Electric flux

Yesterday I watched some of the videos of Walter Lewin lectures on Electricity and Magnetism. He is really amazing especially when he is doing experiments. Thought the concepts are a familiar one it gave me a good time pass. I spend a little time on thinking about Electrostatics.

We need to know that Electric field lines are not real. It is just a simple representation invented by Michael Faraday to visualize Electric field. We should not simply accept it as the real fact.

Electric flux is the measure of the number of field lines passing through the surface that is chosen. But it is not the number of the absolute number of field lines.

The electric flux “ϕ” over a surface S is therefore given by the surface integral:

ϕ = ∬ E. ds

       s

where “E” is the electric field and “ds” is a differential area on the surface S with the normally outward facing direction.

And the electric flux around the closed surface “S” is given by:

ϕ = ∯ E. ds = q / ϵ

But be careful that it is not absolute that, there is exactly 

“q / ϵ” electric flux around a point charge “q” [In SI unit system].

Electric flux is not really the measurement of the number of field lines around a charge. It is just a calculating tool of Electric strength on the basis of proportionality arguments.

We know that we can draw infinitely many electric field lines as much as we want. But for the sake of simplicity in our calculations, we can’t use “infinite” as a number.

[Note: We need to be very careful that “∞” is not a number. It is just a symbol given for concepts.

It is like instead of saying “Newton’s Laws of Motion”, if I made a code “£” in a book, it says that where ever I use the symbol “£” it really means “Newton’s laws of Motion”.

In the same manner, the symbol “∞” is also used just to represent a Mathematical and Physical concept. The “∞” symbol just says that “it gets bigger and bigger where there is no end”. Simply it means “no limit or end”.]  

So we made a proportionality factor that is related with the number of field lines. Though the number of lines is infinite it is a proportional and dependent quantity.  

It was defined the Electric flux as it is proportional to the number of field lines.

It is already known from the definition that charge “q” is also proportional to the number of field lines.

Therefore we made calculations from the conclusion; Electric flux is proportional to “q”

It is first formulated by Carl Freidrich Gauss that is

The net outward normal electric flux through any closed surface is proportional to the total electric charge enclosed within that closed surface.

If the number of field lines was found out to be increasing that implies the charge “q” inside the closed surface is increased.

In SI units the proportionality constant is taken to be “1/ϵ” and so the electric flux  

Thus we are just finding the proportional increase in Electric flux from “q/ϵ” but it is not the measure of the absolute electric flux around the space of the charge “q”. 

Shadows of the Mind

In these days I have been reading two books. The first one is, “The Shadows of the Mind” by Roger Penrose. Second is “Classical Dynamics of Particles and Systems” by Jerry B. Marion.

First I want to share about the Shadows of the Mind.

Though that book is little vague and complicated for me to understand, I enjoyed it reading. I learned some new concepts in physics and some new way of thinking.

First of all I am very much impressed with the beginning of the book where it was told about a little story of a daughter asking ingenious questions to his father. No matter about the names of the people. But it reminded me about my old time where my teacher used to tell me about our minds.

One day I went straight to my teacher and asked some questions, which later I came to know that they are the basic philosophical questions.  But they are simple questions like,

“Where are we? What is the end of the world? Where is the Universe? If Universe is there somewhere then where that place is situated? What is time? What really we are doing here in this Universe?”

These are the questions often comes to my mind and make me to think I am in the middle of a great mystery.

Really we are all in the middle of the very great mysterious and magical world ‼!

After asking these questions, my teacher said,

“Think that, there are fishes living very deep down in Atlantic or Pacific or any other ocean. It is very deep that is its depth is comparable to height of Mount Everest. The fish spends its whole time in the sea below that depth.

Now, if you and go one day and ask the fish “What is Air? What is Sun, moon and What is Space?”

Do you think it will know the answers?

To that fish the ocean is the only world. In other words, it will think the whole world is completely just filled with water. It will only know about the things that behave in the ocean.

But it never knows about air, sun, moon or space. It even can’t simply imagine the things outside the ocean.”

And he finally said that we are also just like those fishes and where else Scientists are like special kind of fishes, which tries to get out from that ocean.     

It is same as the story told in the preface of the book “Shadows of the Mind”. It is true that we can’t even imagine the world outside the Universe.

When you read these kinds of books, and when you understood a little, stop reading and try to think something more about us. Think about the place of humans in this Universe and Just wonder the universe.

From that book I learned some new basic outline of Quantum Mechanics. Though I couldn’t fully understand Elitzur Vaidman bomb testing problem and Magical Dodecahedra problem, I just had some outline of those concepts.

I learned about Turing machine, Church’s thesis, Gödel’s theorem.

Especially I learned a little about the concept of Spin in sub atomic particles which is not the spin we really imagine in real life.

Spin:

The subatomic spin is somewhat different from classical spin where the axis is fixed in one direction. Unlike classical quantum spin is directed in all directions and “h bar” is the unit by which spin is measured.

In quantum mechanical spin, 

first we will chose a direction in space and using Stern-Gerlach instrument we will just find the magnitude of spin in that direction in space. “h bar” is the unit to denote the magnitude of the spin in that direction.

I learned new things about PULSARs and about PSR 1913-16 that is Hulse Taylor Binary Pulsar. I learned how it was proved General Theory of Relativity by the predictions made in Binary Star System and how it was predicted gravitational waves. I learned what is meant by Gravitational lensing.

Though already I know some of the things, the books gave me a lot of information.   

Basic Outline of Relativity

We can understand the basic outline of theory of relativity in a simple following way from Fermat’s principle of least time.

First you need to understand Fermat’s Principle of least time.

It states that the path taken between two points by “a ray of light” is the path that can be traversed in the least time. So it implies light will always travel in the shortest path between two points.

After believing in this principle, we can take an example of moving rocket with 9.8 m/s^2 of acceleration and earth.

From Newton’s Gravitational law, it was known that all objects near to the earth will fall at a rate of acceleration 9.8 m/s^2. Many of them had learnt this in their school days. Consider that the rocket is at first on earth at rest. If you are inside the rocket, you will see the things inside the rocket will fall at a rate of 9.8 m/s^2 when it is subjected to fall from a height not comparable to the radius of the earth.

[Since gravitational field of earth will be different at different places]

Now, I made you to sleep in the rocket by giving you anesthesia. After you had slept, the rocket was started and made to fly into the space with an acceleration of 9.8 m/s^2 .

From Newton’s law it is known that a man inside the rocket will not feel any difference between these two situations. So, he will think he is still at earth, since the experiments done in the rocket will be as same as it is at earth.

Now if you take torch light and pointed it on the horizontal direction, from very careful measurements you can see that light beam bends exactly same amount as it is in earth.

Since all the experiments done with other objects gives same results in earth as well as in rocket, it implies Light should also give same results independent of the place. 

Thus we came to know that Light indeed bend near the gravitational field. 

From this we can get two information.

One is,

• Newton’s Gravitational law says that only masses are attracted by gravitational force. But here light is attracted towards the earth, where light is thought to be pure energy. It shows that energy and mass has some relation.

The second information is derived from Fermat’s principle.

• If light travels in the shortest path between two points,

In horizontal direction the shortest path between the two points is the straight line drawn between those two points. But light here is actually travels in a bend path not following Fermat’s principle.

To make Fermat’s principle the true one, it was just made a small adjustment in the statement that follows as,

The shortest path between the two points in horizontal direction near the gravitational field is really the bend path.

That says that the space itself is a curved one. And light travels in the shortest path in that curved space where the path of the light is curved. Thus we can get two aspects of Relativity theory.

I am explaining here just the simple outline of Relativity theory and not the complete one.

This is to get just a little basic knowledge of Relativity theory to common people.