foreign media [Music] [Applause] [Music] thank you thank you thank you in the game of ice hockey scoring three goals in one game is called a hat-trick I'd like to try to pull off a kind of hat trick today I'd like to tell you what an electric field is solve a problem in field theory that Isaac Newton seems to have had a great deal of trouble with and introduce an important mathematical idea known as gauss's law all of that will turn out to be easier than it sounds because it all flows from the vivid imagination of a great genius named Michael Faraday Faraday's life would have embarrassed the most Shameless novelist he began in the most modest circumstances and he had very little formal education and he eventually wound up being apprenticed to become a book binder but he was intent on self-improvement and he started attending public scientific lectures at the Royal Institution in London and he was so enthralled by those lectures that he begged for the chance to do the most menial kind of work at the Royal Institution and he did begin there and he eventually wound up as the professor of the Royal Institution and the most famous scientist in all of Europe throughout his career Faraday understood mathematics so poorly that he couldn't read the scientific papers of his own competitors and yet he had an intuition that got him to the core of every scientific problem it is one of the greatest ideas that flowed from that intuition that we want to speak about today it's the idea of lines of constant electric force radiating everywhere throughout space in the field of physics surely no tool has dug up more scientific truth than the sharp Spade of mathematics yet when he uncovered the field Theory the groundwork from which much of modern physics grows mathematics was a tool that Michael Faraday had to work without [Music] but he was exposed to one idea that was essentially mathematical in nature [Music] in 1789 Charles Augustine colon confirmed what the scientific Community had suspected for years who long finally demonstrated that the electric force is inversely proportional to the square of the distance between the charges as elegant as Coulomb's experiment was the concept the idea of the inverse Square relation had been a major scientific notion for some time thank you very earlier in the Isaac Newton's Theory stated that the fall of an apple and the orbit of the moon were both consequences of the same basic laws and one of those laws the law of universal gravitation states that any two masses attract each other with a force inversely proportional to the square of the distance between them but this was a difficult law to apply even for Isaac Newton himself [Music] to make the point you'd have to show that when an object's attracted to the Earth it acts as if all of the Earth's mass were concentrated at the center and more difficult you'd have to rationalize what he called action at a distance a phrase meaning that such bodies as the Earth and the Sun apply forces directly to each other even though they're separated by millions of kilometers no tangible connection between them though the great genius was often a bit testy even he himself might have come to admit a certain dissatisfaction with the idea of action at a distance somewhat defensively in the principia Newton wrote I have not been able to discover the cause of those properties of gravity and I feign no hypothesis with that famous phrase I feign no hypothesis Newton felt no obligation to explain by either physical or mechanical means the law of gravity to us it is enough that gravity does really exist he added and act according to the laws which we have explained obviously that was enough in England thereafter the law of gravitation was the law of the land and by the 19th century with the law of gravitation firmly established its followers had discovered that electricity and magnetism obey similar laws in all of them the force decreases with the square of the distance similarity is amazing the question is why perhaps because the inverse Square law is related to a simple geometrical property of three-dimensional space and perhaps because these forces aren't the only things that diminish with the square of distance [Music] the essence of the inverse Square law can be seen in the concept of flux the Latin word meaning flow light flows out from the Sun equally in all directions as it spreads out getting farther from the Sun its intensity decreases but imagine a sphere enclosing the Sun all the light would pass through the sphere no matter what its distance from the Sun and the area of a sphere grows as the square of its radius so the amount of light energy per unit area decreases as the square of the distance [Music] Converse Square law wasn't the only provocative idea to which Faraday was exposed as a Young Man by 1810 he was a regular visitor at the Royal Institution particularly at the lectures of the institution's legendary Professor Sir Humphrey Davy chemiston natural philosopher scholar who was knighted made a baronet and president of the Royal Society Davey was the very crest of British Science with his own research as the subject Davey spoke as the world's Authority on every element from sodium to potassium chlorine to iodine Davey became a scientific father figure for Faraday and remained a mentor and enormous influence for almost 20 years although the relationship was at times a Rocky one but under Davey's influence in the Golden Age of chemistry none shown brighter than Michael Faraday he discovered benzene liquefied chlorine gas and developed new Alloys of Steel the list of his remarkable accomplishments as a chemist goes on and on nonetheless in 1821 Faraday set aside his work in chemistry in that year orsta discovered the effect electric current has on magnets and while that effect can be seen clearly now in 1821 it was still a great scientific mystery indeed why would the compass needle line up perpendicular to the electric current sparked by curiosity to begin with and asked by an Editor to write an article that would end the scientific confusion Faraday set out to solve the mystery for himself faradays saw the possibility of harnessing the force of an electrical current and invented a device to do it that device happened to be the first electric motor how did Michael Faraday manage that perhaps because being unable to analyze them mathematically Tyra day was able to take these circular magnetic forces at face value in any case to Michael Faraday electricity as well as magnetism applied real forces in space and he began his study of them with a number of assumptions anywhere in the vicinity of an electric charge a small test charge experiences a force if it's due to only one charge the pattern of forces detected by the test charge is simple [Music] the pattern's more complex for two opposite charges [Music] or for two charges of the same sign [Music] and more complex still four more complicated Arrangements but in any case here's the point even if the test charge isn't there to feel it pattern of forces Can Be Imagined to exist everywhere in space this is the essence of the idea of the field and although Faraday only imagined it the field can also be expressed mathematically [Music] the force that acts on a test charge at each point in space is equal to the test charge times the quantity due only to the other charges [Music] that quantity is the electric field [Music] Faraday never arrived at that definition of the electric field but by seeing both electric and magnetic phenomena as forces in space he managed to see further than his peers as a result of this and many other discoveries he eventually became director of the research laboratory at the Royal Institution and succeeding Davey he became the professor there as well as a member of the Royal Society but it was as researcher rather than instructor that he saw deeper and deeper into the invisible forces of space the Faraday the one over r squared force between electric charges suggested that the force must be applied by something radiating outward from charges something which like light from the Sun never stops and never ends in space [Music] as Faraday imagined it this something would be lines or tubes each one capable of applying a force to any charge in its path these lines of force would begin only on positive charges and end only on negative ones [Music] foreign and they would flow smoothly through space never Crossing or tangling [Music] no matter the configuration charges would have a characteristic pattern of lines the force they applied would be strong near the charges where the lines are crowded together and weak far from the charges where the lines are farther apart the ability to apply a force resides at each point in space and the force arises from the intensity of lines regardless of the location of the charges that create them even without such Space Age Graphics this is how Faraday pictured the electric field and it still seems the most graphic way to visualize one but satisfying the scientific Community would take another step or two necessarily those steps would be mathematical and one of the more important was taken by Carl Friedrich Gauss physicist astronomer and perhaps the best mathematician of all time gauss's mathematics would offer An Elegant compliment to Faraday's idea and it would become law in parodies terms flux is represented by all the lines of force passing through any surface [Music] gauss's law that for any closed surface total flux is proportional to the net electric charge inside if there's no net charge inside a surface any positive flux outward through it must be balanced by an equal amount of inward or negative flux gauss's law which gives mathematical definition to Faraday's intuitive notion about the electric field is actually an expression of the geometric meaning of any inverse squared law in appropriate form it applies not only to Electric fields but to gravitational and magnetic fields as well and even to light flowing from the Sun in any event gauss's theoretical work combined with Faraday's common sense reveals a number of amazing facts about nature itself [Music] for example Watch What Happens inside a conductor where a lattice of positive ions is neutralized by mobile and constantly moving electrons an electric field passing through a conductor forces the electrons to flow until they pile up at the surface repelling the motion of further electrons [Music] but that means the electric field side in a conductor becomes equal to zero when electrostatic equilibrium is established therefore a closed surface inside the conductor has no flux through it [Music] so the net charge inside must be zero but there can be charge at the surface and no matter what's outside the surface charge makes the field inside equal to zero [Music] and since all the actions at the surface a metal box of any sort even a flimsy screen covered cage can keep out an electric field that fact can be demonstrated with this device a gold leaf electroscope notice how it responds to the field of an electric charge [Music] notice too that even when an electroscopes inside the cage it reacts in the same fashion [Music] however when the box is enclosed an electric field can't enter to disturb the gold leaf [Music] any metal box can do it and to this day any metal box that does do it is called a faraday cake of course not every Faraday cage was designed to protect its contents from Electric fields foreign the steel girders of a bridge are the scaffolding of a tunnel probably couldn't care less about keeping electric fields at Bay but they do a pretty effective job of it nonetheless why because radio waves are a kind of disturbance in the electric field and because whether it's a bridge a tunnel or merely the enclosed container that its name implies a faraday cage isn't a great place to get good reception outside again the reception's fine in any case while cars can go just about anywhere where can the lines of a uniform sphere of charge go an extended region of charge might consist of many point charges in space but if it's symmetrical the electric field has only one place to go and that's outward according to gauss's law the flux through a closed surface outside depends only on the total charge and if the charged region is a sphere the size makes no difference so in other words the electric field outside is the same whether the charge is uniformly distributed in a sphere or concentrated at a point at the center and by the same reasoning because it depends only on its inverse Square nature the gravitational force of the earth is the same as if all its mass were concentrated at the center [Music] Isaac Newton had to use his most powerful mathematics to prove that point which may have contributed to the 20-year delay in the publication of the principia oh but with the help of Michael Faraday's Vivid mental picture the reason behind the idea can be perceived and completely grasped without any mathematics whatsoever not that mathematics wouldn't apply after all in the end the best scientific expression of Faraday's ideas indeed the ultimate Triumph of the electromagnetic field Theory would be the mathematical expression of James Clark Maxwell Faraday would come to admire Maxwell and quite properly the admiration would go both ways responding to a letter from Faraday Maxwell wrote you are the first person in whom the idea of bodies acting at a distance has arisen as a principle to be actually believed in nothing is clearer than your descriptions you seem to see the lines of force curving round obstacles and driving plummate conductors and swerving towards certain directions in crystals and carrying with them everywhere the same amount of attractive power spread wider or denser as the lines widen or contract and thinking of gravity as well as electricity Maxwell concluded your lines of force can weave a web across the sky and lead the stars in their courses [Music] and so Faraday had this idea about lines of force filling all of space and there's no doubt whatsoever that pharah they believed that those lines were really there and then Along Came James Clark Maxwell and he transmuted Faraday's idea into our modern view of the electric field and once that was done Faraday's lines of force no longer existed they were gone and so a reasonable question you might ask is why do we bother teaching you something we no longer believe to be true well you might be able to get some perspective on that question by considering something in today's science we know of course that the nucleus of the atom is made up of smaller particles called protons and neutrons we can smash the nucleus apart and get out the protons and neutrons and study them and so that we know they're real but we also believe today that the protons and neutrons themselves are made up of even smaller inner constituents which are called quarks but it turns out that it's impossible to smash a proton apart and get out the individual quarks the quarks are forever hidden inside of the protons and neutrons and so the question that arises is in view of that are quarks real well that question is very similar to the question of whether Faraday's lines of force are real and in the long run it may turn out to be irrelevant Faraday's lines of force were a kind of mental scaffolding that had to be put up in order to build the final edifice which was the electric field now of course once the building is finished the scaffolding isn't needed anymore so it can be torn down and thrown away but that makes it no less important because the building couldn't have been constructed without the scaffolding someday looking back on our situation today it may turn out that even the idea of quarks which today scientists certainly believe are real turned out to be also just the kind of mental scaffolding in any case we'll get on with studying the final edifice of electric Theory when we meet here again next time [Music] [Music] [Music] [Music] foreign media for information about this and other Annenberg media programs call 1-800 learner and visit us at www.learner.org