Electromagnetic ShieldingPROPOSITION : MATHEMATICAL MODEL

2

PROPOSITION:AN INTRODUCTION TO FARADAY’S CAGE AND APPLICATIONS

3WHAT IT IS??

It is a technique to completely block or reduce the intensity of electromagnetic waves or radio frequency i.e isolating the conductor

To a large degree, though, they shield the interior from external electromagnetic radiation if the conductor is thick enough and any holes are significantly smaller than the wavelength of the radiation.

4HOW IT WORKS??

Electromagnetic radiation consists of  electric and magnetic fields. The electric field produces forces on the charge carriers within the conductor. As soon as an electric field is applied to the surface of an ideal conductor, it induces a current that causes displacement of charge inside the conductor that cancels the applied field inside, at which point the current stops.

5“THE FARADAY CAGE!”

Faraday’s cage is an enclosure that is used to shield any electronic device by blocking electric fields and thus electromagnetic waves.

And here's the real kicker. Although there's no charge inside the conductor, the opposing electric field does have an important effect, it shields the interior from exterior static electric charges and also from electromagnetic radiation, like radio waves and microwaves

6

APPLICATIONS

Microwave ovens works by trapping the waves within a cage and quickly cooking your food.

There are plenty of political and military uses for Faraday cages, too. Politicians may opt to discuss sensitive matters only in shielded rooms that can block out eavesdropping technologies.

The coaxial cable have different levels of coating which reduces the loss of radio frequency through the wire.

7

COLLEGE TRANSFORMERSHIELDED USING FARADAY CAGE

8

MATHEMATICAL MODELAN INDEPENDENT ANALYSIS OF THE PROPOSITION

9ASSUMPTIONS

Electron-Nucleus model simplified to a spring model

Electrons thus have a restoring force

They have a mass “m”

They have a resonant frequency

External field varies with frequency w

10THE MATHEMATICAL MODEL:

The differential equation:

On solving the above equation, we get: (particular solution)

; p is the dipole moment

NB: Not q*2x……think why?

11

“”

THE LIMITING CONDITION :

W MADE TO APPROACH VERY LARGE FREQUENCIES!!!

As omega goes to infinity; x goes to zero!!!

And if x goes to zero, so does p!!!

12The Maths Deciphered!

The moment of inertia of electrons…..causes it to take a certain amount of time to turn and align with the field and then again against the field…..(time lag)

Much like Hysteresis loss in……magnetization and demagnetization of a magnet!

According to values recorded by the American Physics Society Journal:

Above optical/IR frequency the electrons can’t follow…and this leads to little or no electrical shielding…(time lag becomes significant)

13REFERENCE:

14So what did I mean???

I made some approximations:

I took the case of a dipole and used its limiting case…..

i.e. when conductor taken to be the approximation of volume dipole(how?)

When frequency is less, p has a reasonable amplitude BUT at higher frequencies….

Now we replace molecules by electrons in my model…and we conclude the same thing to approximations of first order(think why??

Answer: shm eqn)

Using the limiting condition….

I found out that dipole molecules will not oscillate at such high frequencies…

Again extending the analogy to elctron-nucleus model, neither will the electrons of a pure conductor

But there remains an important difference:

The MOI of electrons is much less than molecules….thus perfect conductors will cease shielding at higher frequencies than impure/dielectric ones!!!...(PROVE IT!)

15

16

THANK YOU!!!