"Annenberg Media" "¶" "For information about this and other Annenberg Media programs call 1-800-LEARNER and visit us at" "WHEN ISAAC NEWTON FORMULATED THE LAW OF GRAVITY," "HE HAD TO POSTULATE FORCES ACTING AT A DISTANCE." "THAT IS TO SAY," "THE SUN COULD EXERT A FORCE DIRECTLY ON THE EARTH" "EVEN THOUGH THEY WERE SEPARATED BY A VAST DISTANCE" "WITH NOTHING IN BETWEEN." "THAT WAS AN IDEA THAT SATISFIED ABSOLUTELY NO ONE." "EVEN ISAAC NEWTON'S MOST ARDENT ADMIRER," "THAT IS, ISAAC NEWTON HIMSELF," "WAS EMBARRASSED BY IT." "THEN, IN THE 19th CENTURY," "MICHAEL FARADAY IMAGINED HIS LINES OF FORCE," "AND IN THE NEXT GENERATION," "MAXWELL TURNED THAT IDEA INTO THE FIELD OF FORCE," "AND EVERYONE WAS HAPPY." "AT FIRST GLANCE," "IT'S HARD TO SEE WHAT HAD CHANGED." "MASSES AND CHARGES STILL APPLIED THE SAME FORCES TO EACH OTHER" "WITH NOTHING IN BETWEEN." "AND YET, THE IDEA OF THE FIELD OF FORCE" "SEEMED TO MAKE ALL THE DIFFERENCE IN THE WORLD." "WHY?" "THE ANSWER IS BECAUSE THE FIELD HAD OBJECTIVE REALITY." "IT HAD PROPERTIES THAT COULD BE PREDICTED," "THAT COULD BE CALCULATED, MANIPULATED, ENVISIONED." "THE FIELD EXISTED." "IT BECAME ITSELF THE PROPER SUBJECT" "OF SCIENTIFIC INQUIRY." "FOR EXAMPLE," "WE KNOW WHAT HAPPENS WHEN THE FIELD IS DISTURBED." "THE DISTURBANCE PROPAGATES AWAY AT THE SPEED OF LIGHT," "A SPEED THAT WAS INHERENT IN THE FORCE LAWS THEMSELVES." "IN RETROSPECT, WE KNOW THAT WAS THE FIRST GREAT TRIUMPH" "OF FIELD THEORY." "AND SO, WE'RE GOING TO STUDY THE PROPERTIES OF THOSE FIELDS." "BUT THE STUDY OF THE PROPERTIES OF FIELDS" "DIDN'T BEGIN WITH ELECTRICITY AND MAGNETISM." "IT BEGAN IN ANOTHER SCIENCE ALTOGETHER," "THE SCIENCE OF HYDRODYNAMICS, THE FLOW OF WATER." "TODAY, WE'RE GOING TO STUDY" "THE PROPERTIES OF ALL OF THOSE FIELDS" "ELECTRIC FIELDS, MAGNETIC FIELDS," "AND THE FIELDS OF FLOWING WATER." "ELECTRIC FIELDS, MAGNETIC FIELDS," "AND FIELDS OF FLOWING WATER." "SINCE THE CREATION OF THE UNIVERSE," "OR, IN SCIENTIFIC TERMS, THE BIG BANG," "NATURE AND EVERYTHING IN IT HAS GONE WITH THE FLOW." "OUT THERE," "MAGNETIC FIELDS STREAM THROUGH THE MOSTLY UNCHARTED OCEANS" "OF OUTER SPACE." "OUT THERE," "ELECTRIC FIELDS BIND MOLECULES AND ATOMS" "INTO THE STUFF OF THE UNIVERSE." "CLOSER TO HOME PORT," "IN THE CHAIN OF PLANETARY ISLANDS" "KNOWN AS THE SOLAR SYSTEM," "MAGNETISM AND ELECTRICITY ALSO MAKE THEIR PRESENCE KNOWN." "BUT DOWN HERE," "ON THE THIRD PLANET FROM THE SUN," "THERE ARE A FEW DIFFERENCES" "AND A FEW CONNECTIONS BETWEEN THEM." "ONE DIFFERENCE IS THAT," "TO THE BEST OF ANYONE'S KNOWLEDGE," "ONLY HERE ON PLANET EARTH" "IS THERE ANY LIQUID WATER." "THE SECOND DIFFERENCE, LIFE," "TOOK SHAPE ON THE BOTTOM OF THE SEA," "AND THE BOND BETWEEN ALL LIFE AND ALL WATER" "REMAINS INTACT." "DURING THE COURSE OF EVOLUTION, SOME LIFE CHANGED," "THOUGHT IT HAD BETTER THINGS TO DO ON LAND," "AND MADE A CRAWL FOR IT." "BUT DESPITE FORM OR FUNCTION, DESTINY OR DIRECTION," "ALL LIVING THINGS RETAIN THAT LINK" "TO THE WATER FROM WHENCE THEY CAME." "PERHAPS THAT'S WHY," "WHEN A FORM OF LIFE CALLED HOMO SAPIENS" "GOT AROUND TO CONTEMPLATING" "THE MYSTERIES OF ELECTRICITY AND MAGNETISM," "IT TURNED FOR INSPIRATION" "TO THE FIELD OF FLOWING WATER." "WHILE THE FLOW OF ELECTRICITY AND MAGNETISM" "MAY SEEM HARDER TO GET INTO THAN A FLOWING RIVER," "THE FIELDS OF ALL THREE HAVE VERY MUCH IN COMMON." "AND EVEN IN THE FIELD OF FLOWING WATER," "THERE MAY BE MORE GOING ON THAN MEETS THE EYE." "FOR EXAMPLE, THE APPARENT CALM OF THIS BOWL OF WATER" "IS SOON PIERCED BY A GROWING WHIRLPOOL." "A BIT OF INK INJECTED INTO THE WATER" "REVEALS THE SWIRLING PATTERN OF FLOW" "AROUND THE VORTEX." "NOT THAT, EVEN WITHOUT THE INK," "IT'S IMPOSSIBLE TO SEE EVIDENCE OF THE FLOWING MOTION OF WATER." "BUT THEN, IT'S MOSTLY THE EFFECTS" "RATHER THAN THE FLOW" "THAT ONE ACTUALLY SEES." "IN THE NATURAL COURSE OF EVENTS," "AIR BUBBLES, LEAVES AND TWIGS," "AND ABOVE ALL" "THE AGITATED SHAPE OF THE SURFACE" "REVEALS THE MOTION OF WATER." "BUT LOOKING MORE DEEPLY INTO THE SUBJECT," "SOMETHING VERY INTERESTING EMERGES." "IT MAY SEEM TO BE A SMALL POINT AT FIRST," "BUT WHEN IT COMES TO THE FIELDS" "OF WATER, ELECTRICITY, AND MAGNETISM ALIKE," "IT STILL HAPPENS TO BE THE NAKED TRUTH." "INSIDE ANY BODY OF WATER," "THERE'S DEFINITE VELOCITY AT EACH POINT IN SPACE" "AND AT EACH INSTANT IN TIME." "AND SINCE VELOCITY IS A VECTOR QUANTITY," "IT FOLLOWS THAT THE FLOW OF WATER," "NO MATTER WHERE IT FLOWS," "CAN BE REPRESENTED BY A PATTERN OF VECTORS." "IN EXACTLY THE SAME WAY," "ELECTRIC FORCES ON A TEST CHARGE" "CAN BE REPRESENTED BY A PATTERN OF VECTORS IN SPACE." "AND SO CAN THE PATTERN OF DIRECTIONS" "TAKEN BY A MAGNETIZED NEEDLE ANYWHERE IN SPACE." "OF COURSE, IN REAL LIFE," "IT'S IMPOSSIBLE TO SEE ELECTRIC AND MAGNETIC FIELDS." "HOWEVER, BY OBSERVING THEIR EFFECTS," "IT'S POSSIBLE TO STUDY THEIR FORMS" "AND TO DISCOVER THAT, LIKE WATER," "ELECTRIC FIELDS AND MAGNETIC FIELDS" "ARE VECTOR FIELDS," "WHICH MEANS THAT ALL THREE" "ARE PATTERNS OF VECTORS IN SPACE" "AND THAT ALL THREE CAN BE DESCRIBED" "WITH THE BEAUTIFUL FLOW OF MATHEMATICS." "ALL VECTOR FIELDS OBEY EQUATIONS DESCRIBING THEIR FORMS." "THE ELECTRIC FLUX THROUGH ANY CLOSED SURFACE" "IS PROPORTIONAL TO THE NET ELECTRIC CHARGE INSIDE." "BUT THE MAGNETIC FLUX THROUGH ANY CLOSED SURFACE" "IS ALWAYS EQUAL TO ZERO." "THE LINE INTEGRAL OF THE ELECTRIC FIELD" "AROUND ANY CLOSED PATH" "IS EQUAL TO ZERO." "BUT THE LINE INTEGRAL OF THE MAGNETIC FIELD" "AROUND A CLOSED PATH" "IS PROPORTIONAL TO THE ELECTRIC CURRENT" "PASSING THROUGH THE PATH." "THESE EQUATIONS ARE THE MODERN EXPRESSIONS" "OF THE ENIGMATIC FORCES OF ELECTRICITY AND MAGNETISM." "BUT WHAT CAN BE SAID ABOUT THE FIELD OF FLOWING WATER?" "CONSIDER, FOR EXAMPLE, THIS SWIFT MOUNTAIN STREAM." "THE FLOW IS RAPID, EVEN TURBULENT IN PLACES." "BUT FOR ALL THE SOUND AND FURY," "IN THE LARGER SCHEME OF THINGS," "THIS IS A MODEST FLOW," "A MINOR TRIBUTARY IN THE EARTH'S GREAT NETWORK" "OF RIVERS AND WATERWAYS." "ITS FLOW PALES IN COMPARISON TO A MAJOR RIVER" "LIKE THE MISSISSIPPI OR THE AMAZON," "WHICH CAN DISCHARGE" "OVER 180,000 CUBIC METERS PER SECOND." "BUT THE LENGTH AND THE VOLUME OF WATER DELIVERED" "AREN'T THE ONLY FACTORS IN THE FLOW OF WATER." "FOR EXAMPLE," "EVEN THOUGH THESE PIPES FROM THE COLORADO RIVER" "MAY CARRY LESS WATER THAN THE AMAZON," "THEY MAY CARRY THEIR WATER WITH A MUCH FASTER FLOW." "THE DIFFERENCE BETWEEN THOSE TWO IDEAS," "TOTAL FLOW VERSUS VELOCITY AT A POINT," "IS BEST EXPRESSED BY THE CONCEPT OF FLUX." "THE WORD FLUX IS LATIN FOR "WATER FLOW,"" "BUT IN THE LANGUAGE OF MATHEMATICS," "HERE'S HOW IT WORKS." "FLUXISTHETOTALAMOUNT OFWATER" "PASSINGTHROUGH ANELEMENTOF AREA" "INA GIVENAMOUNTOFTIME ." "INTIME,t," "THAT'SALLTHEWATER INA BOXOF WIDTH,vt," "AREA,A , ANDVOLUME,vta." "SOTHEFLUX, ORFLOWRATE," "IS EQUAL TO THE VELOCITY, v, TIMESTHEAREA,A." "HOWEVER, IF THE AREA ELEMENT ISTILTED" "WITHRESPECT TOTHEDIRECTIONOFFLOW ," "LESSOFTHEWATER PASSESTHROUGHIT ." "SO FLUX DEPENDS ON THE ANGLE BETWEENTHEFLOWFIELD" "ANDTHEAREAELEMENT." "DEFININGANAREAVECTOR PERPENDICULARTOITSPLANE," "THEFLUX ISCONVENIENTLYEXPRESSED" "BYTHEVECTORDOT PRODUCT." "THE SAME IDEA IS APPLIED TO OTHER FIELDS AS WELL." "FOR EXAMPLE, THE FLUX OF AN ELECTRIC FIELD" "IS FOUND BY ADDING, OR INTEGRATING," "THE VECTOR DOT PRODUCT OF THE FIELD" "AND THE AREA THROUGH WHICH IT PASSES." "THAT'S ALSO THE WAY TO EXPRESS THE MAGNETIC FLUX." "THE IDEA IS TO FIND THE TOTAL NUMBER" "OF LINES OF FORCE THROUGH THE SURFACE." "SO, WHETHER COUNTING TOTAL LINES OF FORCE" "OR TOTAL FLOW OF WATER," "THE MATHEMATICAL EXPRESSION OF FLUX" "IS THE SAME FOR ALL VECTOR FIELDS." "BUT ALL FIELDS ARE NOT CREATED EQUAL" "WHEN FLUX OUT OF A CLOSED SURFACE" "IS CONSIDERED." "IMAGINE A SURFACE" "THAT COMPLETELY ENCLOSES A VOLUME INSIDE A BODY OF WATER." "NO MATTER THE FLOW FIELD," "WHATEVER QUANTITY OF WATER FLOWS OUT" "MUST ALSO FLOW IN AT THE SAME TIME." "THAT'S THE ONLY WAY IT CAN BE" "BECAUSE WATER ISN'T CREATED OR DESTROYED INSIDE." "SO, IN WATER, THE FLUX OUT OF A CLOSED SURFACE" "IS ALWAYS ZERO." "THE SAME IS TRUE IN THE CASE OF MAGNETISM." "THE NET MAGNETIC FLUX OUT OF ANY CLOSED SURFACE" "IS ALWAYS EQUAL TO ZERO." "BUT THE ELECTRIC FLUX" "IS DIFFERENT FROM THAT OF WATER AND MAGNETISM." "THERE CAN BE AN ELECTRIC FLUX OUT OF A CLOSED SURFACE." "ACCORDING TO GAUSS' LAW," "IT'S PROPORTIONAL TO THE NET ELECTRIC CHARGE INSIDE." "THE FLUX OUT OF A CLOSED SURFACE" "EXPRESSES AN ESSENTIAL DIFFERENCE" "AMONG THE VECTOR FIELDS." "THE FLUX OF MAGNETIC FIELD AND OF WATER" "OUT OF ANY CLOSED VOLUME IS ALWAYS ZERO" "BECAUSE NEITHER CAN RADIATE OUTWARD" "FROM A POINT IN SPACE." "ON THE OTHER HAND," "THAT'S PRECISELY WHAT ELECTRIC FLUX DOES" "RADIATE OUTWARD FROM A POINT IN SPACE" "WHICH MEANS THAT RATHER THAN BEING LIKE WATER AND MAGNETISM," "ELECTRIC FLUX IS LIKE THE FLUX OF SUNLIGHT." "THE TOTAL FLUX OF LIGHT THROUGH A CLOSED SURFACE" "IS PROPORTIONAL TO THE STRENGTH OF THE LIGHT SOURCE INSIDE." "THAT'S TRUE WHETHER THE SOURCE IS A STAR IN THE HEAVENS" "OR A BULB IN A FLASHLIGHT" "AND EQUALLY TRUE NO MATTER THE SIZE OF THE SURFACE." "SO THE SUN CREATES A FLUX OF LIGHT" "MUCH THE SAME WAY AN ELECTRIC CHARGE" "CREATES A FLUX IN THE ELECTRIC FIELD." "BUT WHAT ABOUT WATER FLOW AND MAGNETIC FLUX?" "IF THESE FIELDS AREN'T GENERATED" "BY SOURCES THAT CAN CREATE FLUX OUT OF A CLOSED SURFACE," "HOW CAN ANY FLOW BE CREATED AT ALL?" "ONE ANSWER IS THAT WATER" "CAN BE SET IN MOTION BY STIRRING." "FOR EXAMPLE," "LOOK AT A BODY OF FLUID IN CIRCULAR MOTION." "ITS FLOW, MADE VISIBLE BY ALUMINUM PARTICLES," "STARTS AT THE WALLS AND MOVES INWARD." "EVENTUALLY, ALL THE MOTION SETTLES INTO A RIGID STRUCTURE" "WITH THE FLUID ROTATING" "AS IF IT WERE FROZEN INTO A SOLID BODY." "THAT'S ONE WAY TO GET THINGS MOVING." "HERE'S ANOTHER." "WHEN SOMEONE PULLS THE PLUG," "ALL MOTION BREAKS LOOSE," "AND SOONER OR LATER, A NEW PATTERN ALWAYS DEVELOPS," "AND IT'S CALLED VORTEX FLOW." "IT'S AN EXTREMELY STABLE KIND OF MOTION," "ALMOST IMPOSSIBLE TO STOP ONCE IT GETS STARTED." "THIS SAME PRINCIPLE IS AT WORK" "IN THE GENTLE WHIRLPOOL IN THE FAMILY BATH" "AND IN THE DESTRUCTION OF AN ENORMOUS HURRICANE." "IT OCCURS BECAUSE EVEN BEFORE THE STORM BEGAN," "THE MASS OF AIR HAD A SPECIAL KIND OF MOTION." "IT'S CALLED CIRCULATION." "AS IN THE CASE OF A TUB OR A HURRICANE," "A FIRE IN THE FOREST OR A TWISTER ON THE PLAIN," "CIRCULATION LEADS TO A VORTEX." "WHEN THE PLUG IS FIRST PULLED," "WATER NEAR THE CENTER OF THE BOWL," "WHERE THE INTERNAL MOTION IS LEAST," "FLOWS DIRECTLY DOWN," "TO BE REPLACED BY WATER FROM FARTHER OUT." "BUT THAT WATER, CIRCULATING MORE RAPIDLY," "CONSERVES ANGULAR MOMENTUM AS IT MOVES INWARD." "MASS TIMES DISTANCE FROM THE CENTER TIMES SPEED" "IS CONSERVED FOR EACH BIT OF WATER." "SO AS IT GETS CLOSER TO THE CENTRAL AXIS OF THE BOWL," "EACH BIT OF WATER SWIRLS FASTER AND FASTER" "UNTIL THE WATER RUPTURES INTO THE HOLE" "AT THE CENTER OF THE WHIRLPOOL." "BECAUSE EACH BIT OF WATER CONSERVES ANGULAR MOMENTUM" "AS IT SPIRALS INWARD TOWARD THE VORTEX," "THE BASIC PATTERN OF VORTEX FLOW" "IS CIRCLES OF CONSTANT VELOCITY PROPORTIONAL TO 1/R," "THE DISTANCE FROM THE VORTEX CORE," "OR HOLE IN THE FLOW." "THE TRAPPED ANGULAR MOMENTUM" "ACCOUNTS FOR THE REMARKABLE STABILITY OF THE VORTEX FLOW," "AND THE VECTOR FIELD HAS THE SAME FORM" "AS THE MAGNETIC FIELD OF A CURRENT-CARRYING WIRE." "OF COURSE, IN THE VORTEX FLOW," "THE VECTORS REPRESENT VELOCITY OF FLUID," "WHILE IN MAGNETISM," "THE VECTORS REPRESENT STRENGTH OF FIELD," "NOT THE SPEED OF ANYTHING." "BUT THE SHAPE AND THE MATHEMATICS ARE THE SAME," "AND TOGETHER THEY ILLUSTRATE THE FORCE" "OERSTEAD FOUND CIRCLING A WIRE." "THOUGH HIS DISCOVERY" "CREATED AN INTELLECTUAL STORM IN THE SCIENTIFIC COMMUNITY," "NO ONE REALIZED IT ACTUALLY TOOK THE SHAPE OF ONE." "BUT THAT IT DID," "AND THE NEW SCIENCE OF MAGNETISM" "WOULD REVOLVE AROUND THAT VERY FACT." "SINCE THE FIELD OF CIRCULATING FLUID" "HAS THE SAME SHAPE AS A MAGNETIC FIELD," "IT SHOULD COME AS NO SURPRISE" "THAT ITS MATHEMATICAL DESCRIPTION HAS THE SAME FORM." "THE LINE INTEGRAL OF THE VELOCITY FIELD OF WATER" "IS CALLED THE CIRCULATION." "SINCE THE WATER FLOWS NEARLY IN CIRCLES," "WITH VELOCITY INVERSELY PROPORTIONAL" "TO DISTANCE FROM THE CORE," "THE CIRCULATION AROUND A VORTEX CORE" "DOESN'T DEPEND ON THE DISTANCE FROM THE CORE." "IT'S A CONSTANT, PROPORTIONAL TO THE STRENGTH OF THE VORTEX." "IN THE SAME WAY," "THE LINE INTEGRAL OF A MAGNETIC FIELD" "IS PROPORTIONAL TO THE ELECTRIC CURRENT" "THAT CREATES THE FIELD." "MATHEMATICALLY SPEAKING," "THE VORTEX IS THE SOURCE OF FLUID FLOW" "IN EXACTLY THE SAME SENSE" "THAT ELECTRIC CURRENT IS THE SOURCE OF MAGNETIC FIELDS." "JUST AS AN ELECTRIC CURRENT CAN FORM A CLOSED LOOP," "SO CAN A VORTEX CORE" "FORM A LOOP CALLED A VORTEX RING." "THE FLOW FIELD OF A VORTEX RING" "IS THE SAME AS THE MAGNETIC FIELD" "OF A CURRENT LOOP." "VORTEX RINGS, LIKE ALL VORTICES, ARE AMAZINGLY STABLE STRUCTURES." "WHETHER ELECTRIC, MAGNETIC, OR THE FLOW OF WATER," "ANY VECTOR FIELD CAN BE DESCRIBED BY TWO QUANTITIES" "ITS LINE INTEGRAL AND ITS FLUX." "SO FOR EACH TYPE OF VECTOR FIELD," "THE QUESTIONS ARE THE SAME." "FIRST, CAN IT CIRCULATE?" "AND SECOND, CAN IT FLOW RADIALLY TO OR FROM A POINT?" "FOR MAGNETIC AND ELECTRIC FIELDS" "THAT ARE CONSTANT IN TIME," "THE ANSWERS ARE SIMPLE." "MAGNETIC FIELDS CIRCULATE," "BUT NEVER CONVERGE TO A POINT." "ON THE OTHER HAND," "ELECTRIC FIELDS RADIATE FROM POINT CHARGES," "BUT NEVER CIRCULATE." "THESE ARE THE FUNDAMENTAL NATURES" "OF STATIONARY ELECTRIC AND MAGNETIC FIELDS." "ONE WAY OR ANOTHER, IN ANY NUMBER OF SETTINGS," "IT'S COMPARATIVELY EASY TO WATCH WATER CIRCULATE AND FLOW." "HOWEVER, THE FLOW OF ELECTRIC AND MAGNETIC FIELDS" "IS ANOTHER MATTER ENTIRELY." "ELECTRIC AND MAGNETIC FIELDS, THOUGH THEY'RE JUST AS REAL," "ARE HARDER TO GET ONE'S HANDS ON." "NEVERTHELESS, IN PHYSICAL TERMS," "ELECTRIC AND MAGNETIC FIELDS EXIST IN SPACE" "FAR FROM THE CHARGES OR CURRENTS THAT CREATE THEM." "AND ALL THREE VECTOR FIELDS" "HAVE MORE THAN JUST SHAPE AND FORM." "THEY ALSO HAVE ENERGY." "FOR EXAMPLE," "IN AN ELECTRIC FIELD SUCH AS THE ONE IN A CAPACITOR," "ENERGY MAY COME FROM A BATTERY" "DOING THE WORK OF MOVING CHARGES AGAINST THE FORCE" "OF THEIR MUTUAL ATTRACTIONS AND REPULSIONS." "IN A MAGNETIC FIELD," "SUCH AS THE ONE IN A SOLENOID," "SUCH ENERGY MAY ALSO BE PRODUCED BY A BATTERY," "WHICH MAKES THE CURRENT FLOW TO CREATE THE MAGNETIC FIELD." "IN A FLOW FIELD," "WORK IS DONE SETTING THE FLUID INTO MOTION," "AND THE ENERGY RESIDES IN THE MOTION OF THE FLUID." "THE ENERGY IS KINETIC IN NATURE, 1/2 mv-SQUARED FOR EACH BIT OF FLOWING MATTER." "SINCE THE FLUID'S CONTINUOUS," "IT'S BEST TO EXPRESS ENERGY PER UNIT VOLUME" "AS 1/2 THE MASS PER UNIT VOLUME OR DENSITY" "TIMES THE VELOCITY SQUARED." "BUT IN ANY CASE," "ENERGY RESIDES AT EACH POINT IN SPACE" "PROPORTIONAL TO THE SQUARE OF THE VELOCITY FIELD" "AT THAT POINT." "BY THE SAME TOKEN," "THE ENERGY DENSITY IN AN ELECTRIC FIELD" "IS PROPORTIONAL TO E-SQUARED AT EACH POINT." "IN A MAGNETIC FIELD," "IT'S PROPORTIONAL TO B-SQUARED AT EACH POINT." "WHETHER MAGNETIC, ELECTRIC, OR FLOWING LIQUID," "THE ENERGY PER UNIT VOLUME" "STORED IN EACH OF THESE VECTOR FIELDS" "IS PROPORTIONAL TO THE SQUARE OF THE FIELD" "AT EACH POINT IN SPACE." "SO WHETHER IT'S FLUX, ENERGY, OR CIRCULATION," "SOME IMPORTANT PRINCIPLES OF THE PHYSICAL WORLD" "CAN BE SEEN AT WORK" "IN ONE OF ITS MOST PRIMITIVE ENVIRONMENTS," "THE FREE-FLOWING RIVER." "OK." "I KNOW WHAT YOU'RE THINKING." "THERE ARE TOO MANY CANDLES FOR IT TO BE MY BIRTHDAY." "BUT I'M GOING TO BLOW SOME OF THEM OUT." "I'LL DO IT THE HARD WAY," "USING VORTEX RINGS FROM ALL THE WAY OVER THERE." "THOSE SMELLY CHEMICALS I PUT INTO THIS CANISTER" "MAKE SOME SMOKE." "THAT WILL MAKE THE VORTEX RINGS INTO SMOKE RINGS." "THE SMOKE RINGS ARE VERY STABLE STRUCTURES." "THEY'LL LAST LONG ENOUGH TO GET OVER THERE" "AND BLOW OUT THE CANDLES WHEN I TAP ON THIS MEMBRANE." "HOW MANY THINK I CAN BLOW OUT CANDLES THIS WAY?" "YOU CAN LEAVE." "THE REST STAY AND WATCH." "WATCH THIS." "[APPLAUSE]" "THIS DEMONSTRATION," "WHEN IN WAS FIRST DONE IN THE 19th CENTURY," "MADE SUCH A BIG IMPRESSION THAT FOR HALF A CENTURY," "SOME OF THE BEST MINDS IN EUROPE" "THOUGHT THAT ATOMS WERE VORTEX RINGS IN THE ETHER." "THAT'S A STORY WE'LL GET TO LATER." "RIGHT NOW, LET'S GO GET SOME FRESH AIR." "CAPTIONING IS MADE POSSIBLE BY THE ANNENBERG/CPB PROJECT" "CAPTIONING PERFORMED BY THE NATIONAL CAPTIONING INSTITUTE, INC." "CAPTIONS COPYRIGHT 1987 CALIFORNIA INSTITUTE OF TECHNOLOGY," "THE CORPORATION FOR COMMUNITY COLLEGE TELEVISION, THE ANNENBERG/CPB PROJECT" "PUBLIC PERFORMANCE OF CAPTIONS PROHIBITED WITHOUT PERMISSION OF NATIONAL CAPTIONING INSTITUTE" "Annenberg Media" "¶" "For information about this and other Annenberg Media programs call 1-800-LEARNER and visit us at"