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foreign media
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[Music]
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[Applause]
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[Music]
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thank you
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thank you
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thank you
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in the game of ice hockey scoring three
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goals in one game is called a hat-trick
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I'd like to try to pull off a kind of
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hat trick today I'd like to tell you
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what an electric field is
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solve a problem in field theory that
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Isaac Newton seems to have had a great
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deal of trouble with
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and introduce an important mathematical
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idea known as gauss's law
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all of that will turn out to be easier
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than it sounds because it all flows from
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the vivid imagination of a great genius
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named Michael Faraday
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Faraday's life would have embarrassed
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the most Shameless novelist
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he began in the most modest
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circumstances and he had very little
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formal education
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and he eventually wound up being
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apprenticed to become a book binder
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but he was intent on self-improvement
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and he started attending public
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scientific lectures at the Royal
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Institution in London
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and he was so enthralled by those
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lectures that he begged for the chance
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to do the most menial kind of work at
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the Royal Institution
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and he did begin there and he eventually
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wound up as the professor of the Royal
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Institution and the most famous
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scientist in all of Europe
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throughout his career Faraday understood
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mathematics so poorly that he couldn't
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read the scientific papers of his own
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competitors
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and yet he had an intuition that got him
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to the core of every scientific problem
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it is one of the greatest ideas that
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flowed from that intuition that we want
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to speak about today it's the idea of
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lines of constant electric force
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radiating everywhere throughout space
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in the field of physics surely no tool
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has dug up more scientific truth
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than the sharp Spade of mathematics
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yet when he uncovered the field Theory
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the groundwork from which much of modern
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physics grows
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mathematics was a tool that Michael
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Faraday had to work without
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[Music]
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but he was exposed to one idea that was
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essentially mathematical in nature
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[Music]
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in 1789 Charles Augustine colon
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confirmed what the scientific Community
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had suspected for years
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who long finally demonstrated that the
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electric force is inversely proportional
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to the square of the distance between
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the charges
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as elegant as Coulomb's experiment was
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the concept the idea of the inverse
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Square relation had been a major
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scientific notion for some time
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thank you
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very earlier
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in the Isaac Newton's Theory stated that
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the fall of an apple
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and the orbit of the moon
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were both consequences of the same basic
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laws
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and one of those laws the law of
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universal gravitation
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states that any two masses attract each
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other with a force inversely
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proportional to the square of the
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distance between them
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but this was a difficult law to apply
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even for Isaac Newton himself
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[Music]
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to make the point
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you'd have to show that when an object's
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attracted to the Earth
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it acts as if all of the Earth's mass
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were concentrated at the center
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and more difficult you'd have to
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rationalize what he called action at a
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distance
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a phrase meaning that such bodies as the
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Earth and the Sun apply forces directly
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to each other
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even though they're separated by
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millions of kilometers
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no tangible connection between them
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though the great genius was often a bit
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testy even he himself might have come to
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admit a certain dissatisfaction with the
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idea of action at a distance
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somewhat defensively
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in the principia Newton wrote
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I have not been able to discover the
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cause of those properties of gravity
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and I feign no hypothesis
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with that famous phrase I feign no
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hypothesis
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Newton felt no obligation to explain
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by either physical or mechanical means
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the law of gravity
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to us it is enough that gravity does
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really exist he added
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and act according to the laws which we
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have explained
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obviously that was enough
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in England thereafter the law of
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gravitation was the law of the land and
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by the 19th century with the law of
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gravitation firmly established
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its followers had discovered that
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electricity
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and magnetism
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obey similar laws
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in all of them the force decreases with
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the square of the distance
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similarity is amazing
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the question is why
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perhaps because the inverse Square law
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is related to a simple geometrical
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property of three-dimensional space
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and perhaps because these forces aren't
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the only things that diminish with the
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square of distance
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[Music]
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the essence of the inverse Square law
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can be seen in the concept of flux the
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Latin word meaning flow
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light flows out from the Sun equally in
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all directions
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as it spreads out getting farther from
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the Sun its intensity decreases
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but imagine a sphere enclosing the Sun
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all the light would pass through the
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sphere no matter what its distance from
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the Sun
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and the area of a sphere grows as the
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square of its radius
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so the amount of light energy per unit
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area
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decreases as the square of the distance
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[Music]
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Converse Square law wasn't the only
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provocative idea to which Faraday was
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exposed as a Young Man
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by 1810 he was a regular visitor at the
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Royal Institution
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particularly at the lectures of the
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institution's legendary Professor Sir
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Humphrey Davy
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chemiston natural philosopher
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scholar who was knighted made a baronet
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and president of the Royal Society
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Davey was the very crest of British
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Science
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with his own research as the subject
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Davey spoke as the world's Authority on
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every element from sodium to potassium
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chlorine to iodine
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Davey became a scientific father figure
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for Faraday
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and remained a mentor and enormous
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influence for almost 20 years
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although the relationship was at times a
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Rocky one
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but under Davey's influence in the
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Golden Age of chemistry none shown
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brighter than Michael Faraday
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he discovered benzene
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liquefied chlorine gas and developed new
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Alloys of Steel
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the list of his remarkable
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accomplishments as a chemist goes on and
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on
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nonetheless in 1821 Faraday set aside
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his work in chemistry
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in that year orsta discovered the effect
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electric current has on magnets
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and while that effect can be seen
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clearly now
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in 1821 it was still a great scientific
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mystery
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indeed why would the compass needle line
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up perpendicular to the electric current
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sparked by curiosity to begin with and
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asked by an Editor to write an article
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that would end the scientific confusion
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Faraday set out to solve the mystery for
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himself
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faradays saw the possibility of
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harnessing the force of an electrical
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current and invented a device to do it
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that device
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happened to be the first electric motor
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how did Michael Faraday manage that
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perhaps because being unable to analyze
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them mathematically Tyra day was able to
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take these circular magnetic forces at
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face value
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in any case to Michael Faraday
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electricity as well as magnetism
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applied real forces in space and he
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began his study of them with a number of
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assumptions
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anywhere in the vicinity of an electric
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charge a small test charge experiences a
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force
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if it's due to only one charge the
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pattern of forces detected by the test
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charge is simple
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[Music]
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the pattern's more complex for two
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opposite charges
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[Music]
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or for two charges of the same sign
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[Music]
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and more complex still
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four more complicated Arrangements
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but in any case here's the point
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even if the test charge isn't there to
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feel it
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pattern of forces Can Be Imagined to
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exist everywhere in space
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this is the essence of the idea of the
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field
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and although Faraday only imagined it
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the field can also be expressed
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mathematically
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[Music]
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the force that acts on a test charge at
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each point in space
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is equal to the test charge times the
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quantity due only to the other charges
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[Music]
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that quantity is the electric field
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[Music]
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Faraday never arrived at that definition
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of the electric field
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but by seeing both electric and magnetic
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phenomena as forces in space
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he managed to see further than his peers
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as a result of this and many other
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discoveries he eventually became
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director of the research laboratory at
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the Royal Institution
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and succeeding Davey he became the
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professor there as well as a member of
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the Royal Society
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but it was as researcher rather than
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instructor that he saw deeper and deeper
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into the invisible forces of space
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the Faraday
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the one over r squared force between
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electric charges suggested that the
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force must be applied by something
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radiating outward from charges
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something which like light from the Sun
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never stops and never ends in space
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[Music]
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as Faraday imagined it this something
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would be lines or tubes
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each one capable of applying a force to
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any charge in its path
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these lines of force would begin only on
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positive charges
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and end only on negative ones
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[Music]
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foreign
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and they would flow smoothly through
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space
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never Crossing or tangling
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[Music]
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no matter the configuration
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charges would have a characteristic
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pattern of lines
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the force they applied would be strong
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near the charges where the lines are
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crowded together
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and weak far from the charges where the
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lines are farther apart
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the ability to apply a force resides at
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each point in space
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and the force arises from the intensity
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of lines
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regardless of the location of the
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charges that create them
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even without such Space Age Graphics
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this is how Faraday pictured the
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electric field
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and it still seems the most graphic way
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to visualize one but satisfying the
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scientific Community would take another
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step or two
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necessarily those steps would be
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mathematical
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and one of the more important was taken
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by Carl Friedrich Gauss
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physicist
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astronomer
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and perhaps the best mathematician of
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all time
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gauss's mathematics would offer An
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Elegant compliment to Faraday's idea and
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it would become law
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in parodies terms flux is represented by
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all the lines of force passing through
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any surface
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[Music]
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gauss's law
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that for any closed surface
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total flux is proportional to the net
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electric charge inside
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if there's no net charge inside a
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surface
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any positive flux outward
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through it
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must be balanced by an equal amount of
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inward or negative flux
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gauss's law which gives mathematical
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definition to Faraday's intuitive notion
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about the electric field
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is actually an expression of the
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geometric meaning of any inverse squared
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law
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in appropriate form it applies not only
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to Electric fields
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but to gravitational and magnetic fields
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as well
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and even to light flowing from the Sun
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in any event
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gauss's theoretical work
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combined with Faraday's common sense
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reveals a number of amazing facts about
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nature itself
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[Music]
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for example
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Watch What Happens inside a conductor
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where a lattice of positive ions is
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neutralized by mobile and constantly
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moving electrons
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an electric field
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passing through a conductor
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forces the electrons to flow until they
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pile up at the surface repelling the
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motion of further electrons
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[Music]
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but that means the electric field
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side in a conductor becomes equal to
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zero when electrostatic equilibrium is
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established
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therefore a closed surface inside the
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conductor has no flux through it
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[Music]
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so the net charge inside must be zero
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but there can be charge at the surface
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and no matter what's outside the surface
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charge makes the field inside equal to
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zero
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[Music]
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and since all the actions at the surface
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a metal box of any sort
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even a flimsy screen covered cage can
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keep out an electric field
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that fact can be demonstrated with this
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device
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a gold leaf electroscope
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notice how it responds to the field of
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an electric charge
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[Music]
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notice too that even when an
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electroscopes inside the cage
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it reacts in the same fashion
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[Music]
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however when the box is enclosed
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an electric field can't enter to disturb
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the gold leaf
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[Music]
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any metal box can do it
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and to this day
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any metal box that does do it
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is called a faraday cake
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of course not every Faraday cage was
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designed to protect its contents from
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Electric fields
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foreign
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the steel girders of a bridge are the
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scaffolding of a tunnel
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probably couldn't care less about
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keeping electric fields at Bay
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but they do a pretty effective job of it
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nonetheless
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why
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because radio waves are a kind of
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disturbance in the electric field
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and because whether it's a bridge a
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tunnel or merely the enclosed container
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that its name implies a faraday cage
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isn't a great place to get good
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reception
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outside again the reception's fine
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in any case while cars can go just about
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anywhere
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where can the lines of a uniform sphere
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of charge go
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an extended region of charge might
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consist of many point charges in space
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but if it's symmetrical the electric
00:22:05
field has only one place to go and
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that's outward
00:22:10
according to gauss's law the flux
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through a closed surface outside depends
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only on the total charge
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and if the charged region is a sphere
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the size makes no difference
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so in other words the electric field
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outside is the same whether the charge
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is uniformly distributed in a sphere or
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concentrated at a point at the center
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and by the same reasoning because it
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depends only on its inverse Square
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nature
00:22:48
the gravitational force of the earth is
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the same as if all its mass were
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concentrated at the center
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[Music]
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Isaac Newton had to use his most
00:22:58
powerful mathematics to prove that point
00:23:01
which may have contributed to the
00:23:03
20-year delay in the publication of the
00:23:06
principia
00:23:08
oh
00:23:10
but with the help of Michael Faraday's
00:23:12
Vivid mental picture
00:23:14
the reason behind the idea can be
00:23:16
perceived and completely grasped
00:23:20
without any mathematics whatsoever
00:23:23
not that mathematics wouldn't apply
00:23:26
after all in the end the best scientific
00:23:29
expression of Faraday's ideas
00:23:32
indeed the ultimate Triumph of the
00:23:34
electromagnetic field Theory
00:23:37
would be the mathematical expression
00:23:40
of James Clark Maxwell
00:23:44
Faraday would come to admire Maxwell and
00:23:47
quite properly the admiration would go
00:23:50
both ways
00:23:52
responding to a letter from Faraday
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Maxwell wrote
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you are the first person in whom the
00:23:59
idea of bodies acting at a distance has
00:24:02
arisen as a principle to be actually
00:24:04
believed in
00:24:06
nothing is clearer than your
00:24:09
descriptions
00:24:10
you seem to see the lines of force
00:24:12
curving round obstacles and driving
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plummate conductors
00:24:19
and swerving towards certain directions
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in crystals
00:24:23
and carrying with them everywhere the
00:24:26
same amount of attractive power spread
00:24:28
wider or denser as the lines widen or
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contract
00:24:33
and thinking of gravity as well as
00:24:36
electricity Maxwell concluded
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your lines of force can weave a web
00:24:41
across the sky
00:24:43
and lead the stars in their courses
00:24:46
[Music]
00:24:56
and so Faraday had this idea about lines
00:24:59
of force filling all of space
00:25:02
and there's no doubt whatsoever that
00:25:05
pharah they believed that those lines
00:25:07
were really there
00:25:09
and then Along Came James Clark Maxwell
00:25:12
and he transmuted Faraday's idea into
00:25:16
our modern view of the electric field
00:25:18
and once that was done Faraday's lines
00:25:21
of force no longer existed they were
00:25:23
gone
00:25:25
and so a reasonable question you might
00:25:27
ask is
00:25:29
why do we bother teaching you something
00:25:31
we no longer believe to be true
00:25:35
well you might be able to get some
00:25:37
perspective on that question by
00:25:38
considering something in today's science
00:25:42
we know of course that the nucleus of
00:25:44
the atom is made up of smaller particles
00:25:47
called protons and neutrons we can smash
00:25:50
the nucleus apart and get out the
00:25:52
protons and neutrons and study them and
00:25:55
so that we know they're real
00:25:57
but we also believe today that the
00:26:00
protons and neutrons themselves are made
00:26:02
up of even smaller inner constituents
00:26:04
which are called quarks
00:26:08
but it turns out that it's impossible to
00:26:11
smash a proton apart and get out the
00:26:14
individual quarks the quarks are forever
00:26:16
hidden inside of the protons and
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neutrons
00:26:20
and so the question that arises is in
00:26:23
view of that are quarks real
00:26:26
well that question is very similar to
00:26:29
the question of whether Faraday's lines
00:26:31
of force are real
00:26:34
and in the long run it may turn out to
00:26:36
be irrelevant
00:26:39
Faraday's lines of force were a kind of
00:26:41
mental scaffolding that had to be put up
00:26:44
in order to build the final edifice
00:26:47
which was the electric field
00:26:49
now of course once the building is
00:26:51
finished the scaffolding isn't needed
00:26:53
anymore so it can be torn down and
00:26:55
thrown away
00:26:56
but that makes it no less important
00:26:58
because the building couldn't have been
00:27:00
constructed
00:27:01
without the scaffolding
00:27:03
someday looking back on our situation
00:27:06
today it may turn out that even the idea
00:27:09
of quarks which today scientists
00:27:11
certainly believe are real
00:27:13
turned out to be also just the kind of
00:27:16
mental scaffolding
00:27:18
in any case we'll get on with studying
00:27:21
the final edifice of electric Theory
00:27:23
when we meet here again next time
00:27:41
[Music]
00:27:47
[Music]
00:28:05
[Music]
00:28:19
[Music]
00:28:39
foreign
00:28:41
media
00:28:49
for information about this and other
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Annenberg media programs call 1-800
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learner and visit us at www.learner.org
