromagnetism
...
Explain how the information is recorded and retrieved in magneto-optical recording devices
...
Explain the process of recording and retrieving the information in magnetic storage devices
...
What are the different types of transformer core? Discuss in brief any two of them and state
their applications
...
Explain in brief what are paramagnetic materials?
3
...
Explain in brief what are ferromagnetic materials?
5
...
Explain in brief what are ferrimagnetic materials?
7
...
2 Superconductivity
Superconductivity is complete disappearance of electrical resistance (zero electrical
resistance) in some materials when they are cooled below a characteristic temperature
...
The zero resistivity means almost
infinite conductivity
...
Above Tc, the superconducting material
behaves as a normal conductor
...
Different material shows superconductivity below their
characteristic critical temperature
...
72 K), Lead
(7
...
2 K), Aluminium (1
...
However, copper, silver and gold which are very good conductor at room temperature do not show
superconductivity
...
2
...
1
...
2
...
This produces a distortion in the lattice
and there is increase density of positive ions surrounding to electron 1
...
e
...
3
...
Thus, a free electron (electron 1) exerts a small attractive force on another electron
(electron 2) through phonons
...
4
...
Cooper pairs move almost without any resistance
...
5
...
Page 11 of 21
MMIT, Lohgaon, Pune // Engineering Physics [2019-20] // Unit 5 – Magnetism and Superconductivity
5
...
2 Properties of superconductors
Zero electrical resistance
The variation of resistance of
superconductor
with
temperature can be measured
by four probe method
...
Voltage developed is measured with voltage probes (2 and 3)
...
Normal state (T>Tc): A voltage is developed across voltage probes and Ohm’s law 𝑉 = 𝐼𝑅 is obeyed
...
e
...
Persistent Currents
Once a current is started in a closed
loop of superconducting material, it
will continue to keep flowing, of its
own accord, around the loop as long as
the loop is held below T
The persistent current does not require external power to maintain
...
Once the current flow is initiated, it
is estimated it persists for more than 105 years
...
Superconductor coils with persistent current flowing through them produce magnetic fields
and can therefore act as magnets
...
It depends on temperature
...
Changes in either temperature or magnetic field can cause
the phase transition between normal and superconducting
states
...
At that temperature even the weakest
Page 12 of 21
MMIT, Lohgaon, Pune // Engineering Physics [2019-20] // Unit 5 – Magnetism and Superconductivity
external magnetic field will destroy the superconducting state, so the strength of the critical
field is zero
...
𝑇 2
𝑇𝑐
The critical magnetic field at temperature T is given by 𝐻𝑐 𝑇 = 𝐻𝑐 (0) 1 −
Where, Hc(0) is the critical magnetic field at 0 K, Tc is critical temperature
...
3 mT, Sn: 30
...
As current increases, the associated magnetic field also increases
...
If the current in superconductor is increased beyond Ic, the associated magnetic field will
exceed critical magnetic field Hc and superconductor may destroy its own superconductivity
...
The current density associated with
critical current (Ic) is called critical current density (Jc)
...
5
...
3 Meissner Effect and perfect diamagnetism
Meissner effect
When certain superconductors (type-I) are cooled below critical
temperature 𝑇 < 𝑇𝑐 in presence of external magnetic field, magnetic flux is
expelled from the interior of the superconductor and it becomes perfect
diamagnetic
...
Reason for magnetic flux expulsion
In presence of magnetic field, induced circulating currents are
generated on the surface of the material
...
Thus the external
magnetic flux is expelled by the superconductor
...
When a magnetic
field is applied to it, the it penetrates through the material
...
The magnetic induction inside the material B=0
Thus
0 = 𝜇0 (𝐻 + 𝑀)
And
𝑀 = −𝐻
𝑀
Susceptibility of the material, = 𝐻 = −1
Perfectly diamagnetism: Magnetic susceptibility is the degree of magnetization of a material in
response to an applied magnetic field
...
For superconductors, magnetic susceptibility = 𝐻 = −1
...
Page 13 of 21
MMIT, Lohgaon, Pune // Engineering Physics [2019-20] // Unit 5 – Magnetism and Superconductivity
5
...
4 Types of superconductors (Type I and Type II)
In Type I superconductors, the transition from superconducting state to normal state in presence of
magnetic field occurs sharply at critical field Hc
...
The
transition from superconducting to normal state is gradual
...
At
lower critical magnetic field (Hc1) external magnetic field enters into superconductor
...
It the value of external magnetic field is
increased above upper magnetic field (Hc2), they lose their superconductivity
...
1
2
3
Property
Type-I Superconductor
Meissner effect
They exhibit complete Meissner effect
...
4
Variation of
magnetic field
with
temperature
5
Variation of
Magnetization
(M) of
superconductor
with applied
Magnetic Field
(H)
6
States of the
material
Material exists in two states for T
7
Change in
magnetization
Critical
magnetic field
Type
Applications
Examples
The materials loses magnetization
abruptly
Highest value for Hc is about 0
...
2
2
Wb/m
They are known as soft superconductors
Not much useful due to low H c
Aluminum, lead, mercury, etc
8
9
10
11
Type-II Superconductor
They do not exhibit Meissner effect
completely
...
At
lower critical magnetic field Hc1 flux starts
penetrating the superconductor
...
Material exists in three states for T
Hc1 > H < Hc2
– mixed/vortex state
H>Hc2
– conductor
The materials loses magnetization
gradually
2
Highest value for Hc2 is about 30 Wb/m
They are known as hard superconductors
Useful due to high Hc2
Nb-Sn, Nb-Ti, Nb-Zr, Va-Ga, etc
Page 14 of 21
MMIT, Lohgaon, Pune // Engineering Physics [2019-20] // Unit 5 – Magnetism and Superconductivity
5
...
5 Low and high temperature superconductors
Superconductors are classified into low Tc and high Tc superconductors based on their transition
temperatures
...
The superconductors having transisition temperature above 27 K are
high temperature superconductors
...
Property
1
2
3
Transition
temperature
Coolant required
Examples
4
Applications
Low Temperature
Superconductors
Below 24 K
High Temperature
Superconductors
Above 27 K upto 138 K so far
Liquid Helium (4 K)
They are typically elements
Liquid Nitrogen (77 K)
They are generally Nb based
alloys, mixed oxide materials
containing
lanthanum
and
yttrium
...
5
...
6 Josephson Effect
The dc Josephson effect
When two superconductors are separated by a
thick insulating layer (> 10nm) behaves as two
independent superconductors
...
The cooper pairs tunnel easily through the
barrier (insulating layer) as a single unit
...
The
insulating layer introduces a phase difference between the wave function of cooper pairs on
opposite sides
...
This effect is known as dc Josephson effect
...
The ac Josephson effect
If a dc voltage is applied across Josephson junction, it introduces an additional phase on the
Cooper pairs during tunneling
...
Using quantum mechanical calculations, it can be shown that
2𝑒𝑉
∆∅ = 2𝜋𝑡
ℎ
Thus, the alternating current across the junction is given by
Page 15 of 21
MMIT, Lohgaon, Pune // Engineering Physics [2019-20] // Unit 5 – Magnetism and Superconductivity
2𝑒𝑉
ℎ
2𝑒𝑉
This current can be represented by an alternating current of frequency = ℎ
...
This effect is known as ac Josephson effect
...
Also this frequency does not depend on properties of superconductors
such as critical temperature, chemical composition
...
6 MHz is produced
...
2
...
Their working is based on
superconducting loops containing Josephson junctions
...
A radio frequency
(RF) SQUID is made up of one Josephson junction, which is mounted on a superconducting ring
...
Construction
SQUIDs are usually fabricated from lead or pure niobium
...
The entire device is cooled to within a few degrees of absolute zero with liquid
helium
...
It consists of two Josephson
junctions arranged in parallel
...
This current is known as bias current which
enters into the SQUID through arm C
...
I1 and I2 are currents tunneling through Josephson junctions
...
The wave
function experiences a phase shift at the Josephson junctions P and Q
...
This phase difference between reuniting currents 𝛿0 is
directly proportional to the magnetic flux through the ring
...
This voltage depends upon the change in the magnetic flux
...
Total current through parallel Josephson junctions is 𝐼𝑇 = 2 𝐼0 sin 𝛿0 cos ℏc
𝑒∅
Thus, a progressive increase or decrease of the magnetic flux causes the current to oscillate
between a maximum and minimum when the magnetic flux increases by one flux quantum
...
06 × 10−15 𝑤𝑒𝑏𝑒𝑟𝑠
...
This
sensitivity can further be increased using a flux transformer
...
SQUIDs have many applications
...
It can detect
magnetic fields produced naturally in the brain which is of the order of 10-14 T
...
(ii) MRI Scan: Magnetic resonance imaging (MRI), also known as nuclear magnetic resonance
imaging, is a scanning technique for creating detailed images of the human body
...
Water molecules in human body contain
hydrogen nuclei (protons)
...
2
to 3 teslas), which aligns the proton "spins"
...
(iii) Non-destructive corrosion testing: The magnetism of the material changes due to the
corrosion, which can be detected using SQUID
...
(v) Earthquake prediction can be done by detecting change in earth’s magnetism
(vi) Mineral exploration by detecting variation in magnetic fields inside earth crust
(vii) Geothermal energy survey, etc
...
2
...
Generally 10% to 15% of
generated electricity is lost in overcoming resistance of cables
...
The use
of superconducting transmission lines would have following advantages:
Minimum (zero) heat losses
When superconductors will be used as cables, resistive and heat losses are avoided and
electrical power transmission can be done more efficiently
...
Carrying a large power
Using superconducting transmission lines a large power could be transmitted at a fairly low
voltage
...
High current carrying density
Using superconductors such as BSCCO in tape forms and YBCO in thin film forms, current
densities above 10,000 amperes per square centimeter could be transmitted
...
The current
remains trapped forever in the coil as there is absolutely no energy loss
...
Transformers
Superconducting coils in transformers and electrical machines generate much stronger
magnetic fields
...
Therefore,
the size of motors and generators will be drastically reduced
...
They consume large electrical power to
maintain the magnetic field and also require continuous cooling
...
Due to this electromagnets can be constructed that generate intense magnetic
fields with little electrical power input
...
Compact and more efficient setup
Superconducting magnet systems are quite compact and occupy a small space
...
Friction-less bearings
A bearing is a machine element that bears the load and minimizes the friction between moving
parts
...
The use of superconductors in designing of bearings uses principle of
Meissner effect and magnetic field repulsion
...
They need no lubrication or maintenance and can be
used under extreme conditions: vacuum, cryogenic environments
...
High driving speed
Rotational bearings for very high driving speeds are possible
...
Electronics
Variety of devices such as SQUIDs, transistors, ICs, etc can be designed using superconductors
...
Some of the applications
of superconductors in electronics are listed as below:
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MMIT, Lohgaon, Pune // Engineering Physics [2019-20] // Unit 5 – Magnetism and Superconductivity
Josephson junctions
Josephson junctions are used in fast electronic switches or sensitive magnetometers
...
Supercomputers
The semiconductor logic elements have a speed limit
...
Logic elements based on Josephson junction can operate at the speed of
few picoseconds
...
SQUID (superconducting quantum interference device)
SQUIDs are used for Non-destructive corrosion testing, Magnetoencephalography (MEG),
observing neural activities inside the brain (MRI scan), study of magnetic properties of
material, oil prospecting, mineral exploration, earthquake prediction, geothermal energy
survey, etc
...
They will significantly speed up the processing of signals or data in
microprocessors
...
This would have advantage
that information can be transmitted more quickly without losses
...
Use of
superconductors will make ICs more efficient
...
5 Tesla) and detection of smaller magnetic
fields using SQUIDs (of the order of 10-14 Tesla)
Magnetoencephalography (MEG)
Magnetoencephalography (MEG) is a technique for investigating human brain activities on a
millisecond basis
...
Brain generates neuromagnetic signals that are extremely small (of the order of 10-12 Tesla)
...
Magnetic Resonance Imagery (MRI)
Magnetic resonance imaging (MRI), also known as nuclear magnetic resonance imaging, is a
scanning technique for creating detailed images of the human body
...
5 Tesla or higher) and radio waves to generate images of
parts of the body that can't be seen with X-rays, CT scans or ultrasound
...
Water molecules in human body contain hydrogen nuclei (protons)
...
2 to 3 teslas), which aligns the proton "spins"
...
MRI diagnosis is used for investigation of brain, including detection of tumors
...
Page 19 of 21
MMIT, Lohgaon, Pune // Engineering Physics [2019-20] // Unit 5 – Magnetism and Superconductivity
Transport - MagLev Trains
In conventional transportation system, friction between the wheels and ground or rail is one of the
crucial elements
...
Magnetic Levitation Trains (Maglev Trains) is a floating vehicle for land transportation
...
As there is no
mechanical friction, speeds upto 500 km/h can be easily achieved
...
This produces a strong magnetic field of order of almost 5 Tesla enough to levitate the train
...
02 m, the critical magnetic field is 2x103 A/m at 5K
...
Solution:
Ic = 2πRHc = 2 × 3
...
02 × 2 × 103 = 251
...
2 K
...
18 K and 𝐻𝑐 (0)=6
...
Solution:
𝑇 2
4
...
5 × 104 1 −
= 4
...
18
Example: The transition temperature for lead is 7
...
However, at 5K it loses the superconducting
property if subjected to magnetic field of 3
...
Find the maximum value of H which will allow
the metal to retain its superconductivity at 0K
...
3 × 104
=
= 6
...
28
5
Example: The critical field of niobium is 1x10 A/m at 8 K and 2x105 at 0 K
...
Hc 0 =
Solution:
Hc T = Hc 0 1 −
T 2
Tc
T
8
Tc =
H (T) 1/2
1− c
H c (0)
=
1×10 5
1−
2×10 5
1/2
= 11
...
26 K
...
Lead has to be used as a superconductor subjected to a magnetic field of 4x104 A/m
...
Solution:
Hc T = Hc 0 1 −
T 2
Tc
1/2
1/2
Hc (T)
4 × 104
= 7
...
08 K
Hc (0)
8 × 105
Therefore, the temperature of the materials should be kept below 7
...
Calculate its frequency
...
6×10 −19 ×650×10 −6
6
...
13 × 1011 𝐻𝑧
Example: Calculate the voltage required to produce a frequency of 2x1011 Hz across the Josephson
junction
...
63×10 −34
2×1
...
38 𝑉
Questions on superconductivity
6 marks
1
...
Show that superconductors exhibit perfect
diamagnetism
...
Differentiate between type I and type II superconductors
...
What are SQUIDs? Explain principle, construction and working of SQUID
...
Explain following terms in superconductivity
...
Differentiate between type I and type II superconductors
...
Discuss in brief low and high temperature superconductors
...
Explain DC and AC Josephson effect
...
What are SQUIDs? Explain their applications in brief
...
Explain applications of superconductors in the field of (any one of below):
(i) Transmission lines and electricity (ii) Superconducting magnets (iii) Frictionless bearings
(iv) Electronics (v) Medical field (vi) MagLev trains
Title: Magnetism and Superconductivity
Description: These notes are on the topic of Magnetism and Superconductivity. These notes are aimed at first-year students. I made these notes when I was in my first year of engineering and these help me get a 10/10 SGPA. And I'm sure this would help you too. Notes are organized properly and I've also put some questions for revision and tests. Notes also contain visuals and images to visualize the concepts.
Description: These notes are on the topic of Magnetism and Superconductivity. These notes are aimed at first-year students. I made these notes when I was in my first year of engineering and these help me get a 10/10 SGPA. And I'm sure this would help you too. Notes are organized properly and I've also put some questions for revision and tests. Notes also contain visuals and images to visualize the concepts.