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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.

Questions & Answers

Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
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Damian Reply
absolutely yes
Daniel
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Akash Reply
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Maciej
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Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
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Devang Reply
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
Abhijith Reply
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
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
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Sanket Reply
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Cied
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I start with an easy one. carbon nanotubes woven into a long filament like a string
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Porter
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AMJAD
how did you get the value of 2000N.What calculations are needed to arrive at it
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Source:  OpenStax, Solid state physics and devices-the harbinger of third wave of civilization. OpenStax CNX. Sep 15, 2014 Download for free at http://legacy.cnx.org/content/col11170/1.89
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