Thursday, 28 February 2019

Electromagnetic Theory


Electromagnetic theory is a special branch of physics that deal with the basic principles of electromagnetism. The principles are electrostatics, experimental basis, magnetic fields of steady currents, motional and electromagnetic induction. This subject is being taught in an elaborate way in the first year of engineering to provide the basic understanding of electromagnetic mechanisms to the students.

In a nutshell, Electromagnetic Theory is an essential division of Physics which involves the study and research of magnetic forces which is actually physical interactivity that happens between electrically charged particles. This is a graduate level subject that is explained and elaborate with the help of precise mathematical formulas that focuses on physical phenomena and principles.

This branch of Physics consists of a few significant chapters that provide an elaborate idea about what electromagnetic theory is its explanation uses and researchers. The chapters are followed by a simple description here with its basic fundamental idea.

1.Vector analysis

Vector analysis is one of the divisions of mathematics. It constitutes differentiation and integration of vector fields, mainly in three-dimensional Euclidean space.  Vector analysis is utilized significantly in the fields of physics and engineering, specifically in the studies of electromagnetic fields, gravitational fields, and fluid flow.

2.Coulomb’s Law and Electric Field Intensity

In the subject of electromagnetic theories, the Coulomb's law defines the extension and intensity of electric energy within two individual charged vertices which is equivalent to the extent of the charges and is inversely equipment to the space between the vertices.

3.Electric Flux Density

Electric flux density is actually a calculative value of the power of an electric field which is produced by a free electric charge, commensurable to the amount of electric lines of forces passing by a particular region.

4.Gauss’s Law and Divergence

 Gauss's theorem or Ostrogradsky's theorem, it is a result that connects the flow (flux) of a tensor field through a course of surface, to the action of the tensor field within the surface. According to the divergence theory, an outward flux of a tensor field while it passes through an enclosed surface area becomes equal to the fundamental volume of the divergence over the section within the surface.

5.Energy and Potential

Potential energy can be defined as the extent of doing work, which will eventually arise from position or configuration. Potential energy can arise from any accumulations of charges if an electric force or any other type of charge is exerted within the electrical compartment.

6.Conductors and Dielectrics

Conductors are substances which contains free charge carriers, the examples of conducting metals are mercury, gold, copper, aluminum, silver and a few more. The substances that do not have any electric charge carriers are called Dielectrics. The dielectric's molecules/atoms are neutral, and the examples are air, mica, rubber, wood, plastic etc. 

7.Capacitance

Capacitance is explained as the ratio of the modification in an electric charge inside a system to the interrelated change in its electric potential.

8.Steady Magnetic Field

A steady magnetic field is produced by steady currents,  it may be a permanent magnet, a direct current or an electric field which changes accordingly.

9.Magnetic Forces

In the study of Electromagnetic theory, the processes of attraction and abhorrence that emerge within electrically charged particles due to motion is called Magnetic force. The action of an electric motor is an example of the magnetic force. The magnetic force is a repercussion of the electromagnetic force, one of the four fundamental forces of nature.

10.Materials and Inductance

Inductors are a collection of a coil of conducting material, insulated copper wire wrapped on the core of either plastic (to create an air-core inductor) or ferromagnetic (or ferrimagnetic) material; ferromagnet is known as "iron core" inductor.

11.Time-Varying Fields and Maxwell’s Equations

Maxwell's equations envision that static electric fields (a field that does not change with time) are assembled by charges. Charges are origins and sinks of force field lines and Static electric field lines that begin on positive and ends on the negative charges.

12.Uniform Plane Wave

The uniform plane wave is explained as the value of the electric and magnetic fields. They are similar at every point in the direction of propagation.

13.Plane Wave Reflection and Dispersion

Plane-wave reflection is 2-dimensional grids formed by Ω-shaped conducting particles related by their arms, and dispersion characteristics of an infinite set of such grids are studied.

14.Guided Waves

Guided wave testing (GWT) is a fortuitous transformation method. This procedure employs acoustic waves that generate along an elongated build-up while leading by its boundaries. This enables the waves to go through a huge distance with extremely minimal loss in energy.

15.Electromagnetic Radiation and Antennas

Electromagnetic waves are similar kind of radiation as light, ultra-violet, and infrared rays, the only difference here is the wavelength and frequency. These waves are consists of electric and magnetic integrants that are inextricable. Radio signals are also a type of electromagnetic wave because radio signals travel in this way, they have a prime stance on RF antennas and RF antenna design.

16.Transmission Lines

A transmission line, in electromagnetic theory, is a specific cable or other formation made to conduct interchanging current of radio frequency, which frequency is actually accurately high that their wave nature is also noted.

Sunday, 17 February 2019

APPLIED MATHEMATICS – I


As the name suggests, Applied mathematics is the branch of mathematics which deals with the application of mathematics to solve problems which arise in various areas such as, science, engineering or other diverse areas, and/or the development of new or improved methods to meet the challenges of new everyday problems.
Unlike, the traditional branches of mathematics such as, algebra, real analysis etc. which deal with conceptual aspects of mathematics Applied mathematics is concentrated on real-world problems with the dual goal of explaining observed phenomena and predicting new, as yet unobserved, phenomena.
Applied Mathematics will help one understand the concepts of complex numbers, successive differentiation, partial differentiation etc.
Ekeeda offers great online courses for budding mathematicians. Our course structure is comprehensive and following are the chapters of our Applied Mathematics 1 course –
1.      Complex numbers-
One learns the elementary concepts of real numbers and complex numbers. The concept of the one-dimensional number line is extended to the two-dimensional complex plane. One learns about complex numbers as ordered pairs, geometrical representation of complex numbers, curves and regions in complex planes, Extended complex plane, stereographic projections, complex-valued functions etc.
2. The logarithm of complex numbers -
The branch of mathematics which deals with the study of non-zero complex numbers as logarithmic functions. One also learns about
Complex numbers have applications in several scientific sectors like signal processing, control theory, electromagnetism, fluid dynamics, quantum mechanics, cartography, and vibration analysis.
3. Successive differentiation –
This chapter will enable us to differentiate a given function successively n times and the results of such differentiation are called successive derivatives. One also learns “The Leibnitz theorem” and the rules followed while doing successive differentiation. The higher order differential coefficients hold a lot of importance in scientific and engineering applications.
4. Matrices –
This chapter focuses on using matrices for plotting graphs, statistics, seismic surveys and in representing data's like the population of people, infant mortality rate, etc
5. Partial differentiation and its applications –
This unit will help one understand what partial differentiation is, how to do partial differentiation of a function(s), rules followed while doing partial differentiation of a function(s) and the need of partial differentiation. One also learns to form partial differential equations and find their solutions. Partial derivatives are used in vector calculus and differential geometry.
6. Expansion of functions –
Representing a particular function as a sum of powers in one of its variables, or by a sum of powers of another function is called Expansion of that function. This chapter deals with the expansion of functions using various series (Taylor series, Maclaurin series etc.) expansion.
7. Indeterminate forms –
This unit will enable the learner to understand tricky situations when the ratio of two functions tends to zero and an indeterminate form is created. One learns to apply L’Hospital’s rule in finding limits of indeterminate functions.
8. Numerical Solutions of Transcendental Equations –
One learns about transcendental functions (i.e., functions which are not algebraic) and about methods of solving transcendental functions.
9. The system of Linear Equations –
One learns to formulate linear equations, a solution of linear equations(using substitution method etc.) and representation of linear equations on the positive and negative X, Y axes(Euclidean plane) etc.
The industry veterans were the mind behind creating these amazing and detailed chapters on Applied Mathematics-I. For further details or queries, you can reach out to us anytime.
The outcome of the course EKeeda provides a comprehensive online learning resource for mathematics enthusiasts and our online course ensures a perfect learning environment for the individual. All the concepts are backed by good examples that will help you to learn the most complex theory in the simplest way possible. Develop a knack towards online learning and enjoy reading the chapters at the comfort of your home.
So, Stay foolish! Keep growing!
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