Favourite Physics Equations of all times

The_Conductor

As per the BBC-
http://news.bbc.co.uk/2/hi/uk_news/magazine/3721406.stm

You could almost call it Equation Idol - readers of Physics World have voted for their favourite equations of all time. But what do they mean?
Deputy editor of Physics World, Dr Matin Durrani, offers an idiot's guide to the top five equations of all time.


1. (JOINT 1st) CLERK MAXWELL'S ELECTROMAGNETISM THEORY
∇.D=p

∇.B=0

∇xE=-∂B/∂t

∇xH= ∂D/∂t+j

Where D is the displacement field, E is the electric field, B is the magnetic-flux density, H is the magnetic-field strength, p is the free charge density and j is the free current density.

These were written down by the great Scottish physicist James Clerk Maxwell in 1873. They describe how an electromagnetic wave - like a light beam, an X-ray or a microwave - varies with time and position in space.

What is interesting about the equations is that they showed that electricity and magnetism - two forces that scientists previously thought were unrelated - are actually linked to one another. Since then, physicists have also gone on to link electromagnetism with two of nature's other forces - the "weak" and "strong" forces that act inside the nucleus of an atom.

The resulting theory is known as the Standard Model of particle physics. The big challenge is now to find out how nature's fourth fundamental force - gravity - is linked to this model. So Maxwell was essentially the first physicist to start unifying the forces of nature into a single theoretical framework.

What good is it to me? Maxwell's equations are used throughout the telecoms industry - for example, to design the antenna on your mobile phone


1. (JOINT 1ST) EULER'S EQUATION

ei p + 1 = 0


This was joint top with Maxwell's equations and was discovered by the Swiss mathematician Leonhard Euler in the 18th Century. Physicists like this equation because it has nine basic concepts of mathematics - once and only once - in a single equation.

These include, p which is the circumference of a circle divided by its diameter; i, which is the square root of minus one; and e, which is the number 2.71828. The other six concepts are: multiplication; plus; equals; one; zero; and the "exponent operation". The exponent operation describes what you do when you multiply a number by itself a certain number of times: two squared, for example, means 2x2, while two cubed means 2x2x2.

What good is it to me? None. Euler's equation is a purely mathematical construct with no obvious practical relevance, although it is what some physicists might call "beautiful".


3. NEWTON'S SECOND LAW
F=ma

This describes the fact that if you give a force, F, to an object with a mass, m, it will have an acceleration, a. It was derived by Isaac Newton in the late 17th Century and forms the basis of his second law of motion.

What good is it to me? Newton's second law could be used to work out how fast your flashy new Mini Cooper will accelerate from 0 to 60mph.


4. PYTHAGORAS'S THEOREM
a²+b²=c²

A classroom favourite, Pythagoras's theorem explains how the lengths of the sides of a right-angle triangle are related. If a and b are the lengths of the two shorter sides and c is the length of the long side, then all you need to do work out c is to add up the squares of the other two sides and take the square root of the answer. It was devised by the Greek scientist Pythagoras in the 6th Century BC.

What good is it to me? Pythagoras's equation helps in the process of "triangulation", which can pinpoint the location of someone using a mobile phone simply by bouncing signals off three different phone masts.


5. SCHRÖDINGER'S EQUATION
HΨ=EΨ

This was devised by the Austrian physicist Erwin Schrödinger in the mid-1920s. It describes how tiny sub-atomic particles like electrons behave and forms part of the theory known as "quantum mechanics".

With particles like electrons, it's impossible to say where exactly they are in space or how fast they're moving; all you can do is give them a probability of being in a certain place at a certain time. The symbol in the equation is called the "wave function" - it describes the probability of the particle being at different points in space.

What good is it to me? Schrödinger's equation has applications in electronics: it is, for example, being used by a Cambridge firm called Quantum Beam to build a laser-based system that will let your home computer connect to the internet without any wires.


6. EINSTEIN'S EQUATION
E=mc²

This is Einstein's famous equation that shows that mass and energy are not separate but are actually related. What the equation says is that an object with a mass m has an energy E = mc², where c is the speed of light. Since c is so big - light moves at 300 million metres a second - even a tiny mass has a huge energy.

Equally, energy also has mass. You can expect to hear a lot more about the equation in 2005, which marks the 100th anniversary of its discovery by Einstein as part of his special theory of relativity. Events will be held around the world as part of what has been dubbed by the United Nations as the "International Year of Physics".

What good is it to me? E=mc² determines how much energy is generated when atoms are split in your local nuclear-power station.

The_Conductor

SCHRÖDINGER'S theory (on cat mortality) for me.
It was described to us in class as a closed experiment with the wavelength depicting the exact half life of a decaying radioactive substance. If a certain type of radioactivity was discovered inside the half life of the substance it would crack a beaker and break a flask of prussic acid, and kill poor kitty (a cat being placed in the room where these measurements were occuring- and you could not check on the welfare of the cat until the end of the experiment) (we had a picture of kitty mewling at us, as the radioactivity was measured.)
The exact point of the half life of the substance- where you had exactly 50% chance of detecting the radiation, and thus exactly 50% chance of the prussic acid beaker being intact and consequently 50% chance of the cat being alive represented a wavelength of a half dead half alive cat.... This wavelength would not collapse until such time as you actually checked on the wellbeing of the cat........

Who said physics wasn't fun?

S.

rainbow kirby

Euler. So pretty...

Cute_Button

Newton does it for me. Ahh- gravity! I see noone likes their triangles

Jen

planck2

Its just got be the picture of what Einstein is writing on the board: " we 've got a flat space-time people, nothing here but empty space-time, no gravitating nonsense in this universe"

Capt'n Midnight

Should be an option for other in the pole since some are not strictly physics..

Re: Maxwell

Linked Magnetism and Electricty and Photons together, an early step towards an expression of the grand unified theory of everything. Excluding gravity (and nuclear reactions) it links most of the forces we encounter day to day.


The Arrhenius Equation k=A*exp(-Ea/R*T)
reaction rate is faster when it's warmer & stuff with
http://www.shodor.org/UNChem/advanced/kin/arrhenius.html

Reynolds Number just like the shape of it and the way you could use it to describe the way cigarette smoke used to become turbulent about a meter up - though not as topical since smoking banned.


PV = nRT - perfect gas law, you can describe the physical properties of most gasses, by knowing the amount of thermal energy available to the molocues in the gas and assuming molecules bouce off each other perfectly (as an aside I like the way you can work out the size of the molecules/atoms working backwards from this)
* P: pressure
* V: volume
* n: moles of gas molecules
* R: molar gas constant. The value depends on the units of measurement for pressure, volume, and absolute temperature.
* T: absolute temperature.
linkie http://www.zaimoni.com/ClassicalGas.htm




Equations

planck2

Capt'n Midnight wrote:

Should be an option for other in the pole since some are not strictly physics..

QUOTE]

I don't exactly get where you are coming from, all the equations you have listed above are physics equations, they describe what happens in a given situation. Most sciences are linked backed to physics in some way or form. It is the universal science

Capt'n Midnight

EULER'S EQUATION (ei p + 1 = 0) - this is maths pure and simple, not physics specific, I was going to post some chemistry ones but didn't

dudara

Maxwell's Equations are elegant, but for me it has to be Newton's Second Law, written in it's correct form

F = dp / dt

Ali Cat

Though I agree that it is more of a mathematical equation, I still vote for Euler's because of its beautiful use of a number of interesting constants.