Category: Physics Notes PPT

An arbitrarily closed surface in three-dimensional space through which the flux of vector fields is determined is referred to as the Gaussian surface. Their vector field referred here could either be a magnetic field, gravitational field or electric field. Below examples mostly considered an electric field as a vector field. Gauss Law calculates the gaussian surface.                

 [Phi_{E}]   =        [mathop{{int!!!!!int}mkern-14mu bigcirc}] [{_{partial V}E.dA = frac{{Qleft( V right)}}{{{ in _0}}}} ]

Above formula is used to calculate the Gaussian surface. Q(V) refers to the electric charge limited in V.

Let us understand Gauss Law. In real terms, Gauss meaning is a unit of magnetic induction equal to one-tenth of tesla. In physics, Gauss Law also called as Gauss’s flux theorem. This law relates the distribution of electric carrier, i.e., charges following into electric field.  Like mentioned earlier, the surface considered may be closed, confining the volume such as spherical or cylindrical surface. Gauss’s Law is the combination of divergence theorem and Coulomb’s theorem.  

To give you an idea Coulomb’s theorem is the charges opposite in nature attracts. In contrast, the same charges repel with  force, which is directly proportional to the product of charges and inversely proportional to the square of the distance between the charges. Divergence theorem is also known as Gauss theorem. It is an alternate way to defining the behaviour of the flux or flow of some physical quantity. If this quantity is conserved in some manner, the inverse square law is of the same notion as Gauss Law mentions conservation of flux directly.

With this understanding, let us, deep-dive, determine the Gaussian surface of various closed surfaces like sphere or cylinder.

The Gaussian Surface of A Sphere

There could be several reasons when flux or electric field generated on the surface of spherical Gaussian surface –

Imagine a below sphere of radius R, where Q is the charge uniformly distributed. The electric field at a distance ‘r’ would be determined using Gauss Law.         

[Phi_{E}] = [mathop{{int!!!!!int}mkern-14mu bigcirc}_{partial s}] = [mathop{{int!!!!!int}mkern-14mu bigcirc}_{c}]  EdA [Cos^{o}] = E [mathop{{int!!!!!int}mkern-14mu bigcirc}_{s}] dA

The surface area of a sphere is  [iint {_sdA = 4pi {r^2}}], this implies[Phi E = E4pi {r^2}]. By Gauss Law , flux is also [Phi E = frac{{QA}}{{{ in _o}}}]. Equate the above two expression simplifies the equation

[Phi Epi {r^2} = frac{{QA}}{{{ in _o}}} Rightarrow Phi E = frac{{QA}}{{4pi {r^2}{ in _o}}}] 

The Gaussian Surface of The Cylinder

A closed cylindrical surface considered to determine vector field or the flux generated in the due to below parameters-

• Uniform charge present on the uniform infinite long line

• Uniform charge on the infinite plate

• Uniform charge on an infinitely long cylinder

Consider a point charge P present at a distance r containing charge density λ of an unlimited line charge. The rotational axis for the cylinder of length ‘h’ is the line charge, following is the charge q present inside in the cylinder:

[q = lambda h]

Subsequent is the flux out of the cylindrical surface with the differential vector area dA on three different surfaces a, b and c are given as:

                                     

                                 

                                  The Gaussian surface of the cylinder

[Phi_{E}] = [mathop{{int!!!!!int}mkern-14mu bigcirc}_{A}] E. dA =  [mathop{{int!!!!!int}mkern-14mu bigcirc}_{a}] E. dA + [mathop{{int!!!!!int}mkern-14mu bigcirc}_{b}] E. dA + [mathop{{int!!!!!int}mkern-14mu bigcirc}_{c}] E. dA

                           The Equation for Gaussian surface of the cylinder

ΦE=∬aEdAcos900+∬bEdAcos90^o+∬cEdAcos0^o=E∬_c dA ∬_c dA = 2πrh (which is the surface area of the cylinder)

 (which is the surface area of the cylinder)

[Phi E = E2pi rh][Phi E = frac{q}{{{ in _o}}}] (by Gauss law)

[E2pi rh = frac{{lambda h}}{{{ in _o}}} Rightarrow E = lambda 2pi { in _o}r]

The above equation showcases the cylindrical Gaussian surface with a distribution of charges uniformly.

What Is A Gaussian Pillbox?

This surface is commonly aiding to find the electric field due to an infinite sheet of charge with uniform charge density, or a slab of charge with some finite thickness. Imagine a box in cylindrical shape comprising three components: the disk at one end of the cylinder with area πR², the disk at the other end with equal area, and the side of the cylinder. According to Gauss Law, the addition of the electric flux via the above component of the surface is proportionate to the enclosed charge of the pillbox. The field close to the sheet can be estimated constant; the pillbox tilted in such a manner where field lines pierce the disks at the ends of the field at a right angle, and the side of the cylinder is parallel to the field lines.

Fun Facts 

• Do you know the surface which is invalid Gaussian surface? Well, surfaces like a disk, hemisphere, the square cannot be Gaussian surfaces as these surfaces do not include three- dimensional volume and have boundaries. Infinite planes can be an approximate Gaussian surface.

• After reading the Gaussian surface of sphere and cylinder, you must be thinking of limitations of Gauss law. Yes, you are right!. Gauss Law has a specific restriction.Gauss law is limited to calculate the vector field of a closed surface. This law cannot determine the field due to electrical dipole. Thinking what an electrical dipole is? Well, the electrical dipole is nothing but a separation of positive and negative charge. For example, an electret is a permanent electric dipole.

What is the force that holds us down on the Earth and stops us from flying up in space? If you know the answer to this question then you know what is gravity. Gravity is one of the universe’s fundamental forces that dominate every moment of our conscious existence. It helps us to walk on the ground, pulls the basketballs and baseballs back to the ground, and gravity is also something our muscles cannot struggle against. The story of gravity goes together with the story of physics and many famous physicists have found ways to figure out what causes gravity.

What is Gravitation?

Scientists have defined four types of forces in the universe that either attract or repel an object from another. These are:

• Strong force

• Electromagnetic force

• Weak force

• Gravity

(images will be uploaded soon)

Of these 4 types of forces, strong and weak forces operate within the center of an object’s atoms. The EM force applies to objects that have an excess of charge (electrons, protons) like socks that shuffle over a fuzzy carpet.

Gravity is the force that acts upon objects having mass. It is an all-pervasive force that keeps our foot on the ground yet it is still a puzzle for many and the answer to the question what do you mean by gravity.

What do You Mean by Gravitational Force

Gravity can be defined as the force which a planet (or a body) exerts on other objects and draws them towards its center. It is this force of gravity that keeps all the planets in their orbits around the Sun.

()

Newton explained what is meant by gravitational force in his law of universal gravitation as a force of attraction that exists between any two objects having mass. This force is directly proportional to the masses of the objects and inversely proportional to the distance between them. It is mathematically expressed as:

F = G * (m1 m2) / R2 

Where F – Force of gravity.

G – Gravitational constant and its value is 6.67 x 10-11  N * m2/kg2.

R – The distance between the objects.

What is Gravity Made of

Earth’s gravity comes from its entire mass. Earth’s entire mass exerts a combined gravitational pull on your body mass. It is this gravitational pull of the earth which gives you your weight. So if you are on a planet whose mass is less than the earth, then you would weigh less there. You and earth both exert gravitational force on each other, but since earth’s mass is way more than your weight, your force has no effect on the planet.

()

A team of scientists based in the South Pole discovered the celestial fingerprint using a telescope, BICEP2. This fingerprint explains the beginning of time and reveals microscopic details of gravity. Quantum particles in an infant universe gave rise to “inflation,” which is the reason behind why the universe exploded outwards.

It also revealed that gravity is made up of quantum particles called gravitons. A single graviton is too small and massless, but these gravitons’ quantum fluctuations in the infant universe bend pockets of this tiny space-time.

What is the Gravitational Force of Earth

The gravity of the earth is denoted by g and is defined as the net acceleration that is induced in objects owing to the gravitation (mass distribution within the earth) and centrifugal force due to the earth’s rotation.

Earth’s acceleration due to gravity is 9.8 m/s² close to its surface (also called 1 g). Gravity decreases as the distance from the Earth increases.

Gravity on Earth is Not the Same Everywhere

The Sun’s gravity keeps the Earth in such a position that we can enjoy the sunlight without being burnt. Gravity holds our entire atmosphere and the air we breathe in, so living without gravity is impossible for us.

But the force of gravity is not the same at all parts of our planet Earth. There is more gravity in the places where there is more mass underground compared to places with less underground mass. The force of gravity is also dependent on where you are standing, near the equator, or further from it. This is due to Earth rotating on its axis; hence, the force of gravity at the equator is less (9.789 m/s²) than the gravity at the poles (9.832 m/s²). This means you would weigh slightly more at the poles than at the equator due to the centripetal force.

NASA has deployed 2 spacecrafts that measure these variations in Earth’s gravity. These spacecrafts are part of GRACE (Gravity recovery and climate experiment).

GRACE can detect small changes in gravity over time and has revealed crucial details about Earth. As an example, GRACE monitors sea level, and changes in it can make it determine changes in Earth’s crust brought upon by earthquakes.

Examples of Gravity

Some interesting examples of gravity are:

• Gravity is the weakest force amongst all the fundamental forces known. A bar magnet can pull a paperclip upwards due to electromagnetic force, which is stronger than the gravitational pull of the whole earth on that paper clip.

• It is gravity due to which a car coasts downhill even when you are not stepping on the gas.

• Gravity holds the earth and all the planets around the Sun in their proper positions and orbits.

• The force of gravity holds gases inside the Sun.

• Tides in the oceans are led by the force of gravity of the moon.

• The stars and planets have been created by gravity, which has pulled together the materials they are composed of.

• Gravity not just pulls masses, but it affects light as well. Einstein proved this fact. If you send a flashlight upwards, it turns red with time due to gravitational pull. This color change is not perceptible by us, but scientists have been able to measure it.

What is Convection?

Convection is the process of heat transfer in which transfer of heat energy occurs by the mass movement of molecules of the fluids like gases and liquids. Gases and liquids are not a good conductor of heat under normal conditions, but they can easily transfer heat.

Heat transfer through convection occurs other through diffusion or advection or both. Convection does not take place in solids, because no movement of its constituent particles occurs. The diffusion of heat occurs in solids, and it is called thermal conduction.

The process in which heat transfer occurs between a surface and a liquid or a fluid that is in contact with the surface is called convection heat transfer. Convection plays a major role while transferring heat from one liquid to another liquid through a barrier. Heat transfer by convection either occurs due to thermal diffusion (motion of fluid molecule) or advection, in which heat is transferred by the bulk motion of heat currents in the fluid.

Newton’s Law of Cooling

Under normal conditions, the heat transfer due to convection is directly proportional to the temperature difference between the parts. Newton’s law of cooling has expressed this phenomenon, and the law states that:

The heat transfer rate of a body due to convection is directly proportional to the temperature difference between the body and its surroundings. The temperature difference should be small, and the nature of the radiating surface remains the same. This is the convection heat transfer equation:

P = [frac{{dq }}{dt}] = hA(T – T₀)

Where

P = [frac{{dq }}{dt}] is the rate of heat transfer

h is the coefficient of the convection heat transfer

A is the surface area of the body

T is the temperature of the object

T0 is the temperature of the fluid or liquid which is subjected to convection

Heat-transfer coefficient h depends on the following factors:

Density, Thermal conductivity, Viscosity, coefficient of convective heat transfer, and specific heat capacity

The constant of proportionality mentioned in the above formula is an important parameter and is called a coefficient of convective heat transfer ‘h’. It is defined as:

The rate at which heat transfer occurs between a solid and a fluid part per unit surface area and for the unit temperature difference:

𝒉 = [frac{{q}}{ΔT}] 

Where

q is the local heat flux density [W.m^-2]

H is the heat transfer coefficient [W.m^-2.K]

ΔT is the temperature difference [K]

The horizon is a visible line that separates all viewing lines depending on whether or not it intersects the Earth’s surface. The study of the horizon is called horizon astronomy. The horizon definition in astronomy is defined as, the particular line, which can only be observed when it lies on the sea surface. 

When looking at a sea from a seaside, then the part of the sea nearest to the horizon is called the offing. This line is obscured by terrain, towers, trees, houses, and mountains in many places, and the resultant convergence of earth and sky is referred to as the apparent horizon in astronomy.

The true horizon definition astronomy near the observer is generally assumed to be a circle, drawn on the surface of a spherical model of the Earth. 

The horizon centre is under the observer and below sea level. Its distance from the observer differs from day to day due to atmospheric refraction, which is seriously affected by weather conditions. 

Also, the horizon is far away from the observer, the higher the observer’s eyes are from sea level. For example, in standard atmosphere conditions, for an observer with eye-level above the sea level by 2 metres, the horizon is at a distance of about 6 kilometres. 

Types of Horizon

When it is observed from high standpoints, like as a space station, then the horizon is far away and it surrounds a much larger area of Earth’s surface. In this case, the horizon would no longer be an exact circle, not even a plane curve like an ellipse. Especially when the observer is above the equator, as the Earth’s surface can be much better modelled as an ellipsoid than as a sphere.

There are two main types of horizons

1)  Earth-sky horizons 

2) Celestial horizons. 

There are subtypes of earth-sky horizons and celestial horizons. The Local horizons, sea-level horizons and geographic horizons are the sub-parts of Earth-sky horizons.

While, the astronomical and true horizons are celestial horizons. 

Earth-Sky Horizons 

The local horizon is the visible boundary between the Earth and the sky. The local horizon includes trees, buildings, and mountains. The geographic horizon is the visible boundary between the Earth and the sky. Mountains, trees, buildings, and other elevated features are not considered part of the geographic horizon.

 

The spatial horizon is the same as the sea-level horizon, but only at sea level. A beach is one of the best ways to see the sea-level horizon where the Earth seems to touch the horizon, the ocean and sky have a clean, flat surface. If the observer is standing on the beach and looking out at the sea, the offing refers to the part of the sea that “touches” the horizon.

Celestial Horizons

Celestial horizons are used by astronomers, for the measurements of the position of the Earth relative to the rest of the sky. The celestial horizon is a flat passing from the earth’s centre perpendicular to the zenith-nadir axis. The visual horizon approaches this plane at the earth’s surface. 

The astronomy horizon is the type of celestial horizon whose imaginary horizontal plane is always at a 90-degree angle from the observer’s zenith. Celestial horizons are perfect circles that surround the observer. The true horizon is the theoretical plane that passes through the centre of the Earth, its radius is perpendicular. From orbit, the true horizon is spherical, following the shape of the Earth. The altitude of a celestial body is calculated using the celestial horizon as a reference point. Celestial horizons are called rational horizon to compare sensible horizon. 

Important Points

1. The theory of the horizon is important to different types of work, including aviation, navigation, and art. 

2. The horizon is used by pilots to keep the plane level when in the air. This method is called “attitude flying,” Pilots can handle their aircraft by determining the relationship between the aircraft’s front end or the aircraft’s nose, and the horizon. By shifting the horizon to be mostly sky or mostly earth, pilots may adjust their altitude or flight pattern.

3. Before the explanation of the latest tools such as Global Positioning System (GPS) devices, sailors depended on a perfect view of the horizons to navigate the ocean.

4. The sun’s position to the horizon told sailors what time of day it was and what direction they were boat or crew.

5. You will see stars appearing on the eastern horizon astronomy (just as the Sun and Moon), spreading around the dome of the sky during the night, and settling on the western horizon if you lay down in an open field and watch the night sky for hours, as ancient shepherds and travellers did. 

6. In astronomy, the horizon is the point where the sky seems to touch the earth or the sea. (In astronomy it is called the intersection on the celestial horizon sphere of a plane perpendicular to a straight line). The higher the observer, the lower and more distant is his visible horizon in astronomy.

Event Horizon Astronomy

In astronomy, event horizon definition is a partition beyond which events cannot affect an observer. The term was discovered by Wolfgang Rindler.

The event horizon definition astronomy, is the circumstance defining the region of space around a black hole from which nothing can escape. And an object within the event horizon has a faster escape velocity than light. The name arises since it is impossible to observe any event taking place inside it is the horizon beyond which we cannot see. As a result, the event horizon essentially covers the singularity at the black hole’s core, which is a relief for astrophysicists concerned about the collapse in physics at such a point.

All singularities are obscured by an event horizon, according to the cosmic mind regulation hypothesis, and this violation of the laws of physics is not visible. In theory, mass can be compressed sufficiently to form a black hole. The only stipulation is that it must be less than the radius of the event horizon. For example, our Sun would become a black hole if its mass was contained within a sphere about 3 km across.

Have we ever wondered that whatever we want we get it by saying or expression. One of the best modes to express our feelings is by our voice. We can say that voice is one of the medium by which one recognises us as well.

The size that is of vocal cords generally affects the pitch of voice. This opens when there is a process of breathing and vibrating for speech or singing and then the folds are controlled via the recurrent laryngeal branch of the vagus nerve.

(Image to be added soon)

Parts of Production of Voice 

The means of communication is said to be very  essential for the well-being of any animal and human as well. Even the organisms which are the microorganisms communicate with each other by means of chemicals.  Fortunately we can say that our means of communication are far better than that. So we rely on it every day to interact with others. As is the case with walking and seeing, taking as well. We can say that the human voice is very versatile and this is rich both incontent and  range. We generally use it to laugh and cry and scream as well as shout, sing and the list goes on. The human voice which is produced by the vocal cord is capable of producing highly sound intricate. We  can tell if our mother is angry at us by her voice. Some people do one better and can tell if people are lying that too just by their voice.

Following Are Said to Be the Main Parts of Production of Voice

• We can say that the power source: that is lungs.

• The  vibrator: that is the voice box.

• The resonator: that is the throat, mouth, nose and sinuses.

The Power Source: Which is Lungs

We can say that the lungs here perform the essential function of supplying adequate airflow and air pressure in order to vibrate the vocal cord. When we inhale the oxygen that is when we draw air into the lungs. This air is then later exhaled which is creating a stream of air that is through our wide throat and pipe. This is said to be very exciting that the air provides the energy to vibrate the vocal cords in the box or we say the voice box to produce sound. If we want to make a sound that is loud then we have to exhale hard to create a strong airflow.

• The Vibrator: The Voice Box

The part of the throat that generally moves when we swallow is called a voice box. The Voice Box that is the Larynx sits on the top of the wide pipe. The voice box is said to be a part of the wide pipe and the exhaled air which is from our lungs generally passes through the voice box. The vocal cord generally consists of two tight strings that open during breathing and later close when we exhale to make a sound. They vibrate very fast that is almost from 100 to 1000 times per second in terms. We may vary the pitch that is ‎which explains the concept of frequency and pitch etc by controlling the tension in the muscles that is present in the voice box. The vocal cord is generally also known as a fold that is the vocal fold. The vocal cord generally modulates the flow of air from the lungs.

• The Resonator: That Includes Throat and Nose and Mouth and Sinuses

The chords that are the vocal cords by themselves produce only a buzzing sound much like a bee. The sound is not usually created by vocal cords. Instead we can say that it is created by the interactions of the vibrations which are created by our vocal cord with the muscles and tissues which are present in your mouth, nose, throat and tongue. When we talk, our tongue generally darts all around our mouth which is helping us to pronounce complex syllables. The vibrations that are said to be deliberately altered in our throat and mouth to produce the unique voice of humans.

(Image to be added soon)

Disorders of Voice

There are many disorders which affect the voice of humans. These usually include speech impediments and the growths and lesions on the folds of the vocal box. We are talking improperly for long periods of time causing vocal loading which is stress inflicted on the organ of speech. When vocal injury is done then often an specialist of the ENT may be able to help but we can say that the best treatment is said to be the prevention of injuries through good vocal production. The therapy of voice is generally said to be delivered by a speech-language pathologist.

The nodules which are the vocal are generally caused over time by repeated abuse of the vocal cords which results in soft and then the swollen spots on each vocal cord. These spots which usually develop into harder that is the callous-like growths known as the nodules. The longer and the abuse generally occurs the larger and stiffer the nodules will become.  We can say that most polyps are larger than nodules and may be known by other names such as polypoid degeneration or the Reinke’s edema. The polyps are said to be caused by a single occurrence and may require removal from surgery. The irritation which occurred after the removal may then lead to nodules if additional irritation persists for a longer time.  The hoarseness or the breathiness that lasts for more than two weeks is a symptom that is common of an underlying disorder of the voice such as nodes or polyps and should be investigated medically.

In physics, impedance of free space, also recognized as the characteristic impedance of free space, is a physical constant signified by Z0. This narrates the magnitude of the magnetic field and the electric field of electromagnetic radiation roaming through free space.

The impedance of free space (means the wave impedance of a simple wave in free space) is equal to the multiplication of the speed of light in vacuum c0 and the vacuum permeability μ0.

Before 2019, the magnitudes of both these constants were considered to be precise (they were arranged in the descriptions of the ampere and the meter respectively), and the rate of the impedance of free space was taken to be exact similarly. 

However, with the redefinition of SI base units that approached into force on 20 May 2019, the impedance of free space is a matter to experimental measurement because only the speed of light in vacuum recollects a correctly distinct value.

Value of Intrinsic Impedance of Free Space

It is explained as the square root of the proportion of permeability of free space to the permittivity of free space.

The particular value of the impedance of free space is universally acknowledged, and the elaborated value is-

The Impedance of free spaceZ₀ = 376.73Ω.

Intrinsic Impedance of Free Space Formula

The impedance of free space can be accurately inscribed as:

Z[_{0}] = [frac{E}{H}] = [mu _{0}]c[_{0}] = [sqrt{frac{mu _{0}}{c_{0}}}] = [frac{1}{varepsilon _{0}c_{0}}]

Where,

μ₀ is the magnetic constant

ε₀ is the electric constant

C₀ is called the speed of light in free space.

E is the electric field strength.

H is the magnetic field strength.

Z₀ sometimes also denoted the admission of free space.

Let’s hope that you have agreed with the Impedance of free space or the characteristic Impedance of free space alongside units, values, and the formulations.

Characteristics Impedance of Free Space

These are some answers start to appear as we consider these facts such as:

1. Characteristic impedance is a characteristic of any medium that can embrace the transmission of an electromagnetic wave irrespective of whether or not it is associated with a power source at one terminal and a load at the other end.

Characteristic impedance adjusts signal or the current passing through a conductor. But if there is no non-stationary energy at a certain point in time, that does not change the fact that the medium has a precise characteristic impedance. 

A reel of coax in the ware-house has similar characteristic impedance as when it is wired into an active, working network.

()

()

2. Characteristic impedance, nothing like conventional impedance, is free of length or distance over which signals propagate. Consequently, the characteristic impedance of the universe is the equivalent of the characteristic impedance of a circuit navigating about 50 feet of free space.

3. The characteristic impedance of a vacuum is considered equivalent to that of dry air which has almost no effect on conductance.

4. The characteristic impedance of free space is equivalent to the sq root of the proportion of penetrability of free space (henrys per meter) to the penetrability of free space (farads per meter). It figures out about 377 Ω, and that is the characteristic impedance of the universe.

Impedance of Free Space Derivation

The impedance of free space also recognized as the characteristic impedance of free space is a physical constant represented by Z0 which co-relates the magnitude of the magnetic field and the electric field of electromagnetic radiation traveling through free space.

The wave impedance in free space of plane waves is illustrated by:

Z[_{0}] = [frac{E}{H}] = [mu _{0}]c[_{0}] = [sqrt{frac{mu _{0}}{c_{0}}}] = [frac{1}{varepsilon _{0}c_{0}}]

How to Make Notes on Impedance of Free Space

• Go through and click on Impedance of Free Space

• Read the page and then start writing down everything in your own language

• Follow the sequence of the page

• Mark all they key areas using some colour

• Write brief sentences

• Do not just copy-paste from the main page

• Revise from these before an exam

How Prepares Students for Impedance of Free Space in Physics

has Impedance of Free Space on its platform that helps it to understand the chapter. This material has been provided free of cost and is useful for all students to read from. The formulas and other subtopics have also been provided as per the student’s understanding. is India’s leading onlne tutoring platform that employs teachers from all over the country to write for its platform. It has the best of study material which has shaped the careers of multiple students and is instrumental in helping the students get placements in all the premier institutes.

Do You know?

Is there any characteristic impedance in the universe? If yes, then what is the value? 

The universe is collected of huge quantities of blank space between relatively small stars broadly spaced apart. It is believed that when our Milky Way and the Andromeda Galaxy encounter 4 billion years from now, not even one star from galaxies will truly strike. 

Scientists explain if stars were the size of balls like ping pong, they would be spread out on the order of two miles apart. However, there will undoubtedly be no collisions; both galaxies will be deeply exaggerated by the connections of their enormous gravitational fields.

Employing an electrical channel with characteristic impedance, the universe was possibly built with enhanced quality control than our best coaxial cable.