@@ "":53280,0:53281,0_@M$" PHYSICS ELECTRICITY II ":PL$"":60@M$" COPYRIGHT 1988 ":PL$PL$"":60@(M$" PAUL W. MCDANIEL ":PL$PL$"":60@2A$:A$"" 80A<L (M$):MI38L2:I1(M$)19AAFPL$MI)(M$,I)(M$,L(LI)):MIMI1::pAP"":10)"ALL RIGHTS RESERVED"AZ:(147):0,1:5,2:1,7:4,8:(142)Ad""An11)"***********************"Ax11)"* ELECTRICITY II *"B11)"***********************"B::=B 12)" A PHYSICS PROGRAM"GB""`B 16)"DEVELOPED BY"fBB 14)"PAUL W. MCDANIEL"B 14)"4295 WARREN WAY"B 14)"RENO, NV 89509"B""B12)"ALL RIGHTS RESERVED"B:"":""jC6)"THIS IS THE FIRST PROGRAM ON ELECTRICITY IN MY MODERN PHYSICS STUDY COURSE."::"":""C12)"THE CONCEPT OF FIELD"::""C""D6)"IN CLASSICAL PHYSICS, THE CONCEPT OF FIELD APPEARED AS AN AUXILLARY CONCEPT, IN CASES IN WHICH MATTER IS"D"TREATED AS A CONTINUUM. FOR EXAMPLE, IN THE CONSIDERATION OF THE HEAT CONDUCTIONIN A SOLID BODY, THE STATE OF THE BODY"E""IS DESCRIBED BY GIVING THE TEMPERATURE AT EVERY POINT OF THE BODY FOR EVERY DEFINITE TIME. MATHEMATICALLY,THIS MEANS"E,"THAT THE TEMPERATURE K IS REPRESENTED BY A FUNCTION OF THE SPACE COORDINATES AND THE TIME T. THE LAW OF HEAT"F6"CONDUCTION IS REPRESENTED BY A DIFFERENTIAL EQUATION WHICH EMBRACES ALLSPECIAL CASES OF THE CONDUCTION OF HEAT."`F@"THE TEMPERATURE IS A FUNCTION OF THE SPACE COORDINATES AND THE TIME.":sFJ:"":""FT"ANOTHER EXAMPLE OF A FIELD WOULD BE THE DESCRIPTION OF THE MOTION OF A LIQUID. AT EVERY POINT WITHIN THE LIQUID AT ANY "nG^"TIME THERE EXISTS A VELOCITY, WHICH IS DESCRIBED BY ITS THREE COMPONENTS WITH RESPECT TO THE AXES OF A COORDINATE"Gh"SYSTEM. THE COMPONENTS OF THIS VELOCITY (A VECTOR) ARE FUNCTIONS OF THE COORDINATES (X,Y,Z) AND THE TIME T."Hr:"":""JH|6)"THIS LEADS US TO DEFINE WHAT WE MEAN BY A FIELD."UH:""eH""kHH14)"DEFINITION"HI6)"BY FIELD WE MEAN A PHYSICAL PROPERTY EXTENDING OVER A REGION OF SPACE AND DESCRIBED BY A FUNCTION OF"sI"POSITION AND TIME. THE CONCEPT OF FIELD HAS GREAT AND GENERAL USEFULNESS IN PHYSICS."::"":""J6)"THE FIELD CONCEPT WAS DEVELOPED INTHE NINETEENTH CENTURY. FIELDS FAMILAR TO US ARE GRAVITATIONAL, ELECTRIC AND MAGNETIC FIELDS."J:"":""IJ14)" SCALAR FIELDS "::"":""J6)"FIELDS, LIKE THE TEMPERATURE OF THE AIR MASS OVER THE NORTH AMERICAN CONTINENT AT EVERY POINT IN THE VOLUME "BK"OF AIR ARE CALLED 'SCALAR FIELDS' BECAUSE A NUMERICAL FUNCTION CAN EXPRESS THE MAGNITUDE OF THE AIR TEMPERATURE"K"FROM POINT TO POINT IN SPACE. SUCH FIELDS CAN ALSO BE A FUNCTION OF TIME ASTHE TEMPERATURE CAN CHANGE FROM HOUR TO HOUR"K:"":""L&14)" VECTOR FIELDS "::"":""L06)"OTHER FIELDS CAN EXIST WHICH HAVE BOTH MAGNITUDE AND DIRECTION ASSOCIATED WITH EACH POINT IN SPACE. AN EXAMPLE"L:"WOULD BE THE MOVEMENT OF AN AIR MASS OVER THE NORTH AMERICAN CONTINENT AT SOME SPECIFIC TIME." MD:"":""MN6)"A SET OF FIELD EQUATIONS CAN DESCRIBE THE MOVEMENTS OF FIELDS IN SPACE AND TIME."::"":""Mb6)"FIELDS CAN INTERACT WITH EACH OTHER. FOR EXAMPLE, IF THE TEMPERATURE IS HIGH IN SOME REGION THE WARM AIR WILL")Nl"MOVE INTO THE REGION OF COOLER AIR "@Nv:"":""N6)"LET US TURN OUR ATTENTION TO THE SPECIFIC CASE OF THE GRAVITATIONAL FIELDPRODUCED BY A POINT MASS."N/O6)"SUPPOSE THAT WE HAVE A MASS M AND THAT WE PLACE AT DIFFERENT POSITIONS AROUND M, ANOTHER MASS M'. THE MASS M'"iO"WILL EXPERIENCE A FORCE AT EACH POSITIONGIVEN BY":O12)" GMM'"O12)"F = - U "O12)" 2 R"O12)" R "::"":""]P6)"THE NEXT FIGURE ILLUSTRATES THE GRAVITATIONAL FIELD PRODUCED BY A POINT MASS AT SEVERAL POINTS NEAR IT."::""P 1,1:1,2:1,165,100,15,12:1,20,12,"M":1,165,60 165,40P  1,165,60 168,57 162,57 165,60P 1,32,12,"E"P 1,20,4,"A"Q* 1,200,100 245,1000Q4 1,200,100 203,103 203,97 200,100AQ> 1,2,12,"C"TQH 1, 4,12,">"fQR 1,20,15,"^"xQ\ 1,20,16,""Qf 1, 20,18,"D"Qp 1,6,22,"GRAVITATIONAL FIELD PRODUCED BY POINT MASS"Qz 1,2: 1,20,12,"M"Q 12: 0:""tR6)"THE MASS M PRODUCES, IN THE SPACE AROUND IT A PHYSICAL SITUATION WHICH WECALL A 'GRAVITATIONAL FIELD', AND WHICH"R"IS RECOGNIZED BY THE FORCE THAT M EXERTSON ANOTHER MASS, M', BROUGHT INTO THAT REGION.":RS6)"THE GRAVITATIONAL FIELD STRENGTH PRODUCED BY THE MASS M AT A POINT P IS DEFINED AS THE FORCE EXERTED ON THE UNIT"sS"OF MASS PLACED AT P. THEN"ySS12)" GMM' "S12)"G = - U"S12)" 2 R"S12)" R"T" "YT"THUS THE GRAVITATIONAL FIELD G IS IN THEDIRECTION OPPOSITE TO THAT OF THE UNIT"T"VECTOR U , WHICH GOES FROM THE MASS"T" R"T"PRODUCING THE FIELD TO THE POINT WHERE THE FIELD IS COMPUTED."::""`U6)"A GRAVITATIONAL FIELD CAN BE REPRESENTED PICTORIALLY BY 'LINES OF FORCE'. A LINE OF FORCE IS DRAWN IN SUCH"U$"A WAY THAT AT EACH POINT THE DIRECTION OF THE FIELD IS TANGENT TO THE LINE THAT PASSES THROUGH THE POINT. THE LINES"EV."OF FORCE ARE DRAWN SO THAT THEIR DENSITYIS PROPORTIONAL TO THE STRENGTH OF THE FIELD."::""UV8""}VB12)" MAGNETIC FIELDS "::""VL6)"FROM THE DAWN OF HISTORY MEN OBSERVED THAT CERTAIN IRON ORES, SUCH ASLOADSTONE, HAVE THE PROPERTY OF "qWV"ATTRACTING SMALL PIECES OF IRON. IT HAS BEEN FOUND THAT THIS PROPERTY IS EXHIBITED BY IRON,COBALT, AND MANGANESE"W`"IN THE NATURAL STATE AND BY MANY COMPOUNDS OF THESE METALS. THIS PROPERTYIS UNRELATED TO GRAVITATION. IT IS NOT "nXj"EXHIBITED BY ALL BODIES AND APPEARS TO BE CONCENTRATED AT CERTAIN SPOTS IN THE MINERAL ORE. IT IS NOT RELATED TO THE "Xt"ELECTRICAL INTERACTION BECAUSE BITS OF PAPER OR CORK BALLS ARE NOT ATTRACTED TOTHESE MINERALS.":SY~6)"THE NAME 'MAGNETISM' WAS GIVEN THIS PROPERTY BECAUSE TRADITION HAS IT THAT THE PROPERTY WAS FIRST OBSERVED IN"Y"THE ANCIENT CITY OF MAGNESIA IN ASIA MINOR. A MAGNETIZED BODY IS CALLED A MAGNET AND THE REGIONS OF A BODY WHERE "$Z"THE MAGNETISM APPEARS TO BE CONCENTRATEDARE CALLED 'MAGNETIC POLES'"::""Z6)"ONE CAN DEMONSTRATE THAT THE EARTHIS A HUGE MAGNET BY SUSPENDING A MAGNETIZED ROD AT ANY POINT ON THE "["SURFACE OF THE EARTH AND ALLOWING IT TO ROTATE FREELY ABOUT THE VERTICAL. THE ROD WILL ORIENT ITSELF SO THAT THE SAME "["END ALWAYS POINTS TOWARD THE NORTH GEOGRAPHIC POLE. WE CALL THE END OF THE MAGNET WHICH POINTS TOWARD THE NORTH "\"GEOGRAPHIC POLE AS THE 'NORTH-SEEKING' OR 'NORTH POLE' AND DESIGNATE IT BY THE LETTER N. THE OTHER POLE WE CALL THE"\"'SOUTH-SEEKING' OR THE 'SOUTH POLE'. WE LEARNED EARLY IN OUR LIFE THAT LIKE MAGNETIC POLES REPEL EACH OTHER AND THAT"]"UNLIKE POLES ATTRACT EACH OTHER. WE KNOWTHAT MAGNETIZED BODIES ALWAYS EXHIBIT POLES IN PAIRS, EQUAL AND OPPOSITE"]6)"ALTHOUGH MANY STUDIES HAVE BEEN MADE TO ISOLATE A MAGNETIC POLE OR TO IDENTIFY A FUNDAMENTAL PARTICLE HAVING"]"ONLY ONE KIND OF MAGNETISM NO SUCH ENTITY HAS BEEN DISCOVERED."]:""]"":1,2)^6)" DEFINITION OF MAGNETIC FIELD "::""^ 6)"IF WE PLACE AN ELECTRIC CHARGE Q NEAR THE POLE OF A PERMANENT MAGNET WE OBSERVE NO FORCE ACTING ON THE CHARGE"_"DUE ONLY TO THE PRESENCE OR ABSENCE OF THE MAGNET. BUT IF WE FIRE THE TEST CHARGE Q THROUGH A POINT P WITH A "K_" "_("VELOCITY V, WE FIND A SIDEWAYS FORCE F ACTS ON IT IF THE MAGNET IS IN PLACE. BYA SIDEWAYS FORCE WE MEAN A FORCE AT"_2" "J`<"RIGHT ANGLES TO V. WE SHALL DEFINE B,THEMAGNETIC FIELD, AT THE POINT P IN TERMS "Y`F" "p`P"OF F, V, AND Q."`Z6)"IF WE KEEP THE MAGNITUDE OF THE VELOCITY OF THE TEST CHARGE Q UNCHANGED BUT THE DIRECTION OF THE VELOCITY "ad"IS VARIED, WE FIND THAT THE FORCE WILL ALWAYS REMAIN AT RIGHT ANGLES TO THE VELOCITY BUT ITS MAGNITUDE WILL CHANGE."::""bn6)"FOR A PARTICULAR ORIENTATION OF THE VELOCITY THE MAGNITUDE OF THE FORCE BECOMES ZERO. WE DEFINE THIS ORIENTATION"bx" ""%p CIRCLE1,160,100,20,407p1, 38,11,""Ip1, 38,12,"B"p 1,160,100,3,2:1,160,100 160,40 163,43 157,43 160,40:1,160,100 200,40 202,45 194,43 200,40p1,17,5,"":1,26,5,""p1,17,6,"V":1,26,6,"F"q 1,6,17,""/q1,6,18,"V = POSITIVE CHARGE VELOCITY"?q 1,6,19,""aq*1,6,20,"B = MAGNETIC FIELD"qq41,6,21,""q>1,6,22,"F = MAGNETIC FORCE (INTO THE SCREEN)"qH 20: 0:""LrR6)"WE MAY WRITE THE RELATION BETWEEN CHARGE VELOCITY, MAGNETIC FIELD AND MAGNETIC FORCE BY THE VECTOR PRODUCT":br\12)" "rf12)"F = QV X B.":""rp6)"WHEN A CHARGED PARTICLE MOVES IN AREGION WHERE THERE AN ELECTRIC FIELD ANDA MAGNETIC FIELD THE TOTAL FORCE IS":sz12)" "2s12)"F = Q(E + V X B.":s6)"THIS EXPRESSION IS CALLED 'THE LORENTZ FORCE.'"::"":"" t6)"BECAUSE THE MAGNETIC FORCE IS PERPENDICULAR TO THE VELOCITY, ITS WORK IS ZERO AND THEREFORE THERE IS NO CHANGE"Mt"IN THE KINETIC ENERGY OF THE PARTICLE."::"":""Wt 1,1xt1,6,1,"THE RIGHT HAND RULE"t1,3,20,"* THUMB IN DIRECTION OF FORCE * FOREFINGER IN DIRECTION OF PARTICLE MOTION"u1,3,23,"* MIDDLE FINGER IN DIRECTION OF FIELD"5u1,190,105 180,100 172,48u1,55,83 140,82 150,86:1,55,88,8,5,180,360:1,55,93 120,93:1,92,92 92,82u1,70,92 70,82u 1,167,46,6,7:1,230,75,80,64,260,300:1,167,46,1 v1,103,117,6,5,180,360:1,106,128,6,5,180,360`v 1,112,143,50,48,320,360:1,90,108,8,6:1,115,100,8,6,0,180:1,105,103,8,6,20,150v DRAW1,102,103 TO 64,135 TO 68,131 TO 64,128 TO 64,135v 1,93,115 120,105:2:1,116,100 60,120 65,121 61,116 60,120:1w$ 1,142,117,5,3:1,138,126,5,3,w. 1,142,117,1:1,138,126,1nw8 1,99,113 144,113:1,102,122 142,121:1,104,132 140,131wB ,155,80,80,64,160,210wL 1,4,10,"V":1,6,16,"B":1,6,15,"":1,4,9,"":1,23,5,"^ F":1,23,4," ":1,23,6,""xV I 0 4 2:1,166,70I 174,70I: IEx` 1,40,75 100,75:1,4,9,"_":1,40,76 100,76cxj 20: 0:"":""xt 6)" UNIT OF MAGNETIC FIELD STRENGTH "::y~ 6)"THE UNIT OF MAGNETIC FIELD STRENGTH IS THE TESLA, IN HONOR OF NICHOLAS TESLA (1856-1943)."y 6)"ONE TESLA CORRESPONDS TO A MAGNETIC FIELD THAT PRODUCES A FORCE OF ONE NEWTON ON A CHARGE OF ONE COULOMB "y "MOVING PERPENDICULAR TO THE FIELD AT A VELOCITY OF ONE METER PER SECOND."::"":""z 14)" PROBLEM ":""z 6)"CALCULATE THE FORCE EXERTED ON A COSMIC RAY PROTON WHICH ENTERS THE MAGNETIC FIELD OF THE EARTH."::"":""z 14)" SOLUTION ":::6)"THE STUDENT SHOULD MAKE THIS CALCULATION BEFORE PROCEEDING"::""r{ 6)"ASSUME THAT THE PROTON MOVES WITH A VELOCITY OF 1E+7 METERS PER SECOND ANDTHAT IT ENTERS THE EARTHS MAGNETIC FIELD"{ "AT THE EQUATOR WHERE THE FIELD STRENGTH IS ABOUT 1.3E-5 TESLA. ASSUME ALSO THAT THE PROTON MOVES IN A DIRECTION"f| "PERPENDICULAR TO THE FIELD. SINCE THE CHARGE ON THE PROTON IS Q = +E= 1.6E-19 COULOMBS THE FORCE ON THE PROTON IS":| 1,135,96,7,4:1,145,107,7,4:1,142,117,5,3:1,138,126,5,3:1,135,96,1:1,145,107,1| 12)"F = QVB = 2.1E-17 NEWTONS.":b} 6)"THIS IS ABOUT 1E+9 TIMES LARGER THAN THE FORCE OF GRAVITY ON THE PROTON (1.6E-26 NEWTONS). THE ACCELERATION DUE"} "TO THIS MAGNETIC FORCE IS":} 12)"A = F/M = 1.2E+10 METERS/SEC"::~ "THUS THE MAGNETIC ACCELERATION OF THE PROTON IS ALSO 1E+9 TIMES LARGER THAN THE ACCELERATION DUE TO GRAVITY."::"":""~ " MOTION OF A CHARGED PARTICLE IN A UNIFORM MAGNETIC FIELD "::"" 6)"CONSIDER THE CASE OF A CHARGED PARTICLE MOVING IN THE DIRECTION OF THE MAGNETIC FIELD. THE FORCE IS THEN GIVEN BY"0( 6)"F = QVB":2 6)"SINCE THIS FORCE IS PERPENDICULAR TO THE VELOCITY, ITS EFFECT IS TO CHANGE THE DIRECTION OF THE VELOCITY ")< "WITHOUT CHANGING ITS MAGNITUDE, RESULTING IN UNIFORM CIRCULAR MOTION. NOW WE HAVE SEEN ELSEWHERE THAT THIS IS"[F "CENTRIPETAL ACCELERATION AND IS GIVEN BY"nP 12)" 2"Z 12)" MV "d 12)"F = "n 12)" R":x 6)"THE NEXT FIGURE ILLUSTRATES THIS CASE."::""뀂 1,1@ 1,2,1,"CIRCULAR PATH OF A POSITIVE CHARGE IN A UNIFORM MAGNETIC FIELD"u I 0 13: J 0 20:1,6J,6I,".": J: I 1,28,11," SCREEN)" 1,28,10,"B (OUT FROM" 1,27,9," "Ձ 1,28,13,"OMEGA (INTO" 1,28,14," SCREEN)"S 1,140,100,50,40:1,16,17,"<+":1,17,7,"+>":1,140,100 100,100:1,140,99 100,99:1,11,12,"_"m 1,6,20," 2" 1,6,21," MV" 1,6,22,"WE HAVE = QVB" 1,6,23," R"ۂ 1,25,22,"OR R = MV/QB" 1,14,11,"R": 20:"": 0:""N " MAGNETIC FORCE ON AN ELECTRIC CURRENT "::"":""Ƀ" 6)"WHEN A CONDUCTOR CARRYING AN ELECTRIC CURRENT IS PLACED IN A MAGNETICFIELD IT EXPERIENCES A FORCE WHICH IS "C, "THE RESULTANT OF THE MAGNETIC FORCES EXERTED ON EACH OF THE MOVING CHARGES. THIS FORCE IS PERPENDICULAR TO THE"6 "CURRENT AND TO THE MAGNETIC FIELD. THE NEXT FIGURE WILL ILLUSTRATE THIS POINT."::"": 1,1)@ 1,2,1,"VECTOR RELATION BETWEEN THE MAGNETIC FORCE ON A CURRENT CARRYING CONDUCTOR, THE CURRENT, AND THE MAGNETIC FIELD."^J I 0 12: J 0 20:1,6J,6I,".": J: IwT 1,28,11," SCREEN)"^ 1,28,10,"B (OUT FROM"h 1,27,9," "r 1,140,50,10,4: 1,140,150,10,4,15,280:1,140,125,10,4:1,140,110,10,4, 15,280q| 1,130,52 130,148:1,150,52 150,148:1,140,170 140,90:1,140,80 140,35 143,38 137,38 140,35:1,142,130,1 1,142,80,1:1,138,132 1,19,5,"I (CURRENT) = NQVS" :1,140,100 180,100:1,140,97 180,97:1,22,12,">" 1,23,12," FORCE"* 1,19,15,"S=CROSS SECTION AREA"; 1,17,19,""r 1,17,20,"^":1,6,22,"N PARTICLES PER UNIT VOLUME" 20: 0:"" 6)"CONSIDER THAT THE CONDUCTOR IN THEFOREGOING FIGURE HAS A CHARGE Q MOVING WITH A VELOCITY V THROUGH IT. IF THERE"~ "ARE N CHARGED PARTICLES PER UNIT VOLUME,THEN THE TOTAL NUMBER OF PARTICLES PASSING THROUGH THE UNIT AREA PER UNIT " "TIME IS NV. SO THE CURRENT DENSITY VECTOR IS"ʈ 12)" " 12)"J = NQV. AND THE CURRENT IS": 12)"I = JS = NQVS.":g 6)"WHEN THE CONDUCTOR IS IN A MAGNETIC FIELD THE FORCE ON EACH CHARGE IS" 12)" ": 12)"F = Q(E + V X B)":& 6)"SINCE THERE ARE N CHARGED PARTICLES PER UNIT VOLUME, THE FORCE PERUNIT VOLUME IS"%0 12)" "H: 12)"F = NQV X B = J X B.":D 6)"THE TOTAL FORCE ON A SMALL VOLUME DV OF THE MEDIUM IS"N 12)" "֊X 12)"DF = FDV = J X BDV."::"":""8b " MAGNETIC FIELD AROUND A STRAIGHT WIRE CARRYING A CURRENT ":""l 6)"KEEP IN MIND THAT THE DIRECTION OFTHE 'CURRENT FLOW' IS OPPOSITE TO THE DIRECTION OF THE ELECTRON FLOW"::""v 1,16 1,5,1,"THE RIGHT HAND RULE FOR DETERMINING THE DIRECTION OF THE MAGNETIC FIELD AROUND A WIRE CARRYING A CURRENT" 1,6,19,"GRASP THE CURRENT CARRYING WIRE IN THE RIGHT HAND WITH THE EXTENDED THUMB"݌ 1,0,21,"POINTING IN THE DIRECTION OF THE CURRENT THE CURLED FINGERS WILL"$ 1,25,22,"INDICATE THE CIRCULAR DIRECTION OF THE MAGNETIC FIELD"F 1,190,105 180,100 172,48 1,167,46,6,7:1,230,75,80,64,260,300:1,140,140,80,64,330,8:1,167,46,1 1,100,91,8,4,180,360:1,100,104,8,5,180,360:1,103,116,7,5,180,360:1,106,128,7,5,180,360K 1,135,96,7,4:1,145,107,7,4:1,142,117,5,3:1,138,126,5,3:1,135,96,1:1,145,107,1 1,142,117,1:1,138,126,1:1,16,6,"^ I":1,131,55 131,90:1,131,132 131,160Ɏ 1,100,86 140,92:1,100,97 138,100 1,100,98 144,104:1,99,110 144,112:1,102,123 142,122:1,104,133 140,131: ,155,80,80,64,160,210h 1,180,140 200,140:1,185,100 200,100я 1,140,94 140,99:1,150,104 150,109:1,145,114 145,119:1,140,124 140,129:1,162,41 171,41 I 0 4 2:1,166,70I 174,70I: I 20: 0:""! ""W* 12)" MAGNETIC MATERIALS "::"":""Ԑ4 6)"SOME MATERIALS ARE MAGNETIC AND SOME MATERIALS ARE NOT MAGNETIC. LET US TRY TO UNDERSTAND WHY THIS IS SO."::""`> 6)"WE MAY PICTURE THE ORBITING ELECTRONS IN AN ATOM AS FORMING TINY CURRENT LOOPS. A CURRENT LOOP PRODUCES A DIPOLE MOMENT"rH 12)" "R 12)"M = IA":\ 6)"THE COMPLETE PATH OF AN ELECTRON IN A CIRCULAR ORBIT OF RADIUS R IS DESCRIBED BY":f 12)"2R = VT":jp "WHERE V IS THE ORBITAL SPEED AND T IS THE PERIOD OF REVOLUTION. THE ELECTRIC CURRENT E IS THEN":z 12)"I = E/T = EV/2R" 12)" 2"ڒ "AND THE MAGNITUDE OF THE ELECTRON DIPOLEMOMENT IS" 12)"M = IA = EV(R)/2R = EVR/2"::"" 6)"IN ADDITION TO THE MAGNETIC MOMENTRESULTING FROM THE ORBITING ELECTRON THEELECTRON ITSELF HAS AN INTRINSIC 'SPIN' MAGNETIC MOMENT." 6)"A THIRD CONTRIBUTION TO THE MAGNETIC MOMENT OF AN ATOM IS ASSOCIATED WITH THE NUCLEUS." 6)"THE MAGNETIC EFFECTS OF THESE COMPONENTS IN MOST ATOMS TEND TO CANCEL EACH OTHER SO THAT MOST ATOMS ARE NOT MAGNETIC."::"" 6)"ATOMS OF SOME MATERIALS, HOWEVER, HAVE EFFECTIVE MAGNETIC MOMENTS. NORMALLY SUCH MATERIALS DO NOT EXHIBIT " "MAGNETIC EFFECTS BECAUSE THEIR ATOMS ARERANDOMLY ORIENTED. BUT WHEN PLACED IN AN EXTERNAL MAGNETIC FIELD THE ATOMIC" "MAGNETS ARE ALIGNED WITH THE EXTERNAL FIELD AND THE MATERIAL AS A WHOLE ACTS AS A MAGNET. THE STRENGTH OF THE INDUCED" "MAGNETIZATION DEPENDS ON THE DEGREE OF ALIGNMENT. IT HAS BEEN OBSERVED THAT THERE IS A DECREASE OF INDUCED " "MAGNETIZATION WITH INCREASING TEMPERATURE. THE INDUCED MAGNETIZATION MAY BE MADE PERMANENT IN CERTAIN "O "MATERIALS BY ALLOWING A SUFFICIENTLY HOTMATERIAL TO COOL IN A MAGNETIC FIELD."ߗ 6)"MOST MAGNETIC MATERIALS ARE CLASSIFIED INTO THREE MAJOR TYPES: PARAMAGNETIC, FERROMAGNETIC, AND DIAMAGNETIC."::""""10)" PARAMAGNETISM "::""6)"FOR MATERIALS IN WHICH THE THERMALEFFECTS ARE APPRECIABLE THE DIPOLE ALIGNMENT IS SMALL AND THE INDUCED "$"MAGNETISM IS RELATIVELY WEAK. SUCH MATERIALS ARE CALLED PARAMAGNETIC AND INCLUDE PLATINUM, ALUMINUM, NEON AND OXYGEN.".6)"THE MAGNETIZATION OF A MATERIAL IS EXPRESSED IN TERMS OF ITS PERMEABILITY (MU). THE PERMEABILITY OF A VACUUM IS"8"(MU). WE WRITE PERMEABILITY AS"B" 0"ڙL10)"(MU) = K (MU)"V10)" M 0":3`"WHERE (MU) IS THE PERMEABILITY OF A MATERIAL, AND"Lj8)"K = (MU)/(MU)"ft8)" M 0"~6)"IS THE RELATIVE PERMEABILITY. A VACUUM HAS A K = 1."Κ6)" M"::"":""I6)"THE RELATIVE PERMEABILITY OF PARAMAGNETIC MATERIALS IS ONLY SLIGHTLY GREATER THAN UNITY, INDICATING LITTLE ""MAGNETIC DIPOLE ALIGNMENT WHEN A PARAMAGNETIC MATERIAL IS PLACED IN A MAGNETIC FIELD."::""Ǜ""雰12)" FERROMAGNETISM ":b6)"FERROMAGNETIC MATERIALS ARE USED IN MOST COMMON MAGNETIC APPLICATIONS. THESE INCLUDE IRON, NICKEL, COBALT, "ߜ"SEVERAL RARE EARTH ELEMENTS, AND SOME ALLOYS OF THESE AND OTHER ELEMENTS, SUCHAS ALNICO, AN ALUMINUM-NICKEL-COBALT "^"ALLOY. IN FERROMAGNETIC MATERIALS, A SPECIAL EFFECT PRODUCES A HIGH DEGREE OFMAGNETIC DIPOLE ALIGNMENT IN A MAGNETIC""FIELD IN SPITE OF THE THERMAL MOTIONS OFTHE ATOMS. AS A RESULT, FERROMAGNETIC PERMEABILITIES ARE OF THE ORDER OF100- 100000."::""h6)"A SPECIAL FORM OF INTERACTION OCCURS BETWEEN THE ATOMS OF FERROMAGNETIC MATERIALS AND CAUSES THE ""MAGNETIC MOMENTS OF THE ATOMS TO LOCK INPARALLEL DIRECTIONS. THIS EFFECT GIVES RISE TO 'DOMAINS', OR LOCAL REGIONS OF"b"ALIGNMENTS WITHIN A MATERIAL. WHEN PLACED IN A MAGNETIC FIELD, A DOMAIN AS A WHOLE MAY BECOME ALIGNED WITH THE ""FIELD. DOMAINS THAT ARE ORIENTED MAY GROW AT THE EXPENSE OF THOSE THAT ARE NOT. IF THE TEMPRERATURE IS RAISED ABOVE"] "A CERTAIN CRITICAL TEMPERATURE FOR A MATERIAL THE COUPLING DISAPPEARS AND THEMATERIAL BECOMES PARAMAGNETIC. THIS"۠"CRITICAL TEMPERATURE IS CALLED THE CURIETEMPERATURE IN HONOR OF PIERRE CURIE (1859-1906). THE CURIE TEMPERATURE FOR""IRON IS 770 DEGREES CENTIGRADE."::"":""9(12)" DIMAGNETISM "::""26)"WHEN PARAMAGNETIC AND FERROMAGNETIC MATERIALS ARE BROUGHT NEARTHE POLE OF A STRONG MAGNET, THEY ARE ".<"ATTRACTED TO IT BECAUSE OF THE INDUCED MAGNETIZATION. HOWEVER CERTAIN MATERIALS, CALLED DIAMAGNETIC, ARE"?F"REPELLED."P6)"SUCH MATERIALS INCLUDE WATER, LEAD, COPPER, BISMUTH, AND HYDROGEN." Z"DIMAGNETISM ARISES FROM MAGNETIC FORCE EFFECTS ON THE ORBITAL ELECTRONS OF ATOMS. DIAMAGNETISM IS A SMALL EFFECT."d"IT OCCURS IN ALL SUBSTANCES. THE MAGNETIC FORCE CAUSES THE ORBITAL VELOCITIES OF THE ELECTRONS TO INCREASE " n"OR DECREASE DEPENDING ON THE FORCE WHICHIS DETERMINED BY THE ORIENTATION OF THE FIELD AND THE ORBITAL VELOCITY. THIS"x"EFFECT IS EASILY DETECTED IN MATERIALS WITHOUT FERROMAGNETISM AND PARAMAGNETISM BUT IS MASKED IN THESE LATER MATERIALS."::""""Ĥ14)" THE BETATRON "::""A6)"ONE CAN LEARN A GREAT DEAL ABOUT THE INTERACTION BETWEEN MOVING ELECTRIC CHARGES AND MAGNETIC FIELDS BY STUDYING ""THE ACTION WITHIN A BETATRON, A DEVICE INVENTED BY D KERST IN 1941. IN THIS DEVICE ELECTRONS ARE INJECTED INTO A "="REGION WHERE A VARYING MAGNETIC FIELD EXISTS. IF THE FIELD HAS AXIAL SYMMETRY ELECTRONS WILL BE ACCELERATED BY THE""ELECTRIC FIELD ASSOCIATED WITH THE DEVICE. AS AN ELECTRON GAINS VELOCITY ITS PATH WILL BE BENT BY THE MAGNETIC "7"FIELD. IF THE FIELDS ARE ADJUSTED, THE ORBIT OF THE ELECTRON WILL BE A CIRCLE. IN EACH REVOLUTION THE ELECTRON WILL"ȧ"BE ACCELERATED AND WITH EACH REVOLUTION THE ELECTRON GAINS ENERGY. THE GREATER THE NUMBER OF REVOLUTIONS, THE GREATED THE ENERGY"::""֧1,1:1,2"1,0,0,"ACCELERATING TUBE AND POLE FACES OF A BETATRON"?1,160,10,100,50,115,245f1,17,6,"MAGNET":1,17,16,"MAGNET"1,160,60,90,30,65,295:1,160,60,72,20,80,280 : TUBE1,70,10 70,30:1,250,10 250,30:1,70,90 70,140:1,250,90 250,1401,70,30 90,65:1,250,30 230,65W1,160,88,1:1,20,10,"A":1,250,90 230,62:1,70,90 90,62t"1,160,69,100,50,115,245,1,6,19,"A = TORROIDAL TUBE"6 10:"": 0@6)"THE MAGNETIC FIELD IN THE BETATRONHAS SEVERAL FUNCTIONS:":1J6)"(1) IT GUIDES THE ELECTRONS IN A CIRCULAR PATH,"ƪT6)"(2) ITS CHANGING MAGNETIC FIELD GENERATES AN ELECTRIC FIELD THAT ACCELERATES THE ELECTRONS IN THIS PATH,"::^6)"(3) IT KEEPS THE RADIUS OF THE ORBIT OF THE ELECTRONS ESSENTIALLY CONSTANT,"Ыh6)"(4) IT INTRODUCES THE ELECTRONS INTO ORBIT INITIALLY AND REMOVES THEM FROM ORBIT AT PROPER TIME,"Mr6)"(5) IT PROVIDES A RESTORING FORCE THAT STABILIZES THE ORBIT OF THE ELECTRONS BOTH VERTICALLY "k|6)" AND RADIALLY.":欆6)"IT IS POSSIBLE TO DO ALL THESE THINGS BY PROPER SHAPING AND CONTROL OF THE MAGNETIC FIELD."::"":""b6)"THE CURRENT IN THE COILS OF THE MAGNET IS MADE TO ALTERNATE PERIODICALLY60 TIMES A SECOND TO PRODUCE A CHANGING"⭚"MAGNETIC FLUX THROUGH THE ORBIT. THE NEXT FIGURE SHOWS A CROSS SECTION OF A BETATRON WITH ITS MAGNETS, COILS AND THE"^"DOUGHNUT SHAPED ACCELERATING TORUS. THE ELECTRON ORBIT IS SHOWN, A INDICATING THAT THE ELECTRON IS MOVING INTO THE""SCREEN AND A DOT INDICATIG THAT THE ELECTRON IS COMING OUT OF THE SCREEN."::"": 1,1鮸1,6,1,"CROSS-SECTION OF A BETATRON"d1,40,78 100,78 100,98 200,98 200,78 260,78 260,128 200,128 200,108 100,108 100,128 40,128 40,78I05:J01:1,6I,10J,".":J:II05:J01:1,6I,14J,".":J:IݯI05:J01:1,26I,10J,"+":J:II05:J01:1,26I,14J,"+":J:In1,70,102,12,6:1,230,102,12,6:1,70,102,3,2:1,70,102,2,1:1,230,98 230,106:1,226,102 234,1021,16,8,"MAGNET":1,16,18,"MAGNET"Ű1,14,11,"S S S S":1,14,14,"N N N N"1,9,8,"C":1,28,8,"C":1,9,17,"C":1,28,17,"C"U1,6,20,"C = COILS":1,34,12,"D":1,240,98 270,98:1,6,21,"D = DOUGHNUT SHAPED TORUS"s& 10: 0:"":""06)"IF THE ELECTRONS ARE TO CIRCULATE IN THE DIRECTION SHOWN THEY MUST DO SO DURING THE POSITIVE HALF-CYCLE, MARKED "n:"AC IN THE NEXT FIGURE. THE ELECTRIC FIELDS SET UP BY THE CHANGING MAGNETIC FIELD ACCELERATES THE ELECTRONS. SINCE"D"WE WISH THE ELECTRONS TO BE SPEEDED UP WE MUST CHOOSE THE CORRECT DIRECTION FORTHE ACCELERATING FIELD."::""N""pX6)"CONSIDER AN ELECTRON AT POINT P INTHE NEXT FIGURE. IF THE VELOCITY OF THE ELECTRON AND THE MAGNETIC FIELD IS JUST"b"RIGHT THE ELECTRON WILL DESCRIBE A CIRCLE OF RADIUS R. THE ELECTRIC FIELD WILL PRODUCE A TANGENTIAL MOTION"l"FROM NEWTONS SECOND LAW OF MOTION WE HAVE"9v12)"M DV/DT = F = -E E"Z12)" T 0":z6)" D ER D B"6)"OR M V = AVE (A)"Ĵ6)" DT 2 DT":=6)"TO GENERATE CIRCULAR MOTION THE MAGNETIC FIELD MUST PRODUCE THE NECESSARY CENTRIPEDAL FORCE. USING":L12)" 2"_12)"MV /R":6)"FOR THE CENTRIPEDAL FORCE WE HAVE"::""10)" 2"10)"MV "ӵ10)" = EVB OR MV = ERB"10)" R"6)"TAKING THE TIME DERIVATIVE WE HAVE":<10)"M DV/DT = ER DB/DT (B)": 6)"COMPARING EQUATIONS (A) AND (B) WEFIND THAT FOR THE ELECTRON TO DESCRIBE A CIRCULAR ORBIT AT A RADIUS R THE"Ӷ"MAGNETIC FIELD MUST BE": 10)" 1"*10)"B = B "410)" 2 AVE":<>6)"NOW FOR THE FIGURE ......."::""EH1,1R1,2,0,"ELECTRIC FIELD PRODUCED BY A TIME DEPENDENT MAGNETIC FIELD HAVING CYLINDRICAL SYMMETRY"\1,308,100,3,2:1,308,100,2,1:1,258,100,50,40&f1,308,100 308,40:1,36,4,"E ^":1,36,3,""Lp1,258,100 308,100:1,34,11,"R"z1,31,13,"Z":1,258,100,2,1:1,16,23,"Z = Z-AXIS":1,37,13,"P":1,16,22,"E = ELECTRIC FIELD":1,16,21,""1,29,18,"TOP VIEW":1,10,18,"SIDE VIEW":1,16,19,"":1,16,20,"M = MAGNETIC FIELD"'1,100,100,60,20=1,75,50 75,140Z I0 7:1,9I,6,"^": J0 56 7:1,75J,50 75J,140:湶1,100,160 100,30 96,34 104,34 100,30:1,100,100 160,100:1,160,100,2,1:1,20,13,"P"1,16,12,"R":1,10,4,"Z"1,65,140 65,50 67,52 63,52 65,50:1,50,140 50,50 52,52 48,52 50,50:1,30,140 30,50 32,52 28,52 30,50 1,140,140 140,50 137,52 142,52 140,50:1,153,140 153,50 155,52 151,52 153,50:1,172,140 172,50 170,52 174,52<1,174,52 172,50:1,23,6,"B":1,23,5,""O 20:"": 0_""̻6)"THE NEXT FIGURE REPRESENTS THE VARIATIONS IN THE MAGNETIC FLUX IN A TYPICAL BETATRON."::""H1:I1:K0:L0:R49:V20:G0:O0:W0 4900""Y = H * SIN (I*X - K) + L6$KK3.14159180P. 0,1:1,3:4,1: 1,1[8 5390sB 1,160,0 160,199L 1,0,100 319,100V 1,0,13,"0"` 1,9,13,"4"j 1,19,13,"8"Ҽt 1,30,13,"12"~ 1,38,13,"16" T 100 199 R 1,155,T 165,T: T. U 100 0 RH 1,155,U 165,U: U] J360 1 VuWW2:G0:FJ180CH(IFK)LD 360F180E D53120X (E.5)ν C0 5140ؽGCR C0 G(G.5)  C0 G(G.5)Y100G# W3 51705( 1,A,B X,Y=2AXI<BY: JbF 1,A,B X,Y: 5450vP J1 360 VZG0:WW2dFJ3.14159180nCH(IFK)LxDF180ȾED53120ھX160(E.5)ﾖ C0 5310GCR C0 Y(G.5)& C0 Y (G.5)2Y100GE W3 5340W 1,A,B X,YgAX:BY: Jڿ 1,A,B X,Y :1,40,50 40,100:1,36,90,1:1,3,10,"A":1,2,19,"A = ACCELERATION":1,6:1,42,90,1:1,6,10,"D"/1,200,50 200,100:1,3:1,196,90,1:1,23,10,"A":1,6:1,204,90,1:1,26,10,"D":l1,2:1,2,20,"D = DECELLERATION":1,24,4,"INA BETATRON"1,24,3,"MAGNETIC FLUX":1,17,0,"WEBERS":1,16,6,"+1.8":1,16,18,"-1.8":1,16,24,"-3.6":1,0,14,"T, 10 SEC":1,2,13," -3": 5520 NH(I2 K) L  N0 5440*"ONR@, O0 O(O.5)V6 O0 O(O.5)p@B100O:O0:X160:O0vJ:TNH(IOK)L^N0 5510:5510hONRrO0O(O.5)|O0O(O.5)Y100O: 20:"": 0\š6)"THE TIME AVERAGE VALUE OF THE FLUXDURING THE QUARTER-CYCLE OF THE ACCELERATION PHASE IS":r¤12)"1.8 WEBERS"®12)" = 430 VOLTS"¸12)"4.2E-3 SEC":&6)"THE ELECTRON WILL THUS INCREASE ITS ENERGY BY 430 VOLTS EVERY TIME IT MAKES A TRIP AROUND THE ORBIT IN THE ""CHANGING FLUX. IF THE ELECTRON GAINS THIS AMOUNT PER REVOLUTION, IT MUST MAKE230,000 REVOLUTIONS TO GAIN 100 MILLION"2"ELECTRON VOLTS FINAL ENERGY. FOR AN ORBIT RADIUS OF 33 INCHES, THIS CORRESPONDS TO A PATH LENGTH OF SOME 750MILES."::""B""6)"IN AN OPERATING BETATRON THE ELECTRONS ARE MOVED TO A LARGER ORBIT BYAN AUXILIARY SET OF CURRENT CARRYING ":"COILS. THIS ALLOWS THE ELECTRONS TO BE REMOVED FROM THE BETATRON OR TO STRIKE AN INTERNAL TARGET WHICH BECOMES A "f"SOURCE OF X-RAYS."::"":""12)" ELECTRIC CURRENTS "::"":""6)"MANY PRACTICAL APPLICATIONS OF ELECTRICITY INVOLVE ELECTRIC CURRENTS. WHILE CURRENTS MAY BE PRODUCED FROM""STORED ELECTROSTATIC ENERGY, AS IN A CAPACITOR DISCHARGING THROUGH A WIRE CONNECTED ACROSS IT, MOST CURRENTS ARE"&"PRODUCED BY BATTERIES OR GENERATORS. THESE DEVICES PRODUCE A POTENTIAL DIFFERENCE BY CONVERSION OF OTHER FORMS "N0"OF ENERGY INTO ELECTRICAL ENERGY."::"":"":14)" BATTERIES "::"":"":1,2:4,1D6)"ALESSANDRO VOLTA (1745-1827) IS CREDITED WITH THE CONSTRUCTION OF THE FIRST PRACTICAL BATTERY."lN6)"BASICALLY A BATTERY CONSISTS OF TWO DISSIMILAR METALS IN AN ELECTROLYTE.VOLTA USED ZINC AND COPPER ELECTRODES"X"IN DILUTE SULFURIC ACID. ONE ELECTRODE BECOMES NEGATIVELY CHARGED THROUGH CHEMICAL PROCESSES AND IS THE NEGATIVE"cb"(-) TERMINAL OF THE BATTERY. THE OTHER ELECTRODE WITH A DEFICIENCY OF ELECTRONSIS POSITIVELY CHARGED AND IS THE "l"POSITIVE (+) TERMINAL"::""v 1,1:1,2:4,1ɀ1,8,0,"THE CHEMICAL BATTERY"ʊ1,60,90 60,170 180,170 180,90 178,90 178,168 62,168 62,90 60,90: CONTAINERWʔ1,80,78 80,152 100,152 100,78 80,78: ANODE~ʞ1,62,90 178,90: LIQUID SURFACEʨ I 0 8:1,11,10I,"+":ʲ1,140,78 140,152 160,152 160,78 140,78: CATHODEʼ J 0 8:1,18,10J,"-":G1,6:1,65,95,1:1,1:2:1,60,90 60,160:1,182,90 182,160:1,21,90,76,3,2:1,150,76,3,2:1,90,72 90,60:1,150,72 150,60:1,1:1,12,8,"<-V ->":1,21,9,22,"ANODE":1,8,23,"(COPPER)"1,19,22,"CATHODE":1,19,23,"(ZINC)"R1,87,50 157,50 157,55 87,55 87,50:1,102,45 142,45 142,50 102,50 102,45q1,90,46,3,2:1,154,46,3,21,123,32,15,12:1,14,4,"" 1,150,46 200,46 200,75 150,75:1,93,46 48,46 48,75 90,75:1,2  1,12,19,"H SO ":1,12,20," 2 4"  20: "": 0*6)"AS A RESULT OF THE CHEMICAL ACTIONA POTENTIAL DIFFERENCE DEVELOPS BETWEEN THE BATTERY TERMINALS. WHEN CONNECTED TO"4"AN EXTERNAL CIRCUIT, THE POTENTIAL DIFFERENCE CAUSES A CURRENT TO FLOW. THEELECTRON FLOW CAN BE ONLY IN ONE ">"DIRECTION. WE CALL THIS A DIRECT CURRENTTHE POTENTIAL DIFFERENCE ACROSS THE TERMINALS OF A BATTERY IS CALLED THE" H"ELECTROMOTIVE FORCE (EMF) OF THE BATTERY. THE EMF IS MEASURED IN VOLTS. THE EMF IS DETERMINED WHEN THE BATTERY"R"IS NOT CONNECTED IN A CIRCUIT. WHEN A BATTERY IS CONNECTED TO A CIRCUIT AND CHARGE FLOWS THROUGH THE CIRCUIT, THE "\"VOLTAGE ACROSS THE BATTERY TERMINALS IS SLIGHTLY LESS THAN THE EMF BECAUSE OF INTERNAL RESISTANCE OF THE BATTERY."f"IF A LARGE CURRENT IS DRAWN FROM THE BATTERY, THE VOLTAGE DECREASES. THE VOLTAGE OF THE BATTERY ALSO DECREASES"p"WITH USE, I.E. THE BATTERY RUNS DOWN."::""Pz6)"PROBABLY THE MOST COMMON BATTERIESARE THE 1.5 VOLT 'D' CELL FLASHLIGHT BATTERY AND THE 24 VOLT LEAD STORAGE BATTERY USED IN AUTOMOBILES."ф6)"THE FLASHLIGHT BATTERY IS CALLED A'DRY CELL'. THE ELECTROLYTE IS AMMONIUM CHLORIDE IN THE FORM OF A PASTE. "::""ю 1,1:1,2Ҙ1,6,1,"CROSS SECTION OF A 'D' CELL"zҢ1, 160,50,50,20,270,90:1,115,150 210,150:1,160,50,35,14,270,90:1,160,50,14,8,270,90:1,160,50,10,5,270,90Ҭ1,150,50 150,150 170,150 170,50 157,50:1,160,100,1:1,30,6,"ELECTRODE":1,30,5,"CARBON":1,160,60 230,45}Ӷ1,110,50 110,150 113,150 113,50 110,50:1,210,50 210,150 208,150 208,50 210,50:1,4,11,"ZINC CAN":1,110,50 155,501,100,80 110,60:1,100,80 208,90:1,170,50 210,501,145,50 145,150 125,150 125,50 145,50:1,175,50 175,150 195,150 195,50 175,501,4,19,"MIX":1,4,20,"MANGANESE":1,4,21,"DIOXIDE,ETC":1,60,150 130,140:1,60,155 190,1451,26,19,"PASTE OF ZINC":1,26,20,"AND AMMONIUM":1,26,21,"CHLORIDES":1,200,105 235,150:1,120,115 235,1501,32,7,"()":1,6,12,"()"4 20:"": 0:""^12)" CURRENT DIRECTION "::""6)"EARLY INVESTIGATORS THOUGHT THAT ELECTRICAL PHENOMENA WERE THE RESULTS OFTWO FLUIDS-THE POSITIVE AND NEGATIVE."U"BENJAMIN FRANKLIN (1706-1790) ADVANCED ATHEORY OF ELECTRICITY IN WHICH HE POSTULATED THE EXISTENCE OF A SINGLE ""TENUOUS, IMPONDERABLE FLUID IN ALL MATTER. ALL BODIES COULD CONTAIN A CERTAIN QUANTITY OF FLUID WITHOUT "O$"MANIFESTING ANY ELECTRICAL PROPERTIES, BUT OBJECTS DID SHOW ELECTRICAL PROPERTIES WHEN THEY CONTAINED A SURPLUS"."OR A DEFICIT OF THE FLUID. AN OBJECT WITH AN EXCESS OF FLUID WAS CONSIDERED TO BE POSITIVELY EXCITED, AND ONE WITH A"O8"DEFICIT OF FLUID, NEGATIVELY EXCITED. THE DESIGNATION OF CONVENTIONAL (POSITIVE) CURRENT FLOW IN CIRCUITS IS A"B"CONSEQUENCE OF FRANKLIN'S SINGLE FLUID THEORY."::"" L6)"WE NOW KNOW THAT IT IS THE ELECTRONS THAT MOVE IN A CONDUCTOR, SO THE CURRENT IS IN THE DIRECTION OF THE "V"ELECTRON MOVEMENT. THAT IS AWAY FROM THENEGATIVE TERMINAL OF A BATTERY AND TOWARD THE POSITIVE TERMINAL (SIMILAR TO" `"THE LAW OF CHARGES). HOWEVER FOR THE HISTORICAL REASONS CITED ABOVE THE DIRECTION OF 'CONVENTIONAL CURRENT' FLOW"j"IS IN THE OPPOSITE DIRECTION - THAT IS IN THE DIRECTION THAT POSITIVE CHARGES WOULD FLOW. THIS TENDS TO BE CONFUSING"t"BUT KEEP IN MIND THAT":1~" ELECTRON CURRENT FLOW IS IN THE REVERSE DIRECTION TO CONVENTIONAL CURRENT FLOW. "::""@ۈ 1,1:1,2Xے1,14,2,"OHM'S LAW"nۜ1,15,4,"E = I*R"ۦ I 0 6:1,12,11I,"":۰1,12,11,"ͯ"ۺ J 0 5:1,30,12J,"":1,12,17,""1,21,17,"")1,6,23,"R = RESISTANCE (OHMS)"_2:1,160,130 160,145:1,165,132 165,142:11,20,19,"E":1,6,21,"E = EMF (VOLTS)":1,22,9,"I":1,6,22,"I = CURRENT (AMPERES)":1,22,12,"R"1,18,16,"":1,22,16,"" 20:"": 0:""& 10)" ELECTRIC POWER "::""6)"WHEN A CURRENT FLOWS THROUGH A CONDUCTOR, WORK IS DONE BECAUSE THE RESISTANCE OF THE CONDUCTOR MUST BE ""OVERCOME; AND WITH TIME, POWER IS EXPENDED. THIS IS BECAUSE THE ENERGY GAINED BY THE ELECTRONS IN MOVING "("THROUGH THE POTENTIAL DIFFERENCE IS TRANSFERRED TO THE ATOMS BY COLLISIONS. THE ENERGY IS MANIFESTED AS HEAT RATHER"2"THAN AS AN INCREASE IN KINETIC ENERGY OFTHE ELECTRONS. NOW THE WORK DONE WHEN A CHARGE Q MOVES AS A RESULT OF A"2<"POTENTIAL DIFFERENCE V IS":MF12)"W = Q*V = I*T":rP6)"SINCE P = W / T WE HAVE":Z12)"P = W/T = I*V*T/T = IV":d6)"SO WE MAY WRITE":n12)" 2 2 "x12)"P = I*V = V /R = I R "::""k6)"THE RESISTIVE PROPERTIES OF A MATERIAL ARE CHARACTERIZED BY ITS RESISTIVITY (RHO) AND"14)" (RHO) * L"14)"R = "14)" A ":Q6)"WHERE (RHO) IS INDEPENDENT OF THE PHYSICAL SHAPE OF THE MATERIAL. THE RESISTIVITY OF SOME COMMON CONDUCTORS ARE SHOWN IN THE NEXT TABLE."d:"":""4)"RESISTIVITY OF COMMON CONDUCTORS":""6)"MATERIAL";20)"(RHO) OHM-METERS":6)"ALUMINUM";23)"2.8E - 8"6)"COPPER";23)"1.7E - 8"$6)"CARBON";23)"3.5E - 5"B6)"IRON";23)"1.2E - 7"c6)"MERCURY";23)"9.5E - 7"6)"NICKEL";23)"7.8E - 8"6)"TUNGSTEN";23)"5.5E - 8"6)"STEEL";23)"1.8E - 7""6)"TUNGSTEN";23)"5.5E - 8",6)"NICHROME ALLOY";23)"1.1E - 6"::""6 1,1E@1,8,2,"COMBINATION OF RESISTORS"_J1,15,3,"(IN SERIES)"T1,6,8,"ͯͯͯ"^1,6,6," R' R'' R'''"h I 1 6:1,6,8I,"":r J 1 6:1,36,8J,"":|1,7,14,"<----------- V ---------->"I1,7,10," V' V'' V'''"[1,2,10,"I ^"1,1,16,"SINCE V = V' + V'' + V'''"1,9,17," = I*R' + I*R'' + I*R'''"1,9,18," = I*(R' + R'' + R''')"1,9,19," = I*R"[1,9,21,"WHERE R IS THE EQUIVALENT RESISTANCE OF THE THREE RESISTORS IN SERIES"1,9,24,"THUS R = R' + R'' + R'''" 20:"": 01,11,8,0,"COMBINATION OF RESISTORS"1,15,1,"(IN PARALLEL)"1,12,3,"ͯ"1,12,6,"ͯ"=1,12,9,"ͯ"]1,12,14," "&2:1,152,110 152,125:1,158,113 158,122:101,15,4,"V = I'*R'": I 0 10:1,28,4I,"":: J 0 10:1,11,4J,"":D1,15,7,"V = I''*R''" N1,15,10,"V = I'''*R'''"KX1,17,15,"":1,21,15,"":1,19,13,"V"mb1,4,17,"I = I' + I'' + I'''"l1,4,18," = V/R' + V/R'' + V/R'''"v1,4,19," = V* (1/R'+1/R''+1/R''')"1,4,20," = V * (1/R)"X1,4,21,"WHERE R IS THE EQUIVALENT RESISTANCE OF THE RESISTORS IN PARALLEL (R=1/R'+1/R''+1/R''')"k1,7,11,"I ^"} 20:"": 0""12)" THE GENERATOR "::"":"":6)"THE ELECTRICAL GENERATOR IS A DEVICE WHICH CONVERTS MECHANICAL ENERGY INTO ELECTRICAL ENERGY. IT IS BASED ON""THE PRINCIPLE OF ELECTROMAGNETIC INDUCTION. THE NEXT FIGURE ILLUSTRATES THE PRINCIPLE OF THE AC (ALTERNATING CURRENT )GENERATOR.:INPUT 1,1:1,21,14,2,"THE AC GENERATOR"N1,20,30 120,60 80,110 20,90:1,80,150 120,100:1,20,130 80,1501,164,80,50,40,240,300:1,123,130,50,40,240,3001,140,150,21,24,30,150:1,150,130 190,80 230,90:1,150,130 230,155:1,150,170 230,1951,113,133 79,167E 1,113,133 83,117 130,60 192,93 145,150 120,136 96,1601,82,170,7,5:1,86,166,7,5,320,180:1,90,162,7,5,320,180:1,96,156,7,5,320,180 1,87,163,1:1,95,153,12:1,94,170 110,170:1,105,160 125,160.1,7,15,"S":1,21,19,"N":1,8,22,"SLIP RINGS":1,8,23,"AND BRUSHES"1,140,50,20,8,280,80:1,160,50 162,46 151,48 160,50: 20:"": 0:""6)"AS THE RECTANGULAR LOOP IS ROTATEDTHE MAGNETIC FLUX THROUGH THE LOOP CHANGES BECAUSE THE MAGNITUDE OF THE"{"PERPENDICULAR COMPONENT OF THE MAGNETIC FIELD CHANGES, AND AN EMF IS PRODUCED INTHE LOOP. THE NEXT FIGURE SHOWS THE""ALTERNATING EMF INDUCED IN THE COIL OF THE GENERATOR DURING ONE REVOLUTION."::""H1:I1:K0:L0:R49:V20:G0:O0:W0  7430,"Y = H * SIN (I*X - K) + L@KK3.14159180Z 0,1:1,3:4,1: 1,1e 7920}$ 1,160,0 160,199. 1,0,100 319,100j T 100 199 Rt 1,155,T 165,T: T~ U 100 0 R 1,155,U 165,U: U  J360 1 V%WW2:G0:FJ1809CH(IFK)LLD 360F180\E D53120kX (E.5)~ C0 7670GCR C0 G(G.5) C0 G(G.5)Y100G W3 7670  1,A,B X,YAXBY: J( 1,A,B X,Y: 7980&2 J1 360 V4<G0:WW2HFFJ3.14159180[PCH(IFK)LiZDF180xdED53120nX160(E.5)x C0 7870GCR C0 Y(G.5) C0 Y (G.5)Y100G W3 7870 1,A,B X,YAX:BY: J) 1,A,B X,Y?1,16,2,"VOLTAGE"J 8050dNH(I2 K) Lw N0 7970ONR O0 O(O.5) O0 O(O.5)"B100O:O0:X160:O0,:6NH(IOK)L@N0 8040:8040JONRTO0O(O.5)&^O0O(O.5)4hY100O:Gr 20:"": 0W|""12)" COUPLED CIRCUITS "::""6)"CONSIDER TWO CIRCUITS SUCH A (1) AND (2) IN THE NEXT FIGURE. WHEN A CURRENT I' CIRCULATES IN CIRCUIT (1), A "|"MAGNETIC FIELD PROPORTIONAL TO I' IS ESTABLISHED AROUNT IT, AND THEREFORE THROUGH CIRCUIT (2) THERE IS A MAGNETIC""FLUX F'' WHICH IS ALSO PROPORTIONAL TO I'. WE MAY THEN WRITE":14)"F'' = M * I'"X6)"WHERE M IS A COEFFICIENT WHICH REPRESENTS THE MAGNETIC FLUX THROUGH CIRCUIT (2) PER UNIT CURRENT IN CIRCUIT ""(1). SIMILARILY, IF A CURRENT I'' CIRCULATES IN CIRCUIT (2), A MAGNETIC FIELD IS PRODUCED, AND IT IN TURN ">"PRODUCES A MAGNETIC FLUX F' THROUGH CIRCUIT (1) WHICH IS PROPORTIONAL TO I''HENCE WE MAY WRITE":V14)"F' = M * I''"6)"WHERE M, THE MUTUAL CONDUCTANCE, DEPENDS ON THE SHAPE OF THE CIRCUITS ANDTHEIR ORIENTATION."::"" 1,1:1,2:4,11,10,2,"MUTUAL INDUCTION"K1,6,4,"A CURRENT IN CIRCUIT (1) PRODUCES A MAGNETIC FLUX IN CIRCUIT (2)"u1,77,110,30,40:1,240,120,30,40,,,45 1,13,12,"^ I'" I 1 15 5:1,130,0I,200,80: I& J 30 50 10:1,140,160J,200,80:J(0 1,8,20,"(1)":1,29,20,"(2)":1,29,14,"F''":1,14,22,"F'' = M * I'"6: 20:""Jl 1,1:1,2:4,3iv 1,10,2,"MUTUAL INDUCTION" 1,6,4,"A CURRENT IN CIRCUIT (2) PRODUCES A MAGNETIC FLUX IN CIRCUIT (1)" 1,77,110,30,40:1,240,110,30,40,,,45 1,34,12,"^ I''"' I 1 15 5:1,130,20I,200,80: IS J 1 15 5:1,140,200J,200,80:J 1,8,20,"(1)":1,29,20,"(2)":1,10,11,"F'":1,14,22,"F' = M * I''" 20:"": 0:4,1= 6)"IF THE CURRENT I' IS VARIABLE THE FLUX F'' THROUGH CIRCUIT (2) CHANGES ANDAN EMF IS INDUCED IN THIS CIRCUIT. THIS EMF IS GIVEN BY"T 12)" DI'"k 12)"V = - M " 12)" M2 DT": 6)"SIMILARILY, IF I'' IS VARIABLE, ANEMF IS INDUCED IN CIRCUIT (1), GIVEN BY": 12)" DI''" !12)"V = -M "# !12)" M1 DT"?!:"":"":4,1 !" FURTHER PROGRAMS IN THIS SERIES MAY BE OBTAINED FROM THE AUTHOR "::1,1:4,1*!14)"DR PAUL W. MCDANIEL"4!14)"4295 WARREN WAY">!14)"RENO, NEVADA 89509" H!:"