Introduction to Electromagnetics


Table of Contents


  1. Introduction
  2. Nature and Definition of Electromagnetics
  3. Fundamental Vector Fields in Electromagnetics
  4. Static vs Time-Varying Fields
  5. Universal Constants in Electromagnetic Theory
  6. Maxwell's Equations : The core of Electromagnetics
  7. Conclusion

Introduction

James Clerk Maxwell gave mathematical shape to electromagnetic fields in a systematic manner. Electromagnetics talks about the interaction of electricity and magnetism and is the basic to everything electric and magnetic.

Understanding electromagnetic means understanding the scalar and vector field associated with it. Before understanding the concept of electromagnetic one should have some understanding of scalar and vector fields in different coordinate systems. The concept of line integral, surface integral and volume integral are important along with the concept of gradient, divergence and curl.

Nature and Definition of Electromagnetics

Electromagnetic talks about the interaction of electricity and magneticism and is the basic to everything electric and magnetic. Electromagnetic is the study of the effect of electrical charges at rest and in motion.

There are two kinds of charges: positive and negative. Both positive and negative charges are sources of an electric field. Moving charges reduce a current, which gives rise to a magnetic field.

A field is a spatial distribution of a quantity, which may or may not be a function of time. A time varying electric field is accompanied by a magnetic field and vice versa. Time wearing electric and magnetic fields are coupled, producing electromagnetic fields. Under certain conditions, time varying electromagnetic fields produce waves that radiate from the source.

 

Fundamental Vector Fields in Electromagnetics

There are four fundamental vector field quantities in electromagnetics. These are electric field intensity E , electric flux density D, magnetic flux density B, and magnetic field intensity H.

Out of these factors, electric flux density D and magnetic field intensity H are useful in the study of electric fields E and magnetic fields H in material media respectively.

Static vs Time-Varying Fields

In static cases that is, no time variation:

  • The electric field quantities:

    • Electric field intensity

    • Electric flux density

  • The magnetic field quantities:

    • Magnetic flux density

    • Magnetic field intensity

...form two separate vector pairs.

In time-dependent cases however, electric and magnetic field quantities are coupled — that is, time varying electric field intensity and electric flux density will give rise to magnetic flux density and magnetic field intensity and vice versa.

All four quantities are point functions — they are defined at every point in space and in general are functions of space coordinates.

Universal Constants in Electromagnetic Theory

In the study of electromagnetic fields we make use of three universal constants related to free space. They are:

  • Velocity of electromagnetic waves (including light in space)

  • Permittivity of free space

  • Permeability of free space

Maxwell's Equations: The Core of Electromagnetics

Maxwell provided a mathematical theory that showed a close relationship between all electrical and magnetic  phenomena. Additionally, theory predicted that electric and magnetic fields can move through space as waves. the theory developed by maxwells is based upon the following for pieces of information;

 1. electric fields originate on positive charges and terminate on negative charges. The electric field due to a point charge can be determined at a location by applying Coulomb's force law to a positive test charge placed at that location.

2. magnetic field lines always form close That is they do not begin or and anywhere.

3. A Varying magnetic field  induces an EMF and hence an electric field that is  Faraday's law.

4. magnetic fields are generated by moving charges or currents as is  mentioned in ampere's law 

Maxwell used these four statements within a corresponding mathematical framework to prove that electric and magnetic fields play a symmetrical role in nature.


The main aim of electromagnetics is to understand the concept of four Maxwell equations and their applications. The four Maxwell's equations are expressed as:


Equation

Differential Form

Integral Form

Physical Significance

Gauss’s Law for Electricity

∇⋅D=ρv​

∮sD ⋅d A =Q enclosed ​


Electric flux out of a closed surface equals the charge enclosed. Describes source of electric fields.

Gauss’s Law for Magnetism

∇⋅B=0

∮sB⋅dA=0

Magnetic monopoles do not exist. Net magnetic flux through a closed surface is zero.

Faraday’s Law of Electromagnetic Induction

∇×E=−∂B/∂t


∮c​E⋅dl=

−d/dt ∫s​B⋅dA







A changing magnetic field induces an electric field (basis of transformers, generators).

Ampère’s Law (with Maxwell’s Addition)

∇×H=J+∂D/∂t

∮cH.dl=Ienclosed​+d/dt

∫s​D⋅dA



​

Magnetic fields are produced by electric currents and changing electric fields. Basis for propagation of EM waves.


Where del is a vector differential operator, E, D, B and H have been defined above, ρv is volume charge density and J is the current density.

Final Note

Electromagnetics deals with space concepts and requires thinking in the three dimensions of the real world.

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