Category: Physics Notes PPT

Stress and strain are two sides of a coin. A very common example among physics enthusiasts, while they are explaining this topic, is to tell students that the stress being referred to here is not the one that students face in their exams. We will not be using this example because we fully understand that students are capable and smart enough to figure that out on their own. Stress in terms of Physics is the force acting on a unit area of a material. The strain, on the other hand, is just a basic measure that gives us an idea of how much an object has deformed or changed due to the stress applied to it. This is the main idea behind the concept of stress and strain.

Longitudinal strain is a very interesting and simple topic that is very easy to understand. This topic literally guarantees marks as students do not really have to spend a lot of time on the understanding part of it because of its simplicity. Plus questions from the topic keep appearing in class 12 School level examinations and even competitive exams like JEE and NEET. In order to secure these marks which can be obtained by simply understanding the topic, we recommend students to read this article thoroughly and throughout. Only then will they be able to understand the chapter fully and figure out what the concept is about.

offers nothing but the best quality articles when it comes to testing preparation. This is the same goal behind this article as well and that is why we plan on giving you the best resource on the topic of longitudinal strain that can be understood with ease at the comfort of your home, school or anywhere. 

Strain is the force inclined to pull or stretch something to an extreme or damaging degree.

When an external force per unit area (stress) is applied to an object, and there is a deformity in its shape. 

The inter-atomic particles inside the body try to regain its original position. While the body exceeds the elastic limit.

Such a condition where the internal restoration force fails to bring the body back to its original shape and this condition is called the strain.

The property of strain is that the elastic strain is irreversible.

SI Unit of Strain

In Mechanics, strain is often said to be “dimensionless” regardless of what system we use as it has no units.

Strain  = Change in length / original length

Δ L/ L  =   [left [ L^{1}right ]]/ [left [ L^{1}right ]]=   [left [ L^{0}right ]] = 1

If we use meters/ meters. It will always come as 1.

So,

SI unit of strain  =  one (no unit)

Unit of Strain

The unit of strain in non-SI units,

Other units of strain = cm/cm or cubits/ cubits will always give 1.

Generally, we identify a number as strain.

We generally use the strain after the number such as 0.012 strain.

The measurement of strain is usually given as the numeric units in (με).

Since the changes in length are usually very small and a typical strain measurement in the English system is given as microinches per inch (i.e., in the order of 10−6

Therefore, the numeric value, which is unitless, will remain the same in any system.

Longitudinal Strain Definition

The longitudinal strain is defined as the ratio of change in length of the material due to the applied force to the original length.

Longitudinal Strain

When stress (external force per unit area) is applied on the body such that this deforming force causes a change in the length alone, and the body exceeds its elastic limit. This condition or strain produced in the body is called the longitudinal strain.

As the name longitudinal strain suggests that we are talking about the length and strain is causing deformity in its shape by elongating its length.

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In Fig.1, a rod of length ‘Lo’ is stretched along the X-axis with enough external force that its length is extended to ‘Δ L’.

Now, the new length of the rod is Lf, which equals Lo + Δ L.

 Δ L is the extended length of the rod.

This has happened due to the strain in the rod.

Longitudinal strain is denoted by a Greek symbol epsilon, ε

So, the formula for the longitudinal strain is given by,

The unit of longitudinal strain is one.

The dimensional formula =[left [ L^{0}right ]]

Young’s Modulus of Elasticity (γ) 

For a given material there can be different types of modulus of elasticity depending upon the type of stress applied, and the resulting strain produced. One of them is young’s modulus of elasticity. Young’s modulus of elasticity corresponds to the ratio of longitudinal stress to the longitudinal strain within the elastic limit. 

Consider a wire PQ (in  Fig.2) of length L of the radius of cross-section, ‘r’ and uniform cross-sectional area ‘A’ is suspended from a rigid support P. When stretched by a suspended load of ‘mg’ from the other end Q.

(The )

Therefore, a force (perpendicular force) F is applied at its free end. Such that there is an elongation in the body by Δ L.

Young’s modulus or γ = Longitudinal stress/ longitudinal strain…(1)

Where,

Longitudinal stress is the deforming force when applied to the body, the stress is produced in the body causing elongation in its length.

Its formula is the same as the stress which is equal to F/A (Force per unit area)

       Longitudinal stress = [frac{F}{A}] = [frac{F}{Pi r^{2}}] …. (2)

and, longitudinal strain  =  Δ L/ L..(3)

So,  putting values of (2) and (3)  in (1) 

=  F/πr²/  Δ L/ L 

Longitudinal Strain

• Within the elastic limit, this ratio always remains constant.

• The unit of γ  in SI is N/m² or Pascal (Pa).

• In CGS system = dyne/cm²

• The dimensional formula for γ is [left [ M^{1} L^{-1}T^{-2}right ]]

Key Point

If the length increases from its natural length, the lon
gitudinal strain is called the tensile strain and if the length decreases from its natural or original length, then it is the compression strain.

Do You Know?

Conclusion 

We hope that this article was able to solve all your doubts about the concept of longitudinal strain. The idea behind stress and strain is not all that complex but is very easy to understand and comprehend. We suggest that students go through this article again and again to get a complete idea of what the entire concept is about. has been a leader in the world of education because we believe in the power of good and easy to understand resources for students of all ages. It is due to the same reason that we have had so many success stories of students from around the world and across the country as they score well in their exams. This article was written with the same intention. The intention was to offer nothing but the best and the easiest to understand study document that can be studied anywhere by students on any device that they own. hopes that we were able to solve all the doubts that you had about the topic.

One or more closed-loop pathways carrying a magnetic flux create a magnetic circuit.

Permanent magnets or electromagnets produce the flux, which is limited to the route by magnetic cores made of ferromagnetic materials like iron, though there may be air holes or other materials in the path. Magnetic circuits are used in a variety of applications to effectively channel magnetic fields like electric motors, generators, galvanometers, transformers, relays, lifting electromagnets, SQUIDs, and magnetic recording heads.

The equations of the magnetic field of an unsaturated ferromagnetic substance and the equations of an electrical circuit have a one-to-one correspondence of a “magnetic circuit.”

The magnetic fields of involved devices like transformers can be easily overcome using the methods for electrical circuits using this principle.

Some Examples of Magnetic Circuits are:

1. horseshoe magnet with iron keeper (low-reluctance circuit).

2. horseshoe magnet with no keeper (high-reluctance circuit).

3. electric motor (variable-reluctance circuit).

4. some types of pickup cartridge (variable-reluctance circuits).

Magnetic Flux

The number of magnetic field lines that travel through the cross-sectional region of a magnetic component determines the magnetic flux through that component.

This is the net sum, which equals the number of people who pass through in one direction minus the number of people who pass through in the opposite direction. The product of the magnetic field and the area element determines the flux by an element of area perpendicular to the magnetic field direction. A scalar product of the magnetic field and the area element vector defines magnetic flux in general.

It has a magnetic nucleus, for starters. The heart can be made of a single material, such as sheet steel, or it can be made up of several parts with an air space between them. At least one pair of wire spins, i.e. a coil built around the core, surrounds the core. Transformers have several sets of turns (in the simplest case, one for the primary and another for the secondary).

Author engineerPosted on May 26, 2024May 26, 2024Categories Physics Notes PPTLeave a comment on [Physics Class Notes] on Magnetic Circuit Pdf for Exam

Superconductivity was first found in 1911 when mercury was cooled to roughly 4 degrees Kelvin by Dutch physicist Heike Kamerlingh Onnes, which acquired him the 1913 Nobel Prize in material science. It is a material that is capable of superconducting at low temperatures.

A superconductor example is “Tungsten”, other examples are “Tin,”, “Zinc,” these materials are when cooled at a critical temperature, they suddenly become superconductors. 

One of the known applications of a superconductor is, they are used in generating the mighty magnetic field between 20 – 30 T.

On this page, you will get sufficient information on superconductors, like the properties of superconductors and applications of superconductors.

Superconductor Materials

A superconductor is a component or metallic alloy which, when cooled under a specific limit temperature, the material significantly loses all electrical obstruction. 

On a fundamental level, superconductors can permit electrical flow to stream with no energy loss (albeit, by and by, an ideal superconductor is difficult to produce). This kind of current is known as a supercurrent. 

The critical/edge temperature beneath which a material changes into a superconductor state is assigned as Tc, which represents basic (critical) temperature. Not all materials transform into superconductors, and the materials that do, have their own value or estimation of Tc.

Examples of Superconducting Materials

The resistivity of most metals increments with expansion in temperature and the other way around. There are a few metals and chemical compounds whose resistivity becomes zero when their temperature is brought close to 0 Kelvin or – 273°C. At this stage, such metals or compounds are said to have achieved superconductivity.

For instance, Mercury becomes superconducting at around 4.5 Kelvin (- 268.5°C). The progress from typical conductivity to superconductivity happens unexpectedly; it happens over an exceptionally restricted range of temperature, i.e., about 0.05 K.

So, the temperature at which the progress happens from the condition of ordinary conductivity (such as Mercury, as mentioned above) to that of superconductivity is called transition/changing temperature.

Types of Superconductors

Superconductors are categorized into types: type 1 and type 2 superconductors.

Type 1 Superconductors

Type I superconductors are delicate superconductors. They are generally pure examples of certain components for example metals. They have almost no utilization in technical applications.

These types of superconductors act as conductors at room temperature, yet when cooled beneath Tc, the sub-atomic movement inside the material decreases sufficiently that the progression of current can move unobstructed.

Type 2 Superconductors

Type 2 superconductors are hard superconductors. They are typically combinations of metals with a high value of resistivity in ordinary states. These are valuable when contrasted with Type 1 materials. 

Type 2 superconductors are not especially acceptable conductors at room temperature, the progress to a superconductor state is more continuous than Type 1 superconductors. The system and the actual reason for this adjustment in the state aren’t, as of now, completely comprehended. Type 2 superconductors are ordinarily metallic alloys and compounds.

Examples of superconducting materials of type 2 are niobium and vanadium. 

               

Magnetic and Electromagnetic Properties of Superconductors

The properties of superconductors lie hereunder:

1. Critical Field 

Use of an adequately strong magnetic field to superconductors causes the obliteration/destruction of their superconductivity, i.e., the rebuilding of their normal conducting state. 

The critical value of the magnetic field for the obliteration of superconductivity is meant by Hc and is practically identified with temperature as;

Hc = Hc (0) [1 – T²/Tc²]

Where

 Hc(o) = critical field at 0 K, and has a particular value for every material.

Point to Note:

The lower the temperature, the higher the estimation of  Hc and the most increased critical temperature happens when there is no magnetic field. 

In this manner, we track down that the superconducting state is steady just in some definite ranges of magnetic fields and temperatures. For higher fields and temperatures, the ordinary state is more steady.

2. The Meissner Effect

As we stated above, a type 1 superconductor as a long, thin cylinder or ellipsoid remaining parts superconducting at a fixed temperature as an axially arranged magnetic field is applied, given the applied field doesn’t surpass a critical value ( Hc). 

Under these conditions, superconductors prohibit the magnetic field from their inside, as could be anticipated from the laws of electromagnetism and the way that the superconductor has no electric obstruction.

An amazing impact happens if the magnetic field is applied similarly to a similar sort of sample at a temperature over the transition temperature and is then held at a fixed value while the sample is cooled. It is tracked down that the example removes the magnetic flux, as it becomes superconducting. We call this effect the Meissner Effect.

3. High-Frequency Electromagnetic Properties

The energy gap in a superconductor directly affects the absorption of electromagnetic radiation. The photon’s energy (E) is identified with its recurrence/frequency () by Planck’s relationship, E = hν.

Here,

“h” is Planck’s steady (6.63 × 10−34 Joule-second). In the absorption process, a photon (a quantum of electromagnetic energy) is consumed, and a Cooper pair is broken; the two electrons in the pair become energized. At low temperatures, at which an immaterial part of the electrons are thermally excited to states over the gap, the superconductor can absorb energy just in a quantized sum that is, at any rate, double the gap energy (at total zero, 2Δ0). 

Henceforth the superconductor can retain electromagnetic energy just for frequencies in any event as extensive as 2Δ0/h.

Science is an application-based subject of learning the environment in different ways. For students, there are three major divisions of this subject namely, Physics, that is, the study of the behaviour of the universe. Chemistry, which involves the study of substances and their chemical reactions and properties in nature. And finally, Biology involves the study of living beings in the environment. 

As mentioned earlier, Physics is a branch of science that studies the behaviour of the universe in the form of matter and energy. Physics is highly used in our everyday lives. Car seat belts, earphones, camera lenses, ballpoint pens, steam iron are some examples of physics from the everyday life of human beings.

Introduction

The Maxwell equations are the fundamental equations of electromagnetism, which combines Gauss’s law of electricity, Faraday’s law of electromagnetic induction, Gauss’s law of magnetism and Ampere’s law of current in a conductor. Maxwell’s equations are a set of differential equations, which along with the Lorentz force law forms the basic foundation of electromagnetism, electric circuits and classical optics.

Maxwell’s equations provide a mathematical model for static electricity, electric current, radio technologies, optics, power generation, wireless communication, radar, electric motor, lenses, etc. These equations describe the working nature of electric and magnetic fields, and how they are produced by charges, currents and due to change of electric or magnetic field.

These equations are named after a Scottish mathematical physicist James Clerk Maxwell, who formulated the classical theory of electromagnetic radiation. He published these questions by including the Lorentz Force law between the years 1861 and 1862. Maxwell’s first equation proposed that ‘light is electromagnetic in nature’.

Maxwell’s Equations Explained

Maxwell formulated four equations for free space, which are mentioned below:

1. First Maxwell’s Equation: Gauss’s Law for Electricity

Gauss’s law of electricity states that “the electric flux passing through a closed surface is equal to 1/ε0 times the net electric charge enclosed by that closed surface”.

Gauss’s law of electricity describes the relationship between a static electric field and the electric charges which cause the electric field. A static electric field always points in a direction away from the positive charge, and it points in a direction towards the negative charge. It also describes that the net outflow of the electric field through any closed surface is directly proportional to the net amount of charge enclosed by that closed surface.

The electric field lines begin at a positive charge and end at a negative charge. The total number of electric field lines that pass through a closed surface, divided by the dielectric constant of free space (permittivity of vacuum), gives the total amount of charge enclosed by that closed surface.

1. Maxwell’s Equations Integral Form

e = q/e0 ——– (i)

Also, e = [int vec{E}.dvec{A}] —- (ii)

Comparing equations (i) and (ii), we have:

[int vec{E}.dvec{A}] = q/∈₀      —- (iii)

This is the integral form of Maxwell’s 1st equation.

2. Maxwell Equation in Differential Form

The value of total charge in terms of volume charge density is q = ∫pdv

So, the equation (iii) becomes:

[int vec{E}.dvec{A}=frac{1}{e_0}int Pdv]

Applying divergence theorem on the left-hand side of the above equation, we have:

[int (vec{triangledown }.vec{E})d.V=frac{1}{epsilon _0}int pdv]

[int (vec{triangledown }.vec{E})d.V-frac{1}{epsilon _0}int pdv=0]

[int [(vec{triangledown }.vec{E})-frac{P}{epsilon _0}]d.V=0]

[(vec{triangledown }.vec{E})-frac{P}{epsilon _0}=0]

[(vec{triangledown }.vec{E})-frac{P}{epsilon _0}]

This is the differential form of Maxwell’s 1st equation.

2. Second Maxwell’s Equation: Gauss’s Law for Magnetism

Gauss’s law of magnetism states that “the net magnetic flux of a magnetic field passing through a closed surface is zero”. This is because magnets always occur in dipoles, and magnetic monopoles do not exist.

The magnetic field is generated due to the dipole nature of the magnet. The net outflow of the magnetic field through any closed surface is zero. Magnetic dipoles behave like loops of current with positive and negative (i.e magnetic charges) which cannot be separated from each other.

According to Gauss’s law of magnetism, magnetic field lines make loops, and they start from the magnet and extend till infinity and back. In other words, if field lines enter an object, they will also come out of that object. The total magnetic field through a Gaussian surface is zero, and the magnetic field is a solenoidal vector field.

This is a graphical representation of magnetic field lines which neither benign nor ends, but forms loops.

3. Third Maxwell’s Equation: Faraday’s Law of Electromagnetic Induction

Maxwell modified Faraday’s law of induction. It describes the production of electric fields by a time-varying magnetic field. This law describes, “ work needed for moving a unit charge around a closed loop structure equals the magnetic field transforming around that particular loop”.

The induced electric field lines are similar to that of magnetic field lines unless they are superimposed by a static electric field. This concept of electromagnetic induction is the basic operating principle behind many electric devices like rotating bar magnets for creating changing magnetic fields, which further produces electric fields in a nearby conducting wire.

The Earth’s magnetic field is altered in a geomagnetic storm, due to a surge in the flux of charged particles, which further induces an electric field in Earth’s atmosphere.

∈ = -Ndm/dt- ————– (v)

Since emf, if related to the electric field by the relation

∈ =[int vec{E}.vec{d}A]

Also, 

Putting these values in equation (v), we have:

[int vec{E}.vec{d}A=-Nint vec{E}.vec{d}Aint vec{B}.vec{d}A]

For N = 1, we have

[int vec{E}.vec{d}A=frac{-d}{dt}int vec{B}.vec{d}A]

This is the integral formula of Maxwell’s third equation.

Applying stoke’s theorem on L.H.S of equation (vi), we have:

[int (vec{triangledown }.vec{E})dvec{A}=frac{-d}{dt}int vec{B}.dvec{A}]

[int (vec{triangledown }.vec{E})dvec{A}+frac{d}{dt}int vec{B}.dvec{A}=0]

[(vec{triangledown }.vec{E})+frac{dvec{B}}{dt}=0]

[(vec{triangledown }.vec{E})=frac{-dvec{B}}{dt}]

This is the differential form of Maxwell’s third equation.

4. Ampère’s law with Maxwell’s addition

According to Ampere’s law with Maxwell addition, “magnetic field can either be produced by electric current or by altering the electric field. The first statement is as per Ampere’s law whereas the
latter is according to Maxwell’s addition, the displacement current. The induced magnetic field around any closed loop is directly proportional to the electric current and the displacement current through that closed surface.

Maxwell’s addition to the Ampère establishes a relationship to make a set of equations mathematically consistent with the non-static fields, without changing the Ampère’s and Gauss’s laws for static fields. However, a changing electric field produces a magnetic field and vice versa. Therefore, these equations create a possibility for self-sustaining “electromagnetic waves” to travel through a vaccum.

The speed of electromagnetic waves is equal to the speed of light as per the calculations and observations. Light is also a type of electromagnetic radiation (like X-rays and radio waves).

Maxwell established the relation between electromagnetic waves and light in the year 1861, from there he unified the theories of electromagnetism and optics.

This is a magnetic core memory (1954), an application of Ampère’s law. Each core stores data of the size of one bit.

Merits of learning from the online platform of

This is all about Maxwell’s famous equations used in the different concepts of physics. Understand the meaning of the terms used in each equation to determine their uses and applications. 

They are a class of rocks that result from the alteration of pre-existing rocks in response to changing environmental conditions or any natural situations without any liquefaction process, such as fluctuations with temperature, pressure, and mechanical stress, and the inclusion or subtraction of any available chemical components.

Definition and Examples

Metamorphic rocks arise from the transformation of existing natural rock substances to new types of rock without any exterior liquefaction manually done, in a process called metamorphism. During this process, the original rock is subjected to temperatures of more than 150-200 degrees celsius and often pressures of more than 100 megapascals resulting in vast physical and chemical modifications.

Types and Characteristics

Common metamorphic rocks varieties include phyllite, schist, gneiss, quartzite, and marble. 

Metamorphic rocks can be classified into two main categories based on the way they are formed – those that are foliated as they have been formed due to high pressure and under shear stress and those that are not foliated under any form of pressure. 

Types of Metamorphism

The three major types of metamorphism are Contact, Regional, and Dynamic metamorphism.

• Contact Metamorphism occurs when hot lava comes in contact with an already existing body of rock. When this happens the existing rock’s current temperature rises and also becomes infiltrated with fluid from the volcano. 

• Regional Metamorphism occurs over a much larger surface area. This type of metamorphism produces and forms rocks such as gneiss and schist. Regional metamorphism is mainly caused by large geologic processes such as mountain-building.

• Dynamic Metamorphism, like regional metamorphism, also occurs because of mountain-building. These huge forces of heat and pressure that are applied naturally cause the rocks to be bent, folded, crushed, flattened, and sheared in any manner. As hard as or even harder than igneous rocks, metamorphic is almost always harder than sedimentary rocks. They form the roots of many mountain chains and are exposed to the surface after the softer outer layers of rocks are eroded away due to any natural calamities caused.

A message carrying signal is the one that has to get transmitted over a certain distance, and for it to establish a reliable communication, it requires the help of a high-frequency signal, which should not affect the original properties or characteristics of the transmitted message signal.

If the characteristics of the message signal are changed, then the message contained in it also alters. Therefore, it is essential to take care of the transmitted message signal. A high-frequency signal can travel up to a larger distance, that too, without getting affected by external disturbances. We usually take the help of such a high-frequency signal called a carrier signal for transmitting the message signal. The process is known as Modulation.

Modulation refers to the process of changing the parameters of the carrier signal corresponding to the instantaneous values of the modulating signal.

 

What is a Baseband Signal?

A baseband signal refers to a transmission signal that hasn’t been modulated or demodulated to its original frequency. It can be transmitted over optical fibres, coaxial cables. 

 

What is the Need for Modulation?

The baseband signals are not compatible with direct transmission. For such a signal to travel much larger and longer distances, its strength has to be increased by modulating with a high-frequency carrier wave, which doesn’t affect the parameters of the modulating signal.

 

Advantages of Modulation

Before the concept of modulation, the antenna used for transmission had to be large enough. Consequently, the range of communication used to get limited as the wave couldn’t travel to a distance without getting distorted.

The advantages of implementing modulation in the communication systems are as follows:

• The size of the antenna gets reduced

• There’s no scope for signal mixing

• The communication range increases

• Multiplexing of signals occurs

• Adjustments in the bandwidth are allowed

• Improvement in the reception quality

 

What are the Different Types of Modulation?

There are several different types of modulations. Based on the modulation techniques used, they are categorized into the types, as shown in the following figure.

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Modulation is broadly classified into continuous-wave modulation and pulse modulation.

In the continuous-wave modulation, a high-frequency sine wave is used as a carrier wave, whereas, in Pulse modulation, a periodic sequence of rectangular pulses is used as a carrier wave.

 

Amplitude Modulation

If the amplitude of the high-frequency carrier wave is varied following the instantaneous amplitude of the modulating signal, it is known as Amplitude Modulation.

If the angle of the carrier wave is varied, following the instantaneous value of the modulating signal, it is known as Angle Modulation.

The angle modulation is further classified into frequency and phase modulation.

 

Frequency Modulation

If the frequency of the carrier wave is varied, following the instantaneous value of the modulating signal, it is known as Frequency Modulation.

 

Phase Modulation

If the phase of the high-frequency carrier wave is varied following the instantaneous value of the modulating signal, it is known as Phase Modulation.

 

Difference Between Modulation and Demodulation

 Modulation is defined as the process of mixing a signal with a sinusoid to produce a new signal. The new signal has quite a few benefits over an un-modulated signal. To be specific, the mixing of the low-frequency signal with the high-frequency carrier signal is known as modulation.

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The term Demodulation refers to the process of extracting the original information-bearing transmitted signal from a carrier wave. A demodulator is an electronic circuit, which is used to recover the information content from the modulated carrier wave.

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