# 3.18 Sspd_chapter 1_part8_appendixxxxiv_travelling waves

 Page 1 / 1
Appendix XXXIV refers to SSPD_Chapter_Part8 It gives a simple quantitative method of arriving at the solution of Wave Equations of Electro-Magnetic Field Theory. We have a similar methodology of arriving at the solution of Schrodinger Equation.

Appendix XXXIV

Solving the wave equation for plane wave

Maxwell’s four differential equations are:

In free space propogation: 𝝆( charge density) =0 and

Therefore the four differential equations become:

From these four equations we obtain:

But in free space both divergences are zero therefore the above 2 equations become:

In free space €=€ 0 and μ= μ 0

That is free space permittivity = absolute permittivity .

And free space permeability = absolute permeability .

Also c ( velocity of light in free space ) =

Therefore the above two equations become:

We apply separation of variables to solve these two partial differential equations:

Assume E(r,t) = E1(r)E2(t)

H(r,t) = H1(r)H2(t)

In general by assuming the time dependent portion to be of harmonic nature:

That is E2(t) = E20Exp(jωt) and H2(t) = H20Exp(jωt)

The partial derivative

Hence the two equations become:

Now the partial differential equations have reduced to ordinary linear differential equations known as wave equations of 2 nd order and they can be solved applying operator theory.

We also assume that it is a plane wave travelling along z axis hence

Under such circumstances as we will see in Electro-Magnetic Field Theory, only x-component of E1 and y-component of H1 will remain. Hence

Applying Theory of Operator we get two roots in each case namely:

Two roots are =

= =

Hence

So the complete solution for Electric Field is:

1 st Term is backward travelling wave and 2 nd term is forward travelling wave.

How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Abigail
for teaching engĺish at school how nano technology help us
Anassong
How can I make nanorobot?
Lily
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
how can I make nanorobot?
Lily
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
Got questions? Join the online conversation and get instant answers!   By By By  By   By Rhodes