Category: Physics Notes PPT

This term Unified Field Theory was first instituted in all honesty by Albert Einstein almost a century prior, yet, it has far to go. 

We should better consider it speculation as opposed to a hypothesis. However, on the off chance that it made conceivably then Physics will open a higher element of potential outcomes which we actually couldn’t think of as conceivable.

Prior to going in additional details, we might want to reveal to you that you may be confounded on the grounds that there are two additional speculations in particular “Hypothesis of Everything” and “Grand Unified Theory”.

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Point to Note:

There are debates that some call these three speculations or theories the same and some say they are unique. We think they are pretty much something similar yet will clarify in insight concerning Theory of Everything (TOE) and Grand Unified Theory (GUT) separately as they are more noticeable in the logical world. 

The TOE and the GUT are very close to the field hypotheses yet fluctuate by not permitting the basis of reality to be fields, and furthermore by endeavouring to describe natural physical constants.

However, prior endeavours dependent on classical Physics are portrayed on this page are traditionally brought together field speculations. The objective of a bound-together field hypothesis has prompted a lot of progress for future hypothetical science and progress proceeds.

The Idea of Unified Field Theory

A Scottish physicist named James Clerk Maxwell detailed the first field hypothesis in quite a while electromagnetism hypothesis. 

In the twentieth century, Albert Einstein subsequent to presenting general relativity, and the field hypothesis of attraction endeavoured the Unified Field Theory and begat the term. Einstein, just as others, attempted to build up a Unified Field hypothesis of fields in which electromagnetism and gravity would show up as independent parts of a separate fundamental region. 

They all bombed attempting, and gravity stays past endeavours towards bringing together field hypothesis right up till the present time.

Forces in Unified Field Theory

Previously, apparently extraordinary connection fields (or “forces,” in less exact terms) have been unified together. James Clerk Maxwell effectively unified together electricity and magnetism into electromagnetism during the 1800s. The field of quantum electrodynamics, during the 1940s, effectively made an interpretation of Maxwell’s electromagnetism into the terms and science of quantum mechanics. 

During the 1960s and 1970s, physicists effectively unified the solid nuclear attractions and weak nuclear attractions along with quantum electrodynamics to frame the Standard Model of quantum physics.

What is Unified Field Theory?

In Physics, forces can be depicted by fields that intercede connections between independent objects. 

In particle Physics, Unified Field Theory (Universal Field Theory) is an endeavour to portray every fundamental force and the connections between elementary particles regarding a single hypothetical structure.

Or,

In Physics, UFT (unified field theory for dummies) is a sort of field hypothesis that permits writing as far as a couple of physical and virtual fields all that is by and large considered as major forces (gravitational, electromagnetic, solid atomic, and feeble atomic powers) and rudimentary particles. The powers are not sent straightforwardly between collaborating objects, as per ongoing advancements in material science, yet rather are addressed and disturbed by halfway substances called fields.

Einstein Unified Field Theory

Albert Einstein coined the expression “Unified Field Theory,” which depicts any effort to bind together the crucial forces of material science between rudimentary particles into a single hypothetical structure. Einstein spent the last piece of his life looking for a particularly Unified field hypothesis, however, was unsuccessful.

Unified Field Theory for Dummies

The current issue with a completely unified field hypothesis is in figuring out how to join gravity (which is clarified under Einstein’s theory of general relativity) with the Standard Model that depicts the quantum mechanical nature of the other three principal associations. The curve of spacetime that is essential to general relativity prompts troubles in the quantum material science portrayals of the Standard Model.

Some particular hypotheses (universal field theory) that endeavour to bind together quantum physical science with general relativity include: 

Unified Field Theory Equation

For understanding the unified field theory equation, let us consider an equation showing the changing magnetic flux/attractive transition and the electric field:

⛛ x E = – [frac{partial B}{partial t}]

The above equation can be rewritten in the integral form as;                  

                      ∮_C E. dl  =  – [frac{partial phi (R)}{partial t}] 

Where,

[frac{partial phi (R)}{partial t}] = Rate of change of magnetic flux.

The magnetic flux is the number of magnetic field lines crossing the area. The equation for this statement is:

                       ∫_S ф_B = B. dA                   

The equation for Einstein Unified Field theory:

Einstein offered a new unified field theory to unify the laws of cosmos, which is given as;                  

g_ik;S =  0,       

 +-

Γ_i  =  0,

R_ik  =  0,

  ¯   

R_{ik, l}  +  R_{kl, i} +  R_{li, k}      =  0

   ˇ   ˇ         ˇ

The formulas used in the above equation for Einstein’s Unified Field equation (fundamental laws of Physics) are known as Tensors. They are highly condensed mathematical shorthand that represents relationships between the forces of gravitation, and electromagnetism in their relationship to time, space, and physical forces.

Generally, heat is anything that provides warmth but scientifically, heat is the flow of energy from a warmer object to a cooler object in comparison till both the objects attain equilibrium. Every matter on earth has some amount of heat energy stored in it. Heat energy flows due to the difference in temperature of the two bodies. In this article, students will learn about the units and conversions of heat energy but first let’s look at a few terms, definitions and concepts.

Heat: Scientifically, heat is defined as the energy that is spontaneously transferred from one object to another due to differences in temperatures. Heat transfer occurs until the bodies attain equilibrium.

Temperature: Temperature is defined as the kinetic energy of molecules of a body.

Internal Energy: The total energy of all the molecules of a body is the internal energy within the object.

Specific Heat: Specific heat, also known as heat capacity, is the amount of energy required to produce a unit change in its temperature.

Difference between Temperature, Heat, and Internal Energy

• Temperature is the kinetic energy of the molecules of a body. The average kinetic energy of individual molecules is termed temperature.

• The total energy of all the molecules is the internal energy within the object. Internal energy is an extensive property.

• Heat is defined as the energy that is spontaneously transferred from one body to another due to its temperature difference.

For example, if a 5 kg of steel, at 100°C, is placed in contact with a 500 kg of steel at 20°C, heat flows from the cube at 300°C to the cube at 20°C, even though, the internal energy of the 20°C cubes is much greater because there is so much more of it. Mathematically heat can be expressed as:

[C=frac{Q}{mtimes Delta T}]

Where m = mass of the body,

C = specific heat,

Δ T = temperature difference.

Q = heat

 

SI Unit of Heat:

As all the energy is represented in Joules (J), therefore, heat is also represented in Joules. Hence, the SI unit of heat is Joules. Joules can be defined as the amount of energy required to raise the temperature of a given mass by one degree. To increase the temperature of one unit weight of water by one degree, we require 4.184 joules of heat.

 

Other Heat Units:

Other heat units are:

BTU:

BTU is a British thermal unit. It is the amount of energy required to raise the temperature of one pound of water by 10 F at sea level.

 

Conversion:

1 BTU = 1055.06 J = 2.931 x 10-4 kWh = 0.252 kcal = 778.16 ft lbf = 1.055 x 1010 ergs = 252 cal = 0.293 watt-hours

 

Calorie:

The amount of energy required to raise the temperature of one gram of water by 10 C.

 

Conversion: 

1 kcal = 4186.8 J = 426.9 kp m = 1.163 x 10-3 kWh = 3.088 ft lbf = 3.9683 BTU = 1000 cal

 

Joule:

Joule is the SI unit of heat. 

 

Conversion:

1 J = 0.1020 kpm = 2.778 x 10-7 kcal = 0.7376 ft lb = 1 kg m2 / s2 = 1 watt second = 1 Nm = 9.478 x 10-4 BTU

Conversion Table:

 

Temperature Conversion :

Celsius to Kelvin

K = C+273 

For Example:

1000C = 100+273 = 373 K

Kelvin to Celsius

C = K – 273

For Example:

273 K = 273 – 273 = 00C

Celsius To Fahrenheit

0F = 9/5 (0C ) + 32

Kelvin to Fahrenheit

0F = 9/5 (K-273) +32

Fahrenheit to Celsius

0C = 5/9 (0F-32)

Fahrenheit to Kelvin

K = 5/9 (0F-32) + 273

Example 1:  An electric kettle contains 1.5 kg of water. The specific heat capacity of water is 4180 J kg-1 K-1. Calculate the amount of energy required to raise the temperature of the water from 15 0C to 100 0C.

Solution: 

Given:

Specific heat (C) = 4180 J kg-1 K-1

T₁ = 15 0C = 15+273 = 288 K

T₂ = 100 0C = 100+273 = 373 K

m = 1.5 kg

Q = m x Δ T x C

Q = 1.5 x 4180 x (373-288)

    = 533 kJ 

Example 2:  Calculate the energy needed to raise the temperature of the water from 20 0C to 90 0C. 

Solution: Q = mcΔθ

= (0.7) (4200) (90-20) = 205.8 kJ

Methods of Transfer of Heat Energy

Convection:  Transfer of heat energy via fluids. When fluids get heated, they form vapours and rise higher up in the environment.

Conduction: Transfer of heat energy through direct contact between two bodies. Such a method of transfer of heat is generally observed in solids.

Radiation: Radiation from hot objects (such as the sun) warms up the air in all directions which are absorbed by molecules all around.

Try Yourself:

1. Calculate heat required to evaporate 1kg of water at the atmospheric pressure (p = 1.0133 bar) also at the temperature of 100°C.

2. Calculate heat required to evaporate 1 kg of feed water at the pressure of 6 MPa (p = 60 bar) and the temperature of 275.6°C.

3. Calculate the specific heat of a 100 kg mass of water if the temperature changes from 150 C to 1000 C. Heat required is 130 BTU.

4. Calculate the heat required to raise the temperature of 60-milligram mass from 22 K to 273 K. Specific heat given 223 J/K.

5. Calculate the specific heat of a 20 dkg mass of water if the temperature changes from 150 C to 260 C. Heat required is 137 BTU.

6. Calculate the heat required to raise the temperature of 200 kg mass from 2320 C to 300 K. Specific heat given 203 J/K.

7. Calculate the specific heat of a 1000 kg mass of water if the temperature changes from 15 K to 100 K. Assume the rest data.

8. Calculate the heat required to raise the temperature of 29 kg mass from 220 C to 273 K. Assume the rest data.

9. Calculate the specific heat of a 20 kg mass of water if the temperature changes from 1500 C to 1000 C. Heat required is 130 cal.

10. Calculate the heat required to raise the temperature of 505 kg mass from 320 C to 273 K. Specific heat given 320 J/K.

11. Explain how heat is transferred in the body?

12.  Name the other methods for transferring heat.

13.  What is the SI unit of heat?

Voltage can be defined as the electric potential between two points. In a conductor, if the electric field is uniform, the potential difference between the points is,

V = EL

By using various equations of resistivity, current, and resistance, another equation can be derived,

V = EL

V = የJL

V = የ [(frac {I} {A})] L

V = I [(frac {varphi L} {A})]

V = IR

From the above equation, we can deduce that the voltage or the potential difference across the resistor can be found by multiplying the current with the resistance. The unit of potential difference is Volt (V) which is also equal to Joule per Coulomb (J/C).

SI Unit of Voltage

The SI unit for voltage is Volt and is represented by the letter v. volt is a derived SI unit of electromotive force or electric potential. Thus, due to this volt can be defined in a number of ways. Volt can be defined as ‘the electric potential present along with a wire when an electric current of one ampere dissipates the power of 1 watt (W).

V = [frac {W} {A}]

Also, volt can be expressed as the potential difference that exists between two points in an electric circuit which imparts energy of 1 joule (J) per coulomb of charge that flows through the circuit. 

V = [frac {potential energy} {charge}]

V = [frac {J} {C}] = kg m²/As³

It can also be expressed as ampere times ohm, joule per coulomb or watt per ampere.

V = AΩ = [frac {W} {A}] (energy per unit charge) = J[frac {J} {C}] (power per unit current)

It can also be expressed as it is given in its SI unit,

1 V = 1 kg m² s^-3 A^-1 (One-kilogram meter squared per second cubed per ampere).

Below are Some Other Electrical Units

Voltage Source

A voltage source is basically a device that is used in electric circuits having fixed potential differences at both ends. The voltage source can be a battery or any other source which has fixed potential difference and direct current.

In case the ends of the voltage source are connected to a circuit that has multiple numbers of resistors, voltmeters, etc then a complete circuit is formed and the current can now flow from one end to the other. And if the current is flowing, then it is the same on both the terminals of the voltage source.

A voltage source is a part of a complete circuit that can produce an electromotive force. Electromotive force is represented using the symbol ε. The unit of electromotive force is the same as voltage, that is it is volt. Here volt is equal to a joule per coulomb (J/C). In the case of an ideal source, the electromotive force is equal to the voltage difference,

ε = V = IR

Real sources such as batteries are not considered ideal sources as they have some source of internal resistance. If r denotes the internal resistance of a battery, then the voltage difference present across the battery is,

V = ε – Ir

This can also be called the terminal voltage of the battery. When a complete circuit is made using a resistor that has resistance R, then the current flowing through can be found using the equation,

V = IR

IR = ε -Ir

IR + Ir = ε

I (R + r) = ε

I = [frac {(R+r)} {epsilon}]

Thus, the current is equal to the electromotive force of the source divided by the total resistance present in the circuit.

SI Unit of Voltage

SI or System International units is an international system of measurement that is used universally in all technical and scientific research. 

SI units make sure that the students do not get confused while reading about units. A standard unit system helps the entire world understand all the measurements in just one set of unit systems.  The SI unit of voltage is volt and is denoted by the letter v.

The importance of electricity can be seen in our daily lives. We find the application of electricity in various spheres of our life, such as;

• Working efficiently at our home.

• Working at our office.

• We use electricity for accessing data from modes like Fibre, LAN at our workplaces.

• Electricity consumption in supplying water at our home, etc.

There are ample uses of electricity, uses of electrical energy, and the applications of electricity in different fields, and this page discusses the uses of electricity for Class 6 in detail.

Uses of Electricity

Electricity has changed our lives and has become vital in almost all aspects of our life today. 

The list of uses will fill many books but here are a few applications of electricity in different fields: 

• Transport Systems – Trains, buses, trams, and cars all use electricity. 

The use of electricity as motive power, meaning that electricity drives the wheels to make the vehicle move. Even gas and diesel-powered vehicles use electricity to start the engines (self in scooters give a spark to the engine), control the engine, and power the ancillary devices. 

• Home Heating and lighting devices, television, radio, computer, telephones all depend on electricity. 

• Wireless lights such as solar-powered lamps convert light to electricity. 

• For communication and providing power for computers, cell phones, fixed phones, etc.

• We find the application of electrical energy as the medium for the transmission of signals. 

• We also find that high-speed optical fibres rely on an electrical signal at each end of the line. Without electricity, communication would reduce to letters, flag-waving, lighting fires, and shouting at each other. 

So, why is electricity important?

None of the electricity-free methods is as flexible and flawless as any that we are used to today. For instance, industry manufacturing relies on electricity to drive virtually every moving part in a factory. 

Materials like saws, cutters, conveyor belts, furnaces, chillers – whatever the process be, electricity are involved in all places. 

• Entertainment: The MP3 player, the portable battery-powered radio, memory stick are all accepted as core parts of our day-to-day lives; all depend on electricity to operate, whether connected to a mains or a power source like a battery, they all use electricity. The list is by no means exhaustive. 

Uses of Electricity in Our Daily Life

We use electricity in all walks of life, some of the uses of electrical energy that are methods to counteract environmental pollution are discussed below:

    

1. Residential Uses- Various household appliances and objects that use electricity range from basic items to advanced ones. These include small household items, like a coffee maker, dishwasher, and microwave to the big electrical appliances, like air conditioning units, refrigerators, electric heaters, washers, dryers, etc. In the nutshell, the whole lighting system of your house relies on electricity. 

2. Transportation System: As per the latest information, the global transportation system depends entirely on the use of electrical energy, be it travelling from one place to another or even communicating around the world is only possible due to electricity. Electricity is massively used by the public through electric vehicles (electric scooters, e-rickshaw). 

Electricity is used to charge vehicles’ batteries. Metros work as an alternative to counteract the railway systems reliant on fuel. 

3. Industrial Uses: In today’s era, the industrial sector is a vast electricity consumer. 

Without the use of electricity, it would have been a dream to run factories, industrial units, manufacturing processes, and other diverse ranges of activities. 

It is observed that sudden power shutdowns cause severe financial losses to companies that rely on these factories and industrial units. Recently, a rapid rise has been seen in industrial electricity consumption, and it is expected to increase further over the coming years. 

Thus, several industries are working to establish their power plants, so they don’t have to outsource electricity. This way, they are in a better position to cut their utility bills substantially; however, the percentage for industrial usage of electricity varies from country to country.

4. Commercial Usage: Many commercial buildings like workplaces, hospitals, education centres, restaurants, shopping malls, government properties, police stations, etc use electricity. 

There are a few sub-sectors under the commercial sector that require a limitless supply of electricity, such as hospitals and medical facilities, etc.

How to Measure Electricity?

Electricity is calculated in terms of power which is expressed in the form of watts. The SI unit of power is expressed in watts which are named after the scientist James Watt who is the inventor of the steam engine.

What is Electric Power?

Electric power is the power produced by converting one form of energy to another. Electric power is actually based on the flow of electric charge, that is, current or the potential of charge to deliver energy, that is, voltage. Any combination of current and voltage values results in power.

Applications of Electricity – At A Glance

Electricity is a very powerful innovation of science. Electricity is widely used in all sectors like entertainment, engineering, healthcare, transport and communication, household, outdoors, office, commercial, space, and fuel. The ways in which electricity is used in these fields are:

• Entertainment activities like watching television, listening to music from an MP3 player, and playing movies on DVDs, VCRs, and VCDs, all require the use of electricity.

• The use of electricity is very essential in the healthcare sector like the use of electricity in an operation theatre and for running medical devices and machines.

• Electricity is even required for the construction of buildings and structur
  es like building houses, welding of materials, and installing windows and gates.

• Travelling long distances is also possible because of electricity.

• Electricity is used to light the roads, heat water in a pool, the lawnmower is used to cut grasses and also uses electricity and water sprinklers also use electricity.

• A vast range of household appliances like toaster, refrigerator, washing machine, microwave, dishwasher, and electrical chimney uses electricity.

• Electricity is used in factories for running heavy machinery.

• Electricities are widely used in offices for running air conditioners, lights, coffee machines, lifts, biometric scanners, and ID card readers.

• Electricity is even used as a fuel for electric cars.

• Electricity is also used for running satellites and probes which are sent from the earth for space expeditions, for example, the Apollo mission for the landing of humans on the moon also used electricity.

Do You Know?

• Total electricity consumption in the US increased three years between 1950 and 2007, with an average annual increase of around 5%. Between the years 2008 and 2018 growth in total U.S. electricity use was nearly flat, with total electricity consumption in 2018 only 2% greater than in 2008.

• As per the latest information, worldwide, a major portion of environmental pollution is caused by the burning of fossil fuels. So vehicles that run on batteries are safer and eco-friendly for our environment. Therefore, the usage of electric vehicles is expected to rise in the coming years.

The Boltzmann constant (kB or k) is the proportionality factor that relates the typical relative dynamic energy of particles in a gas with the thermodynamic temperature of the gas. It happens in the meanings of the kelvin and the gas steady and Planck’s law of dark body radiation and Boltzmann’s entropy recipe. The Boltzmann constant has measurements of energy separated by temperature, equivalent to entropy. It is named after the Austrian researcher Ludwig Boltzmann.

For instance, air particles at a room temperature of 25 degrees Celsius (300 kelvins, or 77 degrees Fahrenheit) are going at a normal speed of around 500 meters each second (1,100 mph). Be that as it may, some are moving at 223 m/s, some at 717 m/s, etc, and they are for the most part moving in various ways. Every individual property can’t be known.

Applications of Boltzmann Constant (k)

The Boltzmann Constant is utilized in assorted orders of material science. Some of them are recorded beneath:

• In traditional factual mechanics, Boltzmann Constant is accustomed to communicating the equipartition of the energy of a molecule. 

Value of Boltzmann Constant

Having estimations of energy per level of temperature, the Boltzmann constant has an assessment of 1.380649 × 10⁻²³ joule per kelvin (K) or 1.380649 × 10⁻¹⁶ erg per kelvin.

The actual meaning of k is that it gives a proportion of the measure of energy (i.e., heat) relating to the irregular warm movements of the particles making up a substance. 

For a traditional framework at balance at temperature T, the normal energy per level of opportunity is kT/2. In the most straightforward illustration of a gas comprising of N noninteracting iotas, every molecule has three translational levels of opportunity (it can move in the x-, y-, or z-bearings), thus the complete nuclear power of the gas is 3NkT/2.

Boltzmann Constant Units

The conduct of the gases made comprehension a bit nearer by Planck and Boltzmann by presenting constants. The estimation of Boltzmann constant is numerically communicated as- 

K = RNA 

Where, 

K is Boltzmann’s constant. 

NA is Avogadro number. 

R is the gas constant.

Boltzmann Constant in eV

The estimation of Boltzmann constant in eV is 8.6173303 × 10⁻⁵ eV/K 

The estimation of the Boltzmann constant can be communicated in different units. The table given beneath involves the estimation of k alongside various units. 

Estimation of k Units 

1.3806452 × 10⁻²³   m².Kg.s⁻².K⁻¹ 

8.6173303 × 10⁻⁵   eV.K⁻¹ 

1.38064852 × 10⁻¹⁶     erg.K⁻¹

Value of Boltzmann Constant K

The estimations of the Boltzmann constant is obtained by separating gas steady R by Avogadro’s number NA. The estimation of k or kB is 

Boltzmann constant k or kB = 1.3806452 × 10⁻²³ J/K. 

The estimation of the Boltzmann constant can be communicated in different units. The table given beneath included the estimation of k alongside various units. 

Estimation of k Units 

1.3806452 × 10⁻²³     m².Kg.s⁻².K⁻¹ 

8.6173303 × 10⁻⁵   eV.K⁻¹ 

1.38064852 × 10⁻¹⁶     erg.K⁻¹ 

2.0836612(12)×10¹⁰     Hz.K⁻¹ 

3.2976230(30)×10⁻²⁴    cal.K⁻¹ 

0.69503476(63)     cm⁻¹.K⁻¹ 

−228.5991678(40)    dB.WK⁻¹.Hz⁻¹ 

4.10                              pN.nm 

0.0083144621(75)     kJ.mol⁻¹K⁻¹ 

1.0                               Atomic unit (u)

Boltzmann Factors and the Thermal Voltage

The likelihood of a framework in balance at a specific temperature to obtain a specific state with explicit energy is given by the comparing Boltzmann factor. At the point when we guess a warm framework at temperature T and attempt to compute the likelihood of possessing a state I with energy E. 

​To characterize the connection between the electrostatic potential and the progression of electric flow in a semiconductor across a P-N intersection. We need to utilize the Shockley diode condition. This condition relies upon a trademark voltage known as the warm voltage. This voltage is signified by the image VT. The reliance of the warm voltage on supreme temperature takes utilization of the Boltzmann constant. 

The estimation of the warm voltage at the standard temperature of 298.15K is roughly 25.69mV. The warm voltage gives the proportion of impacts on the spatial dispersion of particles or electrons because of a breaking point at a fixed voltage.

One of the most common ways to determine whether two vectors can be combined or not is by multiplying them which is also called the product of two vectors. This process of getting a product between two vectors is called a cross-product of vectors. Wondering how the vector product of two vectors can be found out and what are the techniques used in finding it out? Well, now you can refer to the Vector Product of Two Vectors – Calculation, Examples, Properties, and FAQ article provided by for your reference that will help you understand the basics as well as prepare for your exams.

A vector is used to locate a point in space concerning another and is a quantity having magnitude and direction. In a geometrical representation, it can be pictured as an arrow or a line segment with the direction. Here, the length of an arrow indicates the magnitude of this vector. 

When multiplying two vectors, it can be done using two methods. 

1. Dot product or Scalar product

2. Cross product or Vector product 

Here, we will discuss the cross product in detail.

Vector Product of Two Vectors

The cross product or vector product obtained from two vectors in a three-dimensional space is treated as a binary operation and is denoted by x. The resulting product, in this case, is always another vector having the same magnitude and direction. 

Let us consider the two quantities vectors a and b. 

Two vectors a and b are shown in the picture. To answer what a vector product is, look at the calculations below. 

a x b = |a| . |b|. Sin(ф) n 

Where, 

• |a| is the length or magnitude of vector a. 

• |b| is the length or magnitude of vector b. 

• Θ is the angle between both the vectors b and a. 

• n is a unit vector perpendicular to both vectors a and b. 

As shown in the above picture, if the tail of vectors b and a begins from the origin (0,0,0), then the product of two vectors can be represented as 

Cx = ay . bz – az . by

Cy = az . bx – ax . bz

Cz = ax . by – ay . bx

Example 

Let us define a vector product by taking an example. Consider a vector a = (2,3,4) and b = (5,6,7). Here, ax = 2, ay = 3, and az = 4. bx = 5, by = 6, bz = 7. Putting these values in the above equation and calculating, we get Cx = -3, Cy = 6, and Cz = -3. 

The Direction of Product Vector 

While you can define a vector product of two vectors and its magnitude from the above equation, the direction of its product vector can be determined using the rule of right-hand thumb. 

According to this right-hand thumb rule, we need to curl the fingers of your right hand from vector a to vector b, and then the thumb is pointed towards the direction of the product vector. 

Properties of Vector Product

While the scalar or dot product result of two vectors shows the commutative property, and the cross product is non-commutative. 

This means, a x b ≠ b x a. However, from the definition of vector product, an x b = – b x a. This is true because of the change in direction of the product vector. 

Similar to a scalar product, this vector product determined from multiplying two vectors also shows a distributive property. 

Therefore, a x (b + c) = a x b + a x c

As per the characteristics of the vector product, this calculation of the magnitude value of the vector product equals the area of the parallelogram made by the same two vectors. 

You will be able to understand the concepts of vector and cross products intricately by going through our study materials. Now, you can also download our app for easier access to these study materials, along with the option of online interactive classes to clear your doubts.

 

Types of Vectors seen in Physics

There are three types of vectors that are observed in Physics and can be provided as follows:

1. Proper vectors:

These vectors include displacement vector, force vector, and momentum.

2. Axial vectors:

These vectors are the ones that act along an axis and are hence called the axial vectors. Examples of such vectors are angular velocity, angular acceleration, torque.

3. Pseudo or inertial vectors:

These are used to create an inertial frame of reference and are hence called pseudo vectors or inertial vectors.