Category: Physics Notes PPT

Doppler Effect Definition

In 1842, Austrian physicist Christian Doppler discovered that frequency of wavelengths tends to change with the movement of wave source in relation to an observer. If that sounds too complex, in convenient terms you can ask what is the Doppler Effect simple explanation?

Doppler Effect is the increase or decrease in light, sound or other waves when the source and observer move towards or away from each other. This effect gives rise to not just a crucial theory of physics but also helps in mathematical calculation of waves and their frequencies. Before proceeding to Doppler Effect derivation, let us learn more about it through some examples.

Example 1

Suppose a frog sits in the middle of a lake. It is moving its leg in a way to cause ripples or waves on this water’s surface. These waves arise from this frog’s position and move outward toward the edges of this lake in concentric circles. Two observers, ‘A’ and ‘B’ are standing at the left and right sides of this lake, respectively. 

Figure 1.0 The circles in this image represent the waves moving outward from the frog’s position.

At the position above, both observers will find that the waves reach them at similar frequencies, considering that the frog is equidistant from them. However, the frequency of waves, observable to ‘A’ and ‘B’ will start differing as soon as the frog moves toward observer B.

Figure 1.1 The waveform changes for both observers with the movement of the frog (source of the waves).

At this position, wave frequency for observer B is higher than it is for observer A. B experiences higher frequency because the wave source moves toward it. Similarly, ‘A’ observes lower wave frequency as the wave source moves away from it. This is what the Doppler Effect defines.

Doppler Effect Derivation Class 11 for Moving Source and Stationary Observer

Figure 2.0 Wave source moving toward an observer.

Wave velocity c = λS/T

• In this equation, λS defines the source’s wavelength.

• c is the wave velocity

• T is the time for the wave to move one wavelength distance.

For the Doppler Effect derivation, we can say that

T = λS/c (eq.1)

Now, consider that the source is moving with velocity ‘vS’ towards the stationary observer. In T time, this source can travel d distance,

Thus, d = vST (eq.2)

Suppose the source moves in direction x, and due to the shortening wavelength, λO is the wavelength reaching the observer.

λO = λS – d (eq.3)

Now, substitute the value of T from eq.1 into eq.2.

d = vSλS/c

Substitute this value of d into eq.3

λO = λS – (vSλS/c)

λO = λS (1 – vS/c)

Keep in mind that the sign of vS changes as the source moves away from the observer. Everything else in this formula remains the same.

Example 2

Consider that observer A is riding a bike and moving away from a stationary ambulance whose siren is switched on. At first, pitch and sound of its siren are different to observer A when he is closer to the sound’s source. As he moves away, sound and pitch changes, thanks to the Doppler Effect.

Notice that in this example, source of wave remains stationary, but an observer moves away from it.

Doppler Effect Derivation for Moving Observer and Stationary Source

Determining observed frequency is easy since it is the combination of observer velocity and wave velocity divided by actual wavelength. 

fO = (c – vO)/λS

fO refers to the frequency observed, and vO is the velocity of the observer.

But, fO = c/λO

Thus, c/λO = (c – vO)/λS

Now, reciprocate both sides, we get

λO/c = λS/(c – vO)

Multiplying by c,

λO = λS/[(c − vO)/c]

Thus, λO = λSc/(c − vO)

If you need further assistance, consult our derivation of Doppler Effect equations pdf, available online. You can also attend our live classes online and get ahead on your preparations. Now you can even download our app for further convenience.

The plane of the Earth’s orbit around the sun is known as the ecliptic. From the observer’s perspective who is on the Earth, the movement of the sun around the celestial sphere with a period of one year can trace the path along the ecliptic that has a background of stars against it. It is important to reference the plane and acts as a basis for the ecliptic coordinate system. 

The ecliptic forms as one of the fundamental planes that are used as a reference for the positions these planes are the celestial sphere and the celestial equator. The ecliptic poles are perpendicular to the ecliptic, where the North ecliptic pole is the pole of the North equator. To one of the two fundamental planes, the ecliptic is closer to the unmoving background stars. The spherical coordinates are known as celestial latitude and longitude or ecliptic latitude and longitude. Longitude is measured along the ecliptic from the vernal equinox positively to the eastwards from  0° to 360°, the same direction in which the Sun appears to move. The Latitude can be measured perpendicularly with the ecliptic, which is about -90⁰ to the southwards or northward -90⁰ to the poles of the ecliptic. Where the ecliptic itself has 0⁰ latitudes. To measure a complete spherical position, a distance parameter is required. 

The ecliptic coordinates are convenient and required for specifying the positions of the objects of the Solar System, as most of the orbits of the planets have small inclinations to the ecliptic. Because of the Earth’s orbit, the ecliptic moves very little and it is relative to the fixed reference with respect to the stars.

Ecliptic Plane

The apparent path followed by the sun throughout the year is known as the ecliptic. Since Earth takes one year to orbit around the sun and the apparent position of the sun takes around one year to make a complete circuit along the ecliptic. If there are more than 365 days in a year, then the sun moves less than 1⁰ eastward every day. Thus the small difference in the position of the sun against the stars on the Earth’s surface causes a particular spot so that the sun can be caught up about four minutes each day if Earth did not orbit. Hence a day on the Earth is longer than 24 hours instead of 23 hours 56 minutes a sidereal day. The actual speed at which the Earth orbits the sun will vary every year such that the sun moves along the ecliptic also varies. 

In the Solar System, most of the major bodies orbit the Sun in nearly the same plane. This is due to the way through which the Solar System is formed from a protoplanetary disk. Probably the current closest representation of the disk in the solar system is called the invariable plane of the Solar System. Earth’s orbit, and thus the ecliptic, is inclined a little more than 10 to the invariable plane, Jupiter’s orbit is within a little more than ​1⁰/2 of it, and all other major planets are present within about 6⁰. Due to this reason, most of the bodies of the Solar system appear very close to the ecliptic in the sky.

The invariable plane of the solar system is defined by the angular momentum of the entire Solar System, that is essentially the vector sum of all of the rotational and orbital angular momenta of all the bodies of the system that have more than 60% of the total angular momentum comes from the orbit of Jupiter. Due to the uncertainty about the exact location of the invariable planes, and since the ecliptic is well defined by the sun’s apparent motion, as the reference plane of the Solar System the ecliptic is used both for precision and convenience. Using the ecliptic instead of the invariable plane has a drawback that is over the geologic time scales, that will move against the fixed reference points that are present in the distant background of the sky.

Obliquity of the Ecliptic

The term used by the astronomers to describe the inclination of the equator of the Earth with respect to the ecliptic of the Earth’s rotation axis that is perpendicular to the ecliptic. This term is also known as the obliquity of the ecliptic. Because of the planetary perturbations, it is about 23.4 degrees and it is decreasing per hundred years for about 0.013 degrees. By the observation of the motions of other planets and the Earth, the angular value of the obliquity can be found over many years. As the understanding of the dynamics increases, the astronomers produce new fundamental ephemerides as the accuracy of observation improves, and from these ephemerides, various astronomical values that include obliquity are derived.

Until 1983, the obliquity for any date was calculated from the work of Newcomb, who analyzed positions of the planets until about 1895:

ε = 23⁰ 27¹ 08¹¹ .26 -46¹¹ .845T – 0¹¹ .0059T² + 0¹¹ .00181T³

Where ε is the obliquity and T is tropical centuries.

From the year 1984, the fundamental ephemeris of the Astronomical Almanac was found in the Jet Propulsion Laboratory’s DE series of computer-generated ephemerides. This obliquity was based on DE200, which analyzed some of the observations from 1911 to 1979, it was calculated as:

ε = 23⁰ 26¹ 21¹¹ .45 – 46¹¹ .815T – 0¹¹ .0006T² + 0¹¹ .00181T³

These expressions for the obliquity are planned for over a relatively short time span for the high precision, and perhaps for several centuries. All of these expressions are used for the mean obliquity, which means that the obliquity was found without the nutation of the equator. Whereas the true or instantaneous obliquity has been included with the nutation. Nutation can be defined as a rocking, nodding, or swaying motion of the largely axially symmetric object in the axis of rotation. 

Eclipses always occur on or near it, because the orbit of the Moon is inclined only about 5.145⁰ to the ecliptic and the Sun is always very near the ecliptic. Due to the inclination of the orbit of the Moon, eclipses do not occur at every conjunction and opposition of the Sun and Moon, but it occurs only when the Moon is near an ascending or descending node at the same time it is a conjunction or new moon or opposition or new moon. The ecliptic is named so because the ancients noted that eclipses only occur when the Moon is crossing it.

Conclusion:

The ecliptic plane is the reference plane or the imaginary plane that contains the orbit of the Earth where it rotates around the
sun. The ecliptic forms the centre of the zodiac, a celestial belt that is about 20⁰ wide in latitude through which the Moon, Sun, and planets always appear to move. Traditionally, this region is divided into 12 signs of 20⁰ longitudes, each of which approximates the Sun’s motion in one month. In ancient times, the signs correspond roughly to 12 of the constellations that straddle the ecliptic. Sometimes these signs are still used in modern terminology. The “First Point of Aries” was named when the March equinox sun was actually in the constellation Aries, it has since moved into Pisces because of the precession of the equinoxes. 

What are Elastomers?

Every day we are dependent upon products and use them as have developed through experimentation and discovery.  Having knowledge that evolves regarding the chemical properties, we understand the benefits of developing new products, including products that are made of elastomers.

Countless things like the tires allow the smooth movement of the car over the road. Also, the rubber storage containers in our kitchen and many things with flexible molecular structures are all elastomers. What makes these objects flex and return to original shape? Why are some products rigid compared to others? What holds these structures together? Let us learn more about elastomers.

Elastomers Definition

In chemistry, material made of a long chain of molecules is known as polymer and elastomer. It is known as the polymer having both viscous and elastic properties. A substance which is thick, sticky, and consistent somewhere between the solid and gas stage are known as viscous. How fast or slow a liquid flow is determined by the viscosity of the liquid. When you pour oil from a container, you will see that it pours much slower compared to water, since it is more viscous.

Properties of Elastomers

In chemistry, the bonds that hold several compounds together are very strong compared to size. The flexibility of the object is determined by the bond force and the compound’s ability to manipulate into different shapes.

• Comparatively, elastomers intermolecular forces are weak. The forces of repulsion and attraction between molecules and other particles are known as intermolecular forces.

• As elastomers are not tightly bonded together by attraction to their nucleus, they can stretch apart and have higher failure strain than many other compounds.

• The material that will fail at a molecular level when stain is imparted on them, they are known as non-elastic compounds.

• The elements used to make elastomers are carbon, silicon, hydrogen, and oxygen, which hold together well in different conditions.

Categories of Elastomers

As a consensus, there are two categories of elastomers:

When heated, thermoset elastomers do not melt. When exposed to different types of environmental conditions, they retain their structure. This property of elastomers makes them very useful in different industries where heat and pressure are applied at various levels since they will not break down.

Whereas, thermoplastic elastomers can be melted and reformed into different shapes and configured as per requirement and their use. E.g., you can think of a stick of butter when picturing thermoplastic elastomers. The stick can be cooled and melted many times and molded into different shapes while retaining its original properties.

Elastomers Examples

In manufacturing processes like injection molding, thermoplastic elastomers are used. Thermoplastic polyurethanes are used in many applications, including production of foam seating, seals, gaskets, etc.

All types of saturated and unsaturated rubbers and polysulfide rubbers

•  Natural Rubber – This is used in the manufacture of gaskets, shoe heels…

• Polyurethanes – This material is used in the textile industry for manufacturing elastic clothing such as lycra is also used as foam, wheels, etc.

• Polybutadiene – This type of elastomer material is used on wheels or tires of vehicles, giving them extraordinary resistance to wear and tear.

• Neoprene – This material is primarily used in manufacturing of wetsuits and is also used as wire insulation, industrial belts, etc.

• Silicone – This material is used in a variety of materials and areas since they have excellent chemical and thermal resistance. Silicon is used in manufacture of medical prostheses, pacifiers, lubricants, mold, etc.

Types of Elastomers

Following are the two types of elastomers:

1. Saturated elastomers

2. Unsaturated elastomers

Unsaturated Elastomers:

By using sulfur vulcanization unsaturated elastomers can be cured, and non-sulfur vulcanization is desired, for examples:

• Synthetic polyisoprene

• Butadiene rubber

• Neoprene rubber

• Nitrile rubber

• Butyl rubber

Saturated Elastomers:

This type of elastomers cannot be cured by sulphur vulcanization process, for examples:

• Ethylene propylene rubber (EPR)

• Ethylene-vinyl acetate (EVA)

• Polyacrylic rubber

• Silicone rubber

• Fluoroelastomers

• Polyether block amides.

• Chlorosulfonated polyethylene rubber

Do you know?

Elastomers are used to manufacture duckbills and diaphragms of plastic diaphragm check valves; also, O-rings and gasket seals. This is because of its unique physical and chemical properties. Most designing processes can benefit from a better understanding of elastomeric materials. 

Electric polarization is a part of the study of classical electromagnetism. If one has to define electric polarisation, it can be said that electric polarization (or polarization density or just polarization) is a vector field that defines the density of permanent or induced electric dipole moments in a dielectric material. Polarization is said to be completed when the dielectric is placed in an external electric field and gains an electric dipole moment.

Thus dielectric and polarization definition can be stated as ‘the electric dipole moment induced per unit volume of the dielectric material.’ It also explains the response of material on the applied electric field and how the material changes the electric field. It can be thus used to calculate the forces that come out due to these interactions. 

It is also compared with magnetization which measures the relative response of a material to a magnetic field in magnetism. The unit for measurement is coulombs per square meter and polarization is represented by a vector P. 

Dielectric Polarization Significance

The displacement of bound charged elements of dielectric material occurs due to the external electric field application. These elements cannot freely move around the material because they are bound to the molecules. Elements with a negative charge are displaced opposite and those with a positive charge move towards the field. An electric dipole moment is formed though the molecules are neutral in charge. 

Let’s say that a volume element ∆V in the material with a dipole moment ∆p, the polarization density P can be described as

P =  [frac {Delta p}{Delta V}]

Usually, the dipole moment ∆p varies from point to point within the dielectric therefore the polarization density P inside an infinitesimal volume dV with an infinitesimal dipole moment do is

P = [frac {dp}{dV}]

Qb is indicated for the bound charge of the result of polarization. ‘Dipole moment per unit charge’ is the definition that is now widely accepted. 

How to Explain Dielectric Polarization?

In an insulator or dielectric, the slight change in position of negative and positive charge takes place in opposite directions that are caused by an external electric field. The electrical polarization occurs when, because of the electric field, the negative electrons are pushed towards the positive atom nuclei surrounding it. This distortion of charges results in one side of the atom becoming a little negative and the opposite side becoming a little positive. 

However, in some chemically bound molecules like water molecules, polarization partially takes place due to the rotation of molecules into the same line under the influence of the electric field. 

Electric Polarization in Dielectrics 

Now we will define electric polarization and the effects of the application of electric fields in molecules. There are polar and nonpolar molecules. Let’s consider that Pi Pi is the induced electric polarization and u_i is the induced dipole moment. Now, the induced dipole moment is directly proportional to the strength of the electric field applied (E) . Hence, ui α E. Hyperpolarization occurs within the molecules if the electric force is very low, so we have to say that u_i = α_i F. Here, αi is the proportionality constant. Thus, this is the induced polarizability constant of the polarizing molecules,

Thus, the induced polarization of dielectric material in chemistry means the amount of induced moment in the polarized molecule when the unit electric field of the current strength is applied. 

Unit and Dimension of Polarizability 

The electric polarization constant has the dimension of volume and is derived from the definition and polarizing formula. Unit of dipole moment obtained from Coulomb’s law can be stated as esu X cm and force unit as esu cm^-2.

As the atom size, ionization energy, and atomic number increase, the polarizability of the atom increases. 

Dielectric and Polarization 

Dipolar polarization can be achieved by inducing an electric field in the molecules which can exhibit uneven distortion of the nuclei (distortion polarization). The ‘orientation polarization’ happens because of a permanent dipole (arising from 104.45 deg angle), for eg, oxygen and hydrogen atom in water.  

Effect of Temperature on Polarization –

The orientation polarization is zero because of the fixed polarized chemical bond and inability to orient in a fixed direction. Strong intermolecular forces oppose the free rotation of the polarized molecules like in a condensed system. This is the reason why molecules in carbon dioxide, ethane, propane, methane, nitrogen, hydrogen do not vary with temperature. 

However, molecules in many substances like benzyl alcohol, methyl chloride, hydrochloric acid, nitrobenzene, etc, are temperature-dependent and vary with varying temperatures. 

Clausius Mossotti Equation –

A relation between the polarizability of substances and the dielectric constant of the non-polar medium between the two plates is derived from electromagnetic theory. The distortion of 1 mole of the polarizing substance by a unit electric field gives rise to induced polarizability constant. Hence, the electric polarization constant formula – 

Dielectric constant (D) =  [frac {C}{C_0}]

where 

C = capacitance of the condenser having the polarized substance and 

C₀ = vaccum.

 

Therefore the dielectric is a dimensionless quantity shown with the unit of vacuum.   

Dielectric loss 

When a dielectric material is put through an AC voltage, the insulating material absorbs and dissipates electrical energy in the form of heat. This dissipation of this energy is known as dielectric loss.

A capacitor, which makes proper uses of another electrolyte to achieve more capacitance than the other form of capacitor, is known as an electrolytic capacitor. It is a liquid substance with a highly influential mixture of anion subatomic particles. Usually, three various types of capacitors are termed as an electrolytic capacitor. They are as follows 

• Aluminium electrolytic capacitor

• Tantalum electrolytic capacitor

• Niobium electrolytic capacitor

A particular type of electrolytic capacitor with the capacity to store hundreds and thousands of farads more electric charge is called supercapacitors. They are often familiar as a double-layer electrolytic capacitor.

Electrolytic Capacitor Uses

• All the capacitors under the electrolytic capacitor are neutralized. That is, the voltage of anode is always higher than that of the cathode. Due to the capability of massive electric charge storage, they are mostly employed to deliver low-pass signals. In electrical supply, they are profoundly implemented for noise filtering or decoupling. 

• Sometimes they are used in input and output smoothing. They are employed as a low-frequency filter if the signal is a DC one with a feeble AC constituent.

• Electrolytic capacitors are mostly found working as filters in loud-speakers. It aims to decrease the amplifier’s vibration. The vibration of the prime one is a 50Hz 60 Hz electrical sound persuaded from the mains supply. It could be heard if expanded.

Features of Electrolytic Capacitor

Let’s discuss some features of the electrolytic capacitor:

Accumulation of Capacitance

The electrical features of it depend mostly on the involved electrolyte and the anode. The ability to store an electric charge of the electrolytic capacitors, have huge forbearances 20% and accumulates at the minimum rate as the time goes on. An aluminium capacitor is implemented for this. Whose very little capacitance is 47µF can be anticipated to have a value of something between 37.6µF to 56.4µF.

Tantalum capacitors are also able to tolerate high, but their maximum working voltage is at the bottom. So they can’t work as a substitute for aluminium capacitors.

Electric Charge Storage Capacity, Worth, and Forbearances

The electrolyte and anode are mostly defined as the electrical features of a device. The results and the capacity to store electric charges are dependent on temperature and frequency. The capacitor with non-solid electrolytes contents shows a tremendous capacity over temperature and frequency than the solid electrolytes content capacitor. The basic measuring unit of the electric storage ability of an electrolyte capacitor is microfarad. The value of capacitance, which is mentioned by the producers in the datasheets, is known as nominal capacitance or rated capacitance. If the value of a device’s electrical storage capacity is measured at 1kHz frequency, it will be a 10 per cent deduction of 100/110Hz. The temperature there will be 200 c.

The capacity tolerance can be defined as the percentage of the permitted digression of the measured capacitance from the rated value. Some capacitors are very easy to use following the series of their endurance. Their values are stated hereunder:

• From the E3 series, the capacitance and tolerance capacity measured is ±20%, letter code “M.”

• In the series E6, measured capacitance and tolerance is ±20%, letter code “M.”

• For the E12 series, the valued capacitance and tolerance is±10%, letter code “K.” 

Advantages and Disadvantages of Electrolytic Capacitors

• Most of the storage capacity levels that the electronic capacitors have been obtained from a layer of gas on one plate. It is possible only with the involvement of absolute polarity. The formula will be like: capacitance (C) is the magnitude of charge (Q) on every plate divided by the voltage (V) involved with the plates: C=Q/V. The presence of this gaseous layer and generous dielectric effect provides an electrolytic capacitor, comparatively more capacitance in volume, than the other forms of capacitors.

• There are disadvantages, too, regarding the use of electrolytic capacitors. The possibility of leakage currents is very high in these capacitors. Value tolerances, equivalent series resistance capacity, and short life-span are some other drawbacks of these electrolytic capacitors.

Applications of Electrolytic Capacitors

• It is used to prevent voltage fluctuations in different filtering devices.

• When DC signal is weaker than AC, it is used as an input-output smoothing filter

• These types of capacitors are primarily employed for filtering noise or decoupling in electric supply.

• To control the coupling of signals between amplifier stages and to store power in flash lamps is another function of these capacitors.

The electron volt is not a frequently used unit, but it plays a vital role in electricity and magnetism, nuclear physics, etc. Now the question that arises is what is an electron volt? Basically, the electron volt is a unit of energy and is abbreviated as eV. 

In physics, an electronvolt is the amount of kinetic energy required by a single electron accelerating from rest through an electric potential difference of one volt. It is abbreviated as eV. 

An electron volt is a small unit of energy. When we want to move the charge having a value of 1 electron from lower potential to higher potential, then the charge will accelerate with some kinetic energy of 1eV. The electron volt (eV) is defined as: an electron volt is the amount of energy required to move a charge equal to 1e⁻ across a potential difference of 1eV.

Value of 1eV

We know that in order to move an electron with a potential difference of 1V, then the amount of work done is,

[Rightarrow W = qDelta V = 1e^{-} C (1V)frac{J}{C}]

[Rightarrow W 1eV = 1.6 * 10^{-19} J ]

Relation Between 1eV and Joules

Both electron volt and the joules can be related by unit conversions. One should always keep in mind that unit conversion can be done if and only if both measuring units are of the same scale. Here, both electron volt and joules are the units of energy and hence they are interchangeable.

So, the electron volt and joules have a relation given by:

[Rightarrow 1eV = 1.6 * 10^{-19} J ]

Therefore the value of one electron volt is equal to [1.6 * 10^{-19} J ].

The eV-Joule Conversion is very helpful in solving physics problems. The eV to Joule conversion table is given below:

eV to Joule Conversion

The Joule-eV Conversion is very helpful in solving problems related to electric charge in physics. The table for Joule to eV conversion is given below:

Joule to eV Conversion

Solved Examples:

1: A Particle Carrying Charge of 4e Falls through a Potential Difference of 4V. Calculate the Energy Acquired by the Particle.

Sol: We know that whenever an object falls from a higher level to a lower level the potential energy stored will release in the form of kinetic energy. Thus the energy acquired by the particle will be kinetic energy.

Given,

Charge of the particle = q = 4e 

The potential difference between two levels = ΔV = 4V 

We need to calculate the kinetic energy, then:

[Rightarrow K.E = qDelta V]

[Rightarrow  K.E = (4e)(4)]

[Rightarrow  K.E = 16 e]

[Rightarrow  K.E = 16 * 1.6  * 10^{-13} eV]

[Rightarrow  K.E = 25.6 eV]

Therefore, the energy acquired by a charge of 4e when it falls through a potential difference of 4V is 25.6eV.

2: Define Electron Volt and Prove that 1eV = [10^{-19} J].

Sol:  Electron Volt definition: An electron volt is the amount of energy required to move a charge equal to 1e⁻ across a potential difference of 1eV. This is how we define one e
lectron volt.

Now, to prove that the value of 1eV is [10^{-19} J] we will use the unit conversions for a better understanding.

Now, we know that in order to move an electron with a potential difference of 1V, then the amount of work done is,

[Rightarrow W = qDelta V = 1e^{-} C(1V) frac{J}{C}]

[Rightarrow W = 1eV = 1.6 * 10^{-19} Joules ]

Therefore, 1 electron volt is equal to 1.6 x 10⁻¹⁹ Joules.

3: What is the Value of One Mega Electron Volt?

Sol: 1 mega unit = [10^{6} eV]

Then, 1 mega electron volt is given by,

[Rightarrow 1MeV = 10^{6} * 1.6 * 10^{-19}]

[Rightarrow 1MeV = 1.6 * 10^{-13} eV]

Therefore, the value of one mega electron volt is  [10^{-13} eV].

The article covers all the important concepts of electron volt such as its conversion from one unit to another. Solved examples are also given in the above article that will help students to understand the unit of electron-volt.