Category: Physics Notes PPT

Electric current is the flow of electrons through a conductor. The movement of these charged particles creates a voltage or electrical potential difference between two points in a circuit. This potential difference can be harnessed to power electronic devices and appliances. In order to study electric current in conductors, it is important to understand how these electrons move and what factors affect their flow. By understanding the basics of electricity, you can more effectively learn about electric current in conductors and how to apply it in your own life.

Effect on the Flow of Electrons

There are several things that affect the flow of electrons through a conductor. The most obvious factor is the amount of current flowing through the circuit. This is measured in ampere (A) and can be affected by the resistance of the material as well as the number and size of the conductors. The resistance of a material is determined by its resistivity, which is a measure of how difficult it is for electrons to move through the substance. A higher resistivity means that there will be more resistance to the flow of current and vice versa.

What is Current?

When we apply a potential difference across any material, a flow of electrons (charges) takes place. The rate of flow of this electron is called current. If the material on which the potential difference is applied is a conductor, then we say this current to be the current in the conductor. If Q amount of charge flows through any cross-section of a conductor in time t, then- the current is defined as the rate of the flow of electrons, i.e

[I = frac{Q}{t}]

The SI unit of the current is Ampere (A).

The current is mostly divided into two groups, i.e. alternating current and direct current, depending on the electric charge flow. In direct current, the charges flow through unidirectional while the charges flow in both directions in alternating current.

The Direction of the Current

As per the electron theory, when the potential difference is applied across any conductor in a circuit, some matter flows into it that actually constitutes the flow of current. It is believed that the matter flows from a high potential to a lower potential, i.e from the positive terminal to the negative terminal of the battery. Since the current has the direction, so technically, it should be a vector quantity because it has both the direction and value but in reality, it is a scalar quantity. 

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Thus, conventionally the direction of current flow is from the positive terminal to the negative terminal of the battery.  

Current in the Conductor

We all know that conductors are the substances that allow current to pass through them. When the conductor is not connected to the battery, the free electrons tend to move freely here and there. This electron moves randomly inside the conductor with a certain velocity. This velocity is called thermal velocity. Since the whole motion is random, the average velocity equals zero. 

Next, the external electric field is applied. Once the battery is applied to the conductor, the electron starts moving towards the positive terminal of the battery. As the electrons move towards the positive terminal of the battery, it gets accelerated.  Since the electron is moving in only one direction, it gets collides with the positive ions as well. With this collision, electrons tend to lose the velocity which they had gained because of the acceleration. Whenever any charged particle goes into any conductor, it doesn’t move into a straight line, it collides with the other charged particle. Because of this loss, a very small increase in velocity takes place. The average of this small gain in the velocity is called the Drift velocity. Drift velocity can be defined as the average of the velocity gained in a material due to an electric field.

[V = frac{I}{nAq}]

Where,

v – Drift velocity

I – Electric current

n – no of electrons

A – Area of the cross-section of the conductor

q – charge of an electron in coulombs

Mobility of an Electron

The mobility of an electron is defined as the drift velocity of an electron for a unit electric field. The mobility depends upon the potential difference applied, conductor length, the density of charge carriers, current and area of the cross-section of the conductor. 

[mu = frac{V_{d}}{E}]

Where, μ = mobility of an electron

V_d = Drift velocity of an electron

  E =  Electric field applied

Importance of Electric Current in a Conductor

The electric current in a conductor is important because of multiple reasons:

1. It is the means by which electronic devices and appliances are powered.

2. Without electric current, we would be unable to use many of the devices that we take for granted in our everyday lives. From computers and smartphones to televisions and refrigerators, all of these appliances require an electrical current in order to function. By understanding how electricity works, you can better utilize these devices and make your life a little bit easier.

3. Electricity is also responsible for powering many industrial applications. Factories use large motors to run their machinery, and these motors require a steady supply of electrical current. If there was no electric current in conductors, our world would look very different indeed.

Starting From the Basics Let’s Check the First Point in Our List:

 

Electric Forces and Their Types:

 

There are predominantly two types of electrical forces: Attractive electrical forces and repulsive electrical forces. Unlike charges exert an attractive force on one another and like charges repel each other. If a positive charge comes close to a negatively charged particle, it will be more likely for them to attract each other and come together.

 

Now let’s see what an electric force is and what a charged particle is. 

 

So as stated above, the electric force is a force exist between two charged particles. So, what are charged particles? There are minute particles present in atoms which are called protons and electrons. Protons are positively charged, and electrons are negatively charged ones. Protons and electrons are the smallest existing particles. All substances only get charged due to an imbalance between the number of existing protons and the number of electrons that are present in an atom. 

 

Protons are very tightly packed within a nucleus allowing little to no movement at all. On the contrary, electrons can move freely around the nucleus since they are not perpetually attracted to the nucleus. This is the reason why it is way too easy for electrons to move about from one particle to the other causing an imbalance between the number of protons and electrons being present in the particle and thereby inducing the need to bond with another particle in order to maintain equilibrium. 

 

In regard to the basic electrical charges, the reason behind our hair stands up in the cold dry weather after brushing it. It is because the charges from the comb are transmitted to the hair and thus causing it to stand up. Here the hair stand becomes positively charged in oppose to the negatively charged comb. 

 

It mainly happens in cold dry air because, in a relatively humid and hot climate, a lot of water being present in the air makes it pick up charges from the hair more easily and subsequently the hair lose charge as well way too quickly. 

 

So How to Calculate 

 

The strength of the electric force between two charged particles takes into consideration the amount of charge that each object contains and the relative distance between the two. As the amount of charge gets larger the force between the two gets larger however with the increase in distance the force of attraction between two charges gets smaller and smaller. 

 

So it can be told that the force of attraction between two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. This phenomenon is known as Coulomb’s law. And can be written as:

 

[F_{12} = F_{21} = k q_{1}q_{2}r^{2}]

 

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In the above equation, [q_{1}] and [q_{2}] are the amounts of charge present in two particles, r represents the relative distance between the two particles. Let’s explore the basic difference that is seen between an electric force and an electric field. Though thought to be similar they are actually different. The thing about technologies in the field of physics is that each section has variable differences and each word has a significant meaning. The motive is to explore each word so that the concept is clear in all sections.

 

In the case of electric forces and electric field, the concept it is based on is the same, but both have different actions and different significance. 

 

All charged particles are known to create a field of their own. The force on a charged particle is so immense that the effect causes a particular area to be affected by it. This area is called the field caused by the particle. Similarly, the created by an electric charge is called an electric field in the vicinity of the electric force. 

 

The electric field and in turn the electric force can change variable with time as the charge generating this effect is moving. 

If the said charged particle is static, then it is called an electrostatic field corresponding to the static electric force. 

 

“Electricity focuses on the movement of particle which is usually electrons since the protons are bundled in a nucleus, and thereby slower.”

 

 

Electric Force and Static Equilibrium

Let’s Take two rubber balloons and let us hang them from the ceiling by two long strings such that they hang vertically. Then it is such that each balloon is given 10 average-strength rubbing from an animal fur. The balloons, that are having a greater attraction for electrons than animal fur, would acquire a negatively charged potential. The balloons will have to have the same type of charge and they would start to repel each other. The result of the phenomenon of repulsion is that the strings and balloons that were suspended would now make an angle with the vertical. The angle of the string with the vertical has to be mathematically related to the quantity of charge on the balloons. As the balloons possess a greater quantity of charge, the force of repulsion between them would increase and the angle made by the string with the vertical will have to also increase. Like any situation involving electrostatic force, this situation can be concluded using vector principles and Newton’s law. 

 

Now let’s Jump to the Laws that Govern Electrostatic and Electric Forces of Charged Particles:

I. The electric forces are directly proportional to the product of their strengths.

 

II. They are seen to be inversely proportional to the square of the distance between them.

 

This is known as Coulomb’s Law. 

 

What is to be said for the electric and magnetic fields is that in permittivity of free space is denoted by ε0 and magnetic permeability of free space is denoted by μ0 of free space. As mentioned about electric and magnetic constants before, these two quantities are not independent but are related to “c”, the speed of light and other electromagnetic waves.

The permittivity of any medium with respect to the permittivity of free space is called relative permittivity and is denoted by εr and Absolute permittivity of any medium is given by

                           ε = εr . ε0 

 

An electric field is the force experienced by a charge of 1C when is placed inside an electric field. If a small charge is tested in a field, it would either move along the field lines or in the opposite direction of the field lines. If it is seen that the test charge is moving along the field lines, then it can be said that the charge is positive else it is negative.

 

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One is given a charge q and electric field at a distance r needs to be found. 

 

The electric field equation is:

 

|E| = [frac{kq}{r^{2}}]

 

where:

• |E| is the magnitude of the electric field that is given in newtons-per-coulomb (N/C)

• q is the magnitude of the charge given in coulombs

• k is Coulomb’s constant

• r is the distance from the charge in meters (m)

 

[overrightarrow{F_{E}} = frac{q_{1}q_{2}}{4pi epsilon_{0} R^{2}}widehat{a}(N)]

 

[overrightarrow{E} = frac{q_{1}}{4 pi epsilon_{0} R^{2}} widehat{a} (frac{N}{C})]

 

Here the electric field is established by the source charge q1 and F is the force that has been exerted on q2 R from the q1. And E is the electric field due to q1 at a distance of R from the source charge.

 

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Gauss’s Law states that the total electric flux in a closed surface is equal to the charge that is enclosed divided by the permittivity.

 

Electric flux, on the other hand, is defined as the electric field through an area of the surface projected in a plane perpendicular to the field.

 

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The area integral form of the electric field is given for any closed surface is equal to the net charge in a closed surface divided by the permittivity. 

 

This is the basic information required to start off with the topic of electric forces and fields.

Radio waves are electromagnetic waves that have wavelengths longer than infrared radiations. The range of radio waves is between 30 kHz and 300 GHz in an electromagnetic spectrum. 

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Radio waves have the best use in communication systems like television, mobile phones, radios, etc. 

Natural radio waves occur or emit by lightning, astronomical objects, while artificial radio waves are produced with the help of transmitters, and radio receives it by using antennas. These signals are transformed into mechanical vibrations in speakers to generate sound.

Radio waves have many real-life applications. In this article, we will learn about the radio electromagnetic spectrum and its uses.

Radio Waves Uses

Radio waves in the electromagnetic spectrum are located in the low range frequencies. The wavelength of these waves ranges from 30 cm to 1 km and Radio electromagnetic spectrum is a part of the electromagnetic spectrum with frequencies from 30 Hz to 300 GHz. These waves have great use in communication systems.

In the air, radio wave communication signals traverse a straight path, emit clouds/layers of the ionosphere, or are relayed by satellites in space. 

Radio Waves Are Employed in Various Places; These Are:

Radio Wave Frequency Spectrum

A radio band is a continuous series of the radio wave frequency spectrum. These bands are called the channels and each channel has its specific purpose. To overcome the interference and the overlapping of bands and allow for the efficient use of the radio wave spectrum, alike services are allocated in bands.

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For each channel, ITU (International Telecommunication Union) has a band plan that indicates how each channel has to be used and shared, to prevent interference, overlapping and to set protocol for the affinity of transmitters and receivers. 

What Does ITU Do?

ITU radio bands are specified in the ITU Radio Regulations. It divides the radio frequency spectrum into 12 bands, each of which begins at a wavelength with a power of 10n, with the respective frequency of 3  x 108-n Hz.

The table mentioned below discusses the radio wave frequency bands with their respective ITU band numbers and functions. These recommendations were approved by the International Radio Conference held at Atlantic City, New Jersey, in 1947. Let’s look at these:

Name of the Band	Abbreviation of the Band Name	ITU Band Number	Frequency Range of Radio Waves          & Radio Waves Wavelength	Functions
Extremely low frequency	ELF	1	3-30 Hz 100,000 – 10,000 km	In communication with Marines
Super low frequency	SLF	2	30-300 Hz 10,000 – 1000 km	These are also used for communications in submarines
Ultra low frequency	ULF	3	300 – 3,000  Hz 1,000 – 100 km	Communication with submarines; communication in mines
Very low frequency	VLF	4	3 – 30 kHz 100 – 10 km	Navigation Time signals Submarine communication Wireless heart rate motors Geophysics
Low frequency	LF	5	30 – 300 kHz 10 – 1 km	Navigation Time signals Amplitude modulation longwave broadcasting in Europe and parts of Asia RFID Amateur radio
Medium frequency	MF	6	300 – 3,000 kHz 1,000 – 100 m	Amplitude modulation (medium-wave) broadcasts, amateur radio, avalanche beacons
High frequency	HF	7	3 – 30 MHz 100 – 10 m	Shortwave broadcasts Citizens band radio Amateur radio and over the horizon aviation communications RFID ALE (Automatic link establishment) or NVIS (near-vertical incidence skywave radio) communications Marine communication Mobile phone telephony
Very high frequency	VHF	8	30  – 300 MHz 10 –  1 m	Frequency modulation Television broadcasts Line-of-sight communications for the ground to aircraft and aircraft to aircraft Land mobile maritime and mobile communications Amateur radio, weather radio communications
Ultra-high frequency		9	300 – 3,000 MHz 1 – 0.1 m	Television broadcasts  microwave devices or communications Microwave oven radio astronomy mobile phones wireless LAN Bluetooth ZigBee GPS Two-way radio communications viz: land mobile  FRS GMRS radio communication Amateur radio Satellite radio Remote control Systems
Super high frequency	SHF	10	3 – 30 GHz 10 – 1 mm	Radio astronomy Microwave communications Wireless LAN DSRC, Modern radars Communications satellites Cable and satellite television broadcasting  DBS  Amateur radio Satellite radio
Extremely high frequency	EHF	11	30 – 300 GHz 10 –  1 mm	Radio astronomy high-frequency microwave radio relay, ADSB microwave remote sensing amateur radio directed-energy weapon  millimeter-wave scanner wireless LAN (802.11ad)
Tremendously high frequency (or TeraHertz)	THF (or THz)	12	300 – 3,000 GHz 1 – 0.1 mm	Ultrafast molecular dynamics,  Experimental medical imaging to replace X-rays Condensed-matter physics Terahertz time-domain spectroscopy terahertz computing or communications remote sensing

From the above table, we can see the descending order of frequency and wavelengths. Also, the electromagnetic waves radio waves specifically designate a section of the electromagnetic spectrum having frequencies ranging between 300 GHz and 3 kHz and wavelengths ranging from 1 millimeter to 100 kilometers.



Charge is the characteristic property of mass. There are two types of charges, positive charge and negative charge. The fundamental charge is the charge of an electron. When two charges interact with each other, then a force exists between them called electrostatic force. The magnitude of the electrostatic force between two charges is given by Coulomb’s law. Here, we will discuss electrostatic force in detail and Coulomb’s law which describes electrostatic force acting between two charges. 

Electrostatic Force Acting Between Two Charges

What is electrostatic force?. Electrostatic force is one of the fundamental forces in the universe.There are four fundamental forces in the universe. They are strong nuclear force, electromagnetic force , weak nuclear force and gravitational force. The electrostatic force comes under electromagnetic force. The electrostatic force exists between two charges placed at a distance. The magnitude of  electrostatic force depends on the magnitude of each charge and the distance between them.

When two positive charges or two negative charges are brought together, then the two charges repel each other. The electrostatic force acting between two like charges is called electrostatic force of repulsion. When two opposite charges are brought together, then two charges get attracted towards each other. Then the electrostatic force acting between two opposite  charges is called electrostatic force of repulsion. Therefore, we can say that like charges repel and unlike charges attract. The electrostatic force acting between two charges is greater when the magnitude of two charges are larger. The electrostatic force is larger when the distance between the two charges are less.  

Let us see some electrostatic force examples .We can do a simple experiment to observe the electrostatic force. Take a piece of paper and cut it into very small pieces of paper. Then using a dry scale or ruler, rub it on your dry hair vigorously and repeat it for some time. After doing it for some time, bring the ruler close to the tiny pieces of paper. You can observe that the paper bits are attracted to the ruler. This is because when the ruler is rubbed on your dry hair, the electrons are transferred and electrostatic force acts between them which causes the paper to get attracted to the ruler. Another simple activity to visualise the electrostatic force is to move your hand closer to the screen of the tv. Then you can observe that the skin hairs are getting attracted to the screen of the TV. It is because the screen of the TV is charged due to a cathode ray tube inside the TV which polarises the skin hair and an electrostatic force will be formed that attracts the hairs of the skin. The above activities are electrostatic force examples.

Coulomb’s Law of Electrostatic Force

The magnitude of the electrostatic force is given by Coulomb’s law. According to Coulomb’s law of electrostatic force, the  electrostatic force acting between two charges is directly proportional to the product of magnitude of charges and inversely proportional to the square of the distance between the two charges. 

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Consider two charges q₁ and q₂ placed at a distance r from each other. Then the electrostatic force acting between the two charges is given by,

k=14πε‘ role=”presentation”>$k=\frac{1}{4\pi \epsilon }$

Where,

5μC‘ role=”presentation”>$5\mu C$ placed at a distance of 1 m.

Ans:

The magnitude of first charge =q₁=5μC‘ role=”presentation”>$5\mu C$

The distance between the two charges =r=1 m

The formula to calculate the electrostatic force between two charge is given by,

ב role=”presentation”>$\times$10⁹ Nm²/C².

Substitute the value for the magnitude of charges and distance between the charges to obtain the electrostatic forces between two charges.

⇒FE=9×109Nm2/C2×5μC×5μC(1m)2‘ role=”presentation”>$\Rightarrow F_E=\frac{9\times {10}^{9}N{m}^2/C^2\times 5\mu C\times 5\mu C}{(1m{)}^2}$

ב role=”presentation”>$\times$10^-1 N

2. The electrostatic force acting between two charges q₁ and q₂  is F. What is the new electrostatic force if the distance between the two charges is doubled?

Ans:

Let r be the initial  distance between the two charges.

Then the formula to calculate initial  electrostatic force is given by,

⇒F′=kq1q2(2R)2‘ role=”presentation”>$\Rightarrow F^{\prime }=\frac{k{q}_1{q}_2}{(2R{)}^2}$

⇒F′=FE4‘ role=”presentation”>$\Rightarrow F^{\prime }=\frac{F_E}{4}$

Therefore, when the distance is doubled, the new electrostatic force is reduced to one fourth of the initial value.

Conclusion

The electrostatic force can be the electrostatic force of repulsion or attraction depending on the  polarity of the two charges. The magnitude of the two charges and the distance between the two charges affects the electrostatic force. For a system of two charges, electrostatic forces on the charges are equal in magnitude but opposite in direction. The electrostatic force is a conservative force which means that the work done by the electrostatic force in a closed loop is zero. The electrostatic force also depends on the medium at which two charges are placed and is maximum when the medium is vacuum.

Satellites are launched from the earth to revolve around it. Many rockets are fired from the satellite at a proper time to establish the satellite in the desired orbit. Once the satellite is located in the desired orbit with the correct speed for that orbit, the satellite will continue to move in an orbit under the gravitational attraction of the earth.

So, the energy required by a satellite to revolve around the earth is called its orbiting energy. Since this satellite revolves around the earth, it has kinetic energy and is in a gravitational field, so it has potential energy.

Potential Energy of Satellite

Let’s consider mass m at distance r₁ and distance r₂ from the centre of the earth. Here, we will move radially from distance r₁ to distance r₂ and then move along the circle until we reach the final position.

During the radial portion, the force F is opposite to the direction we are travelling along with distance dr. 

Along the arc, F is perpendicular to dr, so F.dr = 0. Therefore, no work is done while moving along the arc. 

Now, using the expression for the gravitational force and noting the values for 

 Along with the two segments of our path, we have:

                                                             

[Delta  U = -int int_{r1}^{r2} F . dr = GMm int_{r1}^{r2} frac{d}{r2}]

[= GMm (frac{1}{r1} – frac{1}{r2})]

Since  [Delta U = U_{2} – U_{1}], we can find the expression for U, i.e.

[ U = – frac{GMm}{R}]

Kinetic Energy of Satellite

Let’s consider the earth as a reference for a planet. From the top of the earth, we can see the satellite revolving around it. We would consider everything as a function to compute the kinetic energy of a satellite.

Starting with the radius of the earth as ‘r.’

So, r = The distance from the centre from the earth to any point on its surface.

Similarly, r = The distance between the centre of the planet to any point in its orbit.

Here, we are considering the top view of the earth and the front view of the satellite.

The mass of satellite  = m

The mass of the earth  = M

Radius = r

Velocity = v

The two forces are acting on it are gravitational force,   [F_{g}] and a centripetal force due to its velocity, [F_{c}]

Where  [F_{g} = frac{mM}{r^{2}}] and [F_{c} = mv^{2}r].

The magnitude of the forces is equal.

So, [F_{g} = F_{c}]

[frac{mM}{r^{2}} = mv^{2}r]

[ Rightarrow  V^{2} = frac{GM}{r}…(1)]

We know that [ K.E.= frac{1}{2} mv^{2}]

Putting the value of [V^{2}] in eq(1), we get,

K.E. of a satellite = [ frac{GMm}{2r}]

Total Energy of Satellite

The total energy of the satellite is calculated as the sum of the kinetic energy and the potential energy, given by,

T.E. = K.E. + P.E.

[ = frac{GMm}{2r} = -frac{GMm}{2r}]

[ T.E. = -frac{GMm}{2r}]

Here, the total energy is negative, which means this is also going to be negative for an elliptical orbit.

Here, T.E. < 0 or negative, this means the satellite is bound to the earth through gravity.

To make this TE zero, we need to give additional energy of GMm/2r to the satellite, i.e:

[ T.E. = – frac{GMm}{2r} + frac{GMm}{2r} = 0]

We know that if the separation between the two bodies is infinite, then the potential of the system is considered zero.

At an infinite distance, the body of a smaller mass has less effect on the gravitational field of the larger body and the smaller body can escape from the larger one.

It means for a satellite to escape; it has to travel an infinite distance away from the earth. So, at an infinite distance, its energy would become zero on getting additional energy of GMm/r. 

Therefore, satellites would escape from the earth.

Hence, the additional energy required by a satellite to escape the earth = kinetic energy of the satellite.

Gravitational Potential Energy of Satellite

The kinetic energy of a satellite is half the gravitational energy, given by,

If the gravitational energy is GMm/r, then kinetic energy is GMm/2r and this kinetic energy is positive. 

When kinetic energy and the potential energy are added up, the total will come out to be the gravitational potential energy, given by,

T.E. = – GMm/2r = 1/2  P.E. or 1/2 (- GMm/r)

This T.E. is negative, which means the satellite can’t leave or can’t just fly away in outer space and never come back to it.

It is bound to the earth just like the earth is bound to the sun. We are in a bound orbit.

So, anytime the total energy is negative, that is a bound orbit.

It is not about the two particles having a mass, it could be charged particles like the proton and the electron. The electron that orbits the proton has negative energy, which means it is bound to the proton. 

If the electrons were not bound, we won’t get atoms.

Similarly, if a satellite would fly away, we won’t have GPS, nearest Starbucks, etc.

The article provides the calculation of the orbital energies of satellites. The derivation of calculation of potential energy and kinetic energy of satellites are given in detail.

Essentially, when an electron and a positive hole (an empty electron particle in valence band) combine and are able to move freely through a non-metallic crystal as a unit, then the combination of these two particles is called an exciton. It shall be noted that the electron and the positive hole carry opposite charges. Thus they cancel each other’s charges, and there is no electrical charge in the exciton. Owing to this property, detecting an exciton can be challenging at times. Now there are different characteristics of excitons, and they are generally classified in two limiting cases – first, the one has a small dielectric constant and the other, which has a large dielectric constant. 

Frenkel Exciton

Yakov Frenkel was the first one who proposed the concept of exciton when he stated about the excitation of atoms in a lattice of a certain excitonic insulator. The Frenkel exciton has a relatively small dielectric constant, and its binding energy is on the order of 0.1 to 1 eV. This takes place because, at times, the Coulomb interaction between the hole and an electron may be forceful and strong. Owing to this extra force, the exciton tends to be small; thus, they carry less dielectric constant. EEX = -e₂/∈crystals are a general source where Frenkel excitons are found. Further, they can also be located in organic molecular crystals like anthracene and tetracene.

Wannier–Mott Exciton

The dielectric constant is generally large in semiconductors; owing to this, the electric field screen reduces the interaction which takes place in Coulomb between the particles. Through this process, a Wannier-Mott exciton is formed. The said exciton has a radius that is way larger than the lattice spacing. Large exciton radii are favoured greatly by small masses of electrons which are typical of semiconductors. Through this, the said lattice potential can be put into the masses of electron and hole, which forms an exciton polariton. The binding energy in these is quite low, and it is generally in the order of 0.01 eV. These excitons are typically found in semiconductor crystals and liquids such as xenon. 

Charge-Transfer Exciton

There can be an intermediate case between Frenkel and Wannier exciton, and this case has been termed as charge transfer exciton (CT). These generally come to existence when the electron and the hole are present in the adjacent molecules. They occur typically in molecular and organic crystals. Unlike the other two, they have a property to show a static electric dipole. CT excitons may also be present in transition metal oxides. Their concept is always in proximity with a transfer of charge, which mainly occurs from one atomic site to another, this transfer of charge aids in spreading the wave-function around lattice sites. 

Exciton in 2D Semiconductors

In two dimensional objects and materials, the whole systematic process is quantum-confined, and the direction of the same is perpendicular to the normal plane of the said object or material. This reduction in the dimensions of the object greatly manipulates the energies and radii of Warrier excitons; generally, the exciton b exciton effect amplifies in such restricted systems. In most excitons in 2d materials semiconductors, the Rytova–Keldysh provides a good approximation which is indicative of the exciton interaction. The said equation is given below. 

V(r) = [frac{pi}{2r_{0}}] [[H_{0}(frac{kr}{r_{0}})] – [Y_{0}(frac{kr}{r_{0}})]]

Self-Trapping of Excitons

In crystals, the phonons and excitons interact; there is lattice vibration. If the coupling between the two is not cohesive in a semiconductor, then excitons generally get dissipated by phonos. On the other hand, if the coupling between the two is strong, owing to great cohesion, then, in such a situation, excitons can be self-trapped. In the case where interlayer exciton is self-trapped, they get surrounded by a dense cover of clouds made up of virtual phonos. This dressing greatly hinders the ability of the excitons to move across the crystal itself. Essentially, there is a local deformation of the lattice which surrounds the exciton. Self-trapping is quite similar to forming strong polarons which strongly couple together.