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The voltage is defined as the integral of the electic field along a line joining two points. Herein is derived for your pleasure (i)the voltage due to a time varying magnetic field and (ii)the voltage that develops across a resistor.

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In terms of an electromagnetic field, the voltage along a closed line is given by the rate of change of magnetic flux through that circuit. To show this, start with one of Maxwell's equations, Faraday's law

curl E=-δB/δt

Here E is the electric field and B the magnetic field. Now integrate over the surface that the closed circuit describes.

∫curl E.ds=-δ(∫B.ds)/δt

Stoke's Theorem allows us to express the surface integral of the curl of a vector as a closed line integral ∫c of that vector. Furthermore, the surface integral of the magnetic field is simply the magnetic flux Φ through that surface. So the previous equation becomes

cE.dl=-δΦ/δt

To simplify matters, assume that the closed line is a circle of radius R. Then the integral of the electic field over the line is simply 2πRE//, where E// is the component of the electric field along the circle. This, in fact, is the voltage around the circle (since voltage is the integral of electric field around the circuit). Thus,

V=-δΦ/δt
It follows that the faster the increase in magnetic flux, the more negative the voltage generated. This equation relates to the voltage due to a solenoid.

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If there is a steady current flowing through an ohmic resistor, the voltage between the two ends of the resistor is the product of the electric field and the length L of the component.(V=EL). From Ohm's law, we know that the current is proportional to the electric field. The constant of proportionality is the electrical conductivity σ The inverse of σ is the resistivity ρ. Thus we have E=ρL and

Vresistor=ρJL

where J, the current density, in this case is defined as the current per unit cross-sectional area in the resistor.It is beyond the scope of this w/u to explain the the total resistance R of the resistor is directly proportional to the resistivity and length and inversely proportional to the cross-sectional area (R=ρL/A).The previous equation may be rewritten

Vresistor=RAJ

Of course the cross-sectional area multiplied by the current density is simply the total current I flowing in the resistor (assuming that J is uniform across the area) One finally has an expression for the voltage in terms of the more easily measured quantities R and I.

Vresistor=RI
.

Obviously, the greater the resistance encountered by the current the stronger the potential difference (voltage) developed across it.

Polar molecules possess a weak electromagnetic field which is shared with their neighbours (known as the Van Der Waals or cohesive force). At the surface there are fewer neighbours (the Van Der Waals force is also present in non-polar molecules). Molecules on the surface of a liquid will experience a net downward force simply due to the absence of neighbours above. As the surface is pulled downward, the surface area is minimised and the density in the layer increases until limited by Coulomb repulsive forces. The energy density in the surface layer is higher than in the body of the liquid (where viscous forces reign). Surface tension produces effects such as a pin, of density much higher than water, floating if placed on the surface carefully.

Another force to consider in determining how the surface of a liquid will shape itself is the adhesive force between the liquid and a solid with which it is in contact. Water adheres strongly to glass. The water molecules in contact with the glass will tend to be attracted upwards. The surface tension effect will simultaneously rearrange the shape of the surface of the water until it is again in the lowest energy configuration. This process (obviously over a very short time-scale) will continue until the angle that the surface of the water makes with the wall of the vessel reaches a certain critical angle. This turned up at the edges shape is known as the meniscus. Water does not adhere well with wax, explaining why rain falling on the waxed surface of a car will curl up into droplets while that falling on the windscreen will spread all over the surface.

Reducing the surface tension of water will increase the degree to which it will spread over a surface (i.e. its 'wetness'). Raising the temperature of water or adding cleaning agents (surfactants) such as detergent will reduce surface tension. A washing machine is a surface tension reducer! A third method is to physically create turbulence on the surface so that the membrane is broken. Water is sprayed on the spot where a diver will enter the water so that a less painful impact results. OK, since I know by now you will be dying to know how to calculate the surface tension of a liquid, I present to you-

How to determine surface tension by the capillary tube method
What you will need-

  • 1 capillary tube
  • Some liquid (avoid mercury)
  • 1 PC microscope (available for under 100 dollars)
  • 1 PC with printer (most probably you have these)
  • 1 ruler
  • 1 micrometer screw gauge
  • 1 beaker (a transparent cup would do)
  • You will need to know the density of the liquid.
If you don't have a micrometer screw gauge you could try your best with the ruler. First start up your image capture software and clamp the capillary tube into the beaker full of water. Notice the liquid rise up the tube due to a combination of surface tension and adhesive forces with the glass. Now the surface tension (which I will henceforth call Gamma) is the force per unit length along the circumference of the liquid in the tube.
Gamma= F/2*Pi*R
where R is the radius of the tube. This force is balanced out by the force due to gravity, namely the mass of the liquid that has risen multiplied by the acceleration due to gravity g (9.8 ms-2). This mass is the product of volume of liquid in the tube and the density of the liquid (water= 1000 kg m-3). So lets write that out in equation form. Furthermore, the tension force acts parallel to the surface of the liquid where it meets the glass. It is its vertical component which balances gravity. We take care of this by multipying Gamma by Cos(theta) where theta is the angle made between the liquid and the glass.
2*Pi*R*Gamma*Cos(theta)=Volume*density*g
The volume of liquid is best calculated in two parts. First, there is the liquid beneath the lowest part of the meniscus which is at a height h above the level of the main body of water. This is simply given by the volume of a cylinder Pi*R2h. Next there is the water above the lowest part of the meniscus. In a narrow tube such as this the surface of the water assumes a hemispherical shape of radius R. The volume of this hemisphere is 2/3*PI*R3, while the total cylindrical volume of this section (of height R) is PI*R3. This means the water in this section has volume 1/3*PI*R3 which is equivalent to the volume of a cylinder of height R/3. Thus the total volume of the water in the capillary tube is PI*R2(h+R/3) (it might be helpful to draw a diagram of this). Finally, plug this expression for the volume into the equation above and one has
Gamma=(1/2*Cos(theta))*density*R(h+R/3)
or if you have are using browser that supports such symbols
γ=(1/2Cos(θ))*ρR(h+R/3)
So thats the theory and the apparatus has been set up. Better get on with the experiment in that case. We need to find R, h and theta in order to obtain a value for Gamma.

  1. Measure the outer diameter of the capillary tube using the micrometer screw gauge. The accuracy of this device is a fraction of a millimeter.
  2. Take image of capillary tube using microscope. The image should include the level of the main body of liquid and the meniscus in the tube.
  3. Print out image.
  4. Measure outer diameter on capillary tube using your trusty 12".
  5. Calculate ratio of the outer diameter as it is represented on the printed page and the one measured more accurately in step 1. This is your scale factor between reality and image.
  6. From the image measure the height of the liquid in the tube. The position of the base of the liquid may be difficult to ascertain due to the pulling up of the water at the edge of the beaker. Scale down using ratio determined in previous step to find h.
  7. Measure the inner diameter on the image. Scale down and divide by two to find the radius R of the liquid in the tube
  8. Get out your long lost protractor and measure theta on the printed image. Remember this is the angle the surface of the liquid makes with the tube at the glass/liquid interface.
  9. Plug figures for R, h and theta and the known value of density into the formula for the sought after surface tension
Now you are equipped to test the claims of laundary detergent manufacturers. First find the surface tension of tap water. Next add your favourite non-Bio to test if Gamma is reduced. Try replicating conditions in washing machine by raising the temperature of water. Remember any contaminants in the liquid or on the surface of the capillary tube will severely skew the results.

Sources
Undergrad Physics
tdent clarified the physics for me.

When Paul Dirac developed his relativistic theory of the electron, there were certain startling features of it that he had a difficult time reconciling with the known laws of physics. Chief among these is that the Dirac equation, unlike the non-relativistic Schrodinger equation, admits solutions with both positive and negative energy. Moreover, for every positive energy state there is a corresponding negative energy state. The existence of arbitrary negative energy states for the electron is troublesome, as it permits an electron to emit an infinite amount of energy while travelling to the lowest energy state, at minus infinity, which certainly does not occur in reality.

Dirac's solution to this paradox was to invent the Dirac sea. The Pauli exclusion principle prevents two electrons from occupying the same state at the same time, thus it is possible to assume that all the negative energy states predicted by the Dirac equation are already occupied, redefining the vacuum to include an infinite number of negative-energy electrons. Since all of the negative energy states are full, a positive energy electron is prevented from dropping below zero energy by Pauli exclusion, re-establishing the behaviour observed in reality.

The Dirac sea hypothesis does not limit itself to reconciling theory with reality, though. Dirac went on to consider the case where one of the negative energy electrons in the 'sea' is excited into a positive energy state. This produces a vacancy in the Dirac sea which then appears to be a positively-charged particle. Dirac had originally hoped that this particle corresponded to the single positively-charged particle known at the time, the proton. However, when this vacancy encounters another electron, the electron would take the opportunity to decay into a negative energy state and the two particles would appear to annihilate, which was not something protons and electrons were observed to do.

The vacancy in the Dirac sea was then shown to have the same apparent mass as the electron, and this 'positron' was then discovered experimentally in 1932. While this result showed the general correctness of the Dirac theory, the infinite negative charge density of the Dirac sea was deeply uncomfortable to many physicists. When the first quantum field theories were developed in the 1930s, the Dirac theory was reformulated using the tools provided by quantum field theory (QFT). A QFT-based Dirac equation is best written in terms of two separate, but related, particle types, corresponding to the positive- and negative-energy solutions to the original Dirac equation. In this situation, no Dirac sea is necessary and the concept fell into disuse.

A very similar concept to the Dirac sea is used in solid-state physics, especially in the theory of semiconductors. The electrons in a solid act like a finite Dirac sea, and when an electron is excited into a higher-energy state it leaves behind a hole which acts as a positively-charged counterpart to the electron that was excited. In a semiconductor electron-hole pairs are made quite readily, and in many semiconductor applications the conduction due to the motion of holes is at least as important as that due to the motion of electrons.

While the Dirac sea is now considered an obsolete idea in particle physics, it was very useful for making sense of the Dirac theory of the electron, and for its prediction of the existence of antimatter. It is still useful as a teaching tool, as it is a more straightforward qualitative explanation of antimatter than the full QFT treatment.


(CC)
This writeup is copyright 2008 D.G. Roberge and is released under the Creative Commons Attribution-NonCommercial-ShareAlike licence. Details can be found at http://creativecommons.org/licenses/by-nc-sa/3.0/ .

Electrolytes are defined as inorganic substances that form ions in an aqueous solution. Your body needs electrolytes; when these substances are present in sufficient quantities your body functions normally. Your heart beats, your muscles contract, normal blood pressure is maintained, you’re alert and mentally ready. During electrolyte imbalance normal cellular functions are impaired. The degree of impairment, the symptoms and the severity of this depends on whether you have too much or too little of something and to the degree that you have exceeded the normal limits.

The hyper and hypo prefixes are used to denote whether someone has an excess or deficit of a specific electrolyte. For example: someone who is hypernatremic has an above average concentration of sodium ions and a person suffering from hypokalemia requires more potassium ions than are currently available to them. For the average person a normal well balanced diet is sufficient to maintain electrolyte balances but there are several conditions and diseases that can adversely affect the electrolyte balance. These include but are not limited to breast and prostate cancers, digestive disorders including celiac disease, impaired renal function and inherited genetic disorders.

Generally electrolyte imbalances are not life threatening and are usually treated with intravenous solutions or simple dietary changes. Non-disease states may also affect electrolyte imbalances. Routine abuse of antacids, alcohol and other drugs, pregnancy, abnormal stress and injuries can cause electrolyte balances to be disrupted. Depending on the severity of the imbalance it may be asymptomatic and remain undetected. Hypocalcemia is typically asymptomatic and the danger here is that your skeletal system may be under attack as cells harvest the calcium stored within the bone matrix to meet their electrolytic needs. Other complications include congestive heart failure, cardiac arrhythmias, muscle spasms, intestinal cramps and convulsions, in rare cases this can even lead to death.

Electrolytes have several functions: they are used to conduct electricity, the central nervous system sends electrical impulses throughout the body, they can act as secondary messengers, skeletal muscle fibers will respond to a larger than normal electrical stimulus and electrolytes can serve also as catalysts for enzymatic reactions. They also play a critical role in the regulation of fluid balances. There are two separate fluid compartments in your body intracellular fluid and extracellular fluid. Intracellular fluid is the fluid that resides in within your cells and extracellular fluid is the remaining balance.

Changes in electrolytic concentrations in and around cells affects them and their ability to function normally. Unusually high or very low concentrations can alter and damage cells. Your cells have limited mitochondrial energy to function and if they’re expending energy to remove unwanted positively charged electrolytes their energy stores are unnecessarily depleted. Electrolytes travel in and out of cells in different ways. Some electrolytes leak through channels in cell walls, some are actively transported in and others are exchanged for those that the cell needs.

Fluid and electrolyte shifts are constant. Your kidneys are constantly filtering out unwanted ions but they also have the power to capture or recall ions before they are excreted. Excess ions are excreted as waste products but if there is a demand for a certain electrolyte the kidneys may be able to prevent elimination by pulling electrolytes from the filtrate. Electrolytes do not work independently and the fate of one may affect the availability of another. Iron and magnesium ions interfere with the body’s ability to absorb calcium.

One symptom of an inadequate supply of magnesium is hypocalcemia and a symptom of hyperchloremia is hyperkalemia. Chlorine is the most prevalent anion in the body. It has a -1 charge and your body depends primarily on chlorine ions to maintain a negative cellular environment. The negatively charged internal environment gives cells a resting potential. Potential energy can be converted into actual energy and your cells are able to perform work.

Cellular function varies from cell to cell but without electrolytic harmony any cell is unable to function optimally. Suboptimal function is possible. Who among us has the perfect diet and exercise regime, but your body has a built in coping mechanism to deal with us as inhabitants. Normal cellular functions will continue as long as electrolyte concentrations remain within a range of normal values. Electrolytes are lost through sweat, urine, feces and bile. They are gained when you eat, drink and breathe. When considering how to replace lost electrolytes a simple well balanced meal is generally sufficient to restore electrolytic homeostasis although special conditions such as illness or extremely strenuous exercise may require electrolytic supplementation.

A quick word about sports drinks and vitamin waters. They do contain electrolytes but they are a poor choice for electrolyte replacement as they typically contain excessive amounts of sugar and many are artificially colored and flavored to increase palatability. The importance of a well balanced diet cannot be over emphasized, taking great care of your body on a daily basis means you will have electrolyte reserves to restore normal losses so eat, drink and be merry. Laughter is the best medicine even if it has nothing to do with electrolytes.

 

Sources:

Fundamentals of Anatomy and Physiology

Wikipedia

www.nephrologychannel.com

www.chemocare.com

 

Thanks to nocteTem42, Albert Herring, and auraseer for corrections on 4/29/8, 5/19/9, 5/26/9 and 2/3/10 .

Science is certainly awesome. It has been suggested that before it really got off the ground in Western Europe after the Dark Ages, the entire continent of Europe probably knew less about the physical world than just one of the single Ancient Greek philosopher-scientists had done. By learning more we have revolutionized our world in so many ways, not least by releasing the chain of economic growth that has generated such spectacular wealth and lifted so much of humanity - if not enough - out of poverty, superstition, pestilence and ignorance. Not bad going.

However, science has to operate within its own sphere. Science is about understanding the physical world and, man being a tool maker, often results in the generation of technology that can manipulate the world to man's apparent benefit. The purpose for which these tools are employed has to remain a separate question. Despite a brief vogue for "political science", it has long been clear that social and political questions are far too complex for science to say anything about. There are still problems in predicting and controlling even relatively simple physical systems, nevermind whole human societies. Our societies are not like physical systems where one can simply extrapolate from current facts what lies in the future; and so it is very difficult to realize in advance the consequences of scientific developments.

And so it has been clear for some time that science is silent on the ultimate question for humanity, which is "How should we live together?" This question has largely been resolved in North America and Western Europe through the answer "by and with science", but this is not a judgement that science itself was competent to make; we have just been so impressed by the enormous benefits delivered to us by science and economic growth that we have enshrined technological advancement - and hence economic growth - as our guiding star. But despite these huge benefits, there have been warnings along the way - warnings that now seem to be growing louder. I speak of what I believe is called in scientific circles "the law of unintended consequences".

The problem really begun with the discovery of the Archimedean point, when mankind discovered that it could act upon the earth as if he was outside of it, not part of it - and radically change the things around us for our benefit. But by taking on this awesome power, we also took on the enormous risk of changing the world in some very, very negative ways without even realizing what we were doing. And if we're going to have centuries of scientific progress in decades, then that's going to mean centuries of societal change as well - an unsettling prospect when you think that the wars and revolutions of the twentieth century claimed something like as many lives as those of all previous centuries combined, in many cases due to developments linked to the advancement of science.

These unintended consequences have come about because the primary mover in changing the way we live has literally become the extent of what we can do to the physical world and the way we can control it. If we can do it, we do it. Even America, usually and correctly understood as a conservative society, is in reality constantly reinvented by economic and technological progress. Although there were earlier signs, the first really big warning that this might be a bad idea was the creation of the nuclear bomb, which for the first time delivered into mankind's hands the power to totally destroy all life on earth.

This was a radical new development that had huge implications for us all, a fact readily forgotten if you do not remember that these arsenals still exist and the possibility of the complete annihilation of the human species still exists. And it hasn't only changed our relation to our fellow man, but to nature itself: we can now actually destroy nature. In a way this was the logical conclusion of the central trend in modern scientific development, which is the subjugation of nature to mankind. Nature never did us any favours - what with all the scarcity and hardship it subjects us to - but, as Hannah Arendt has noted, destroying nature altogether means destroying our mastery of it.

These huge advancements in human capabilities are one of the ways science has given us unexpected problems. Another example of the same issue that we should be particularly aware of at the moment is the way that the microchip revolution has utterly changed the nature of our economies and the speed at which we do business, a factor not wholly innocent of involvement in the global financial crisis. The ease with which debt was repackaged and sold around the world has been responsible for great economic growth in recent years, but now in the twenty-first century it has also shown its claws: extreme volatility and the emergence of business models that were unsustainably based on these quick global transfers and can do significant damage to the global economy when they fail, like Bear Stearns did over the weekend.

What this example and others like it tell us is that in the twenty-first century, mankind has to be very careful not to let technology outstrip the social and political mechanisms which are needed to cope with that technology. It is the proper sphere of scientists to want to advance their knowledge as much as possible and produce benefits for mankind, but the consequences of their developments need to be subjected to a very different question: what impact will this have on humanity in every important respect and not just in terms of how much it knows about and can tinker with the physical universe? And this problem is only going to become more acute as the speed of scientific advancement and the process of constantly reinventing the world increases.

The most topical recent example is climate change. If the theories about climate change being caused by humanity are true, then the great engine of our economic and technological progress over the last few centuries has actually begun to radically and negatively alter the earth itself. This awesome power was completely unknown to all earlier civilizations, and we really need to be much more humble about just what we're capable of. The ecosystem exists in as precarious a balance as our political systems, and both risk being upended by our careless actions.

And then there is by far the most dangerous of all possibilities, the idea that we might create or tinker with life itself. Biotechnology is dangerous insofar as it promises "enhancements" to human life, through theoretical advances such as the ability to tinker with DNA in the womb and make a person stronger or smarter, or the possibility of somehow combining the human body with a machine to increase its capabilities. Such advancements carry the risk of creating a two-tier society - split between the "enhanced" and the normal - as well as giving new capabilities to humans which actually make them non-human; they change the nature of what it means to be human by eliminating, say, forgetfulness. While the standard by which we alter the physical world is clear - for our own utility - the standard by which we would tinker with human life itself is not clear at all, as we have nothing to measure it against.

By beginning to tinker with human life itself we may deliver some perceived benefits to an individual, but we will make that life less authentically human. The human mind lies in a beautiful and splendid balance which is not understood by the scientists, and to begin to alter the way it relates to the world will carry the most unintended consequences of all. Such advances may lie merely in the realm of theory at present, but if the last few centuries has taught us anything it is to expect the unexpected; and so we need to lay down strict limits on what is allowed and what is not. It seems that to begin to experiment with changing human life or the human brain itself - something so little understood, and involving realms of meaning and value that science is necessarily silent on - will carry the greatest risks of all.

By acting into the world and even on ourselves we risk destroying the conditions that have allowed human life to exist for so many millennia, perhaps completely by accident. We should be humbled by the enormous power of humanity in the twenty-first century, when we have literally taken on the role ascribed to God in all religion, the role of the creator - but remember that in these religious stories, it is God who is also the one with the capability to destroy. We have made these stories a reality for ourselves. But do we possess God's infinite wisdom?