CSLS Chapter 01

Associate Professor

Dept. of Electrical and Electronic Engineering

University of Dhaka

Dr. Mohammad Junaebur Rashid (JR)

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ICT2203

:

Microwave Communication

and Radar Engineering

(2.0 Cr)

Course Teacher

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Lecture 02

Introduction

• The principles of electromagnetic plane waves are based on the relationships between electricity and magnetism.

• A changing magnetic field will induce an electric field, and a changing electric field will induce a magnetic field. Also, the induced fields are not confined but ordinarily extend

outward into space.

• The sinusoidal form of the wave causes energy to be interchanged between the magnetic and electric fields in the direction of the wave propagation.

• A plane wave has a plane front, a cylindrical wave has a cylindrical front, and a spherical wave has a spherical front. The front of a wave is sometimes referred to as an equiphase

surface.

• In the far field of free space, electric and magnetic waves are always perpendicular to each other, and both are normal to the direction of propagation of the wave. This type of wave is

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 Maxwell’s Equation

• E and H are the electric and magnetic field intensities, respectively. D and B are the electric and magnetic flux densities. D is also called the electric displacement, and B, the magnetic induction. The quantities ρ and J are the volume charge density and electric current density of any external charges, respectively.

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 Maxwell’s Equation

• The right hand side of 4th _{equation is zero because there is no magnetic monopole}

charges.

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 Maxwell’s Equation

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 Maxwell’s Equation

Lecture 02

[Note: Lenz's law is shown with the negative sign in Faraday's law of induction:

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 Maxwell’s Equation

• Gauss's law describes the relationship between a static electric field and the electric charges that cause it: The static electric field points away from positive charges and

towards negative charges.

• In the field line description, electric field lines begin only at positive electric charges and end only at negative electric charges.

• Gauss's law for magnetism states that there are no "magnetic charges" (also called magnetic monopoles), analogous to electric charges.

• Instead, the magnetic field due to materials is generated by a configuration called a dipole.

• Magnetic dipoles are best represented as loops of current but resemble positive and negative 'magnetic charges', inseparably bound together, having no net 'magnetic charge'.

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 Maxwell’s Equation

• The Maxwell-Faraday's equation version of Faraday's law describes how a time varying magnetic field creates ("induces") an electric field.

• This dynamically induced electric field has closed field lines just as the magnetic field, if not superposed by a static (charge induced) electric field.

• This aspect of electromagnetic induction is the operating principle behind many electric generators: for example, a rotating bar in magnets creates a changing magnetic field,

which in turn generates an electric field in a nearby wire.

Lecture 02

• Ampère's law with Maxwell's addition states that magnetic fields can be generated in two ways: by electric current (this was the original "Ampère's law") and by changing electric

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 Maxwell’s Equation

• Maxwell's addition to Ampère's law is particularly important: it shows that not only does a changing magnetic field induce an electric field, but also a changing electric field induces a

magnetic field.

• Therefore, these equations allow self-sustaining "electromagnetic waves" to travel through empty space (see electromagnetic wave equation).

[Note: There are in fact two origins for the magnetic field:

1) the current density j, as Ampère had already established,

2) due to ε₀∂E/∂t called as the Displacement current ]

Lecture 02

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 Maxwell’s Equation

• The electric current that passes through a wire or battery would be classified as "free current“. In contrast, "bound current" arises in the context of bulk materials that can be

magnetized and/or polarized.

• When a material is magnetized (for example, by placing it in an external magnetic field), the electrons remain bound to their respective atoms, but behave as if they were orbiting the nucleus in a particular direction, creating a microscopic current. When the currents from all

these atoms are put together, they create the same effect as a macroscopic current,

circulating continually around the magnetized object. This magnetization current J_M is one

contribution to "bound current".

• The other source of bound current is bound charge. When an electric field is applied, the positive and negative bound charges can separate over atomic distances in polarizable materials, and when the bound charges move, the polarization changes, creating another

contribution to the "bound current", the polarization current J_P.

Lecture 02

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 Maxwell’s Equation

• The total current density J due to free and bound charges is then:

J = J

+ J

+ J

with J_f the "free" or "conduction" current density.

Lecture 02

Displacement Current

• In free space, the displacement current is related to the time rate of change of electric field. However, in a dielectric the above contribution to displacement current is present

too, but a major contribution to the displacement current is related to the polarization of the individual molecules of the dielectric material.

• Even though charges cannot flow freely in a dielectric, the charges in molecules can move a little under the influence of an electric field. The positive and negative charges in

molecules separate under the applied field, causing an increase in the state of polarization,

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 Maxwell’s Equation

Lecture 02

• Thus in the expression for displacement current, it has two components:

• The first term on the right hand side is present everywhere, even in a vacuum. It doesn't involve any actual movement of charge, but it nevertheless has an associated magnetic field, as if it were an actual current.

• The second term on the right hand side is the displacement current as originally conceived by Maxwell, associated with the polarization of the individual molecules of the

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 Maxwell’s Equation

Lecture 02

• Treating all charges (disregarding whether they are bound or free charges), the generalized Ampère's equation, also called the Maxwell–Ampère equation, is in

differential form

The Maxwell–Ampère equation

• In both forms J includes magnetization current density as well as conduction and polarization current densities. That is, the current density on the right side of the Ampère–

Maxwell equation is:

where current density J_D is the displacement current, and J is the current density

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Lecture 02

Maxwell’s Equations: Applications

• Prediction of Electromagnetic Waves

Maxwell mathematically manipulated his equations (uncoupling the partial differential equations, applying the curl etc.) and derived a wave equation.

• Speed of Propagation of Electromagnetic Waves

He observed that the speed of propagation of electromagnetic waves was very close to the

speed of light. He wrote (1865): “This velocity is so nearly that of light, that it seems we have strong reason to conclude that light itself (including radiant heat, and other radiations

if any) is an electromagnetic disturbance in the form of waves propagated through the

electromagnetic field according to electromagnetic laws.” Maxwell deduced the speed of these electromagnetic

waves theoretically to 3×108 _m/sec.

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Lecture 02

Maxwell’s Equations: Applications

This statement caused controversy in the beginning. In 1886 Heinrich Hertz, was able to generate and detect electromagnetic waves in the laboratory. The theoretical speed of

these electromagnetic waves equaled the experimental values of the speed of light.

Maxwell thereby demonstrated that light was a type of electromagnetic wave. He published a theory that accounted for the physical origins of light. Thus he unified the fields of

electromagnetism and optics, which were unrelated separate branches until then.

• Theory of Relativity

Maxwell's equations have a close relation to special relativity. Albert Einstein himself

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Lecture 02

Maxwell’s Equations: Applications

• Tools of Modern Technology

Modern technology in the today’s world has its origins in the basic principles as stated in

Maxwell’s equations. Their applications like electromagnetic waves have given rise to tremendous developments in the fields of communications, computation, entertainment etc.

• To describe many theories: Poynting theorem, Lorentz potential,

• To describe transmission line, waveguide, strip line, antenna, etc.

• Magnetic train, Biomedical instruments (MRI, Imaging, etc.), Magnetic tape

• Any devices that use electricity or magnets.

• It is the base of electromagnetic theory…….