2.Maxwell'sEquationsFor the time-varying electromagnetic field, Maxwell summarizedthefollowingfourequations:ThedifferentialformThe integralformaDaDVxH=J.fH .dl -[,(J).dsatataBaBVXEfE·d --dsatISatV.B=0fB.ds=0V.D=pf D.ds =q
2. Maxwell’s Equations For the time-varying electromagnetic field, Maxwell summarized the following four equations: S D H dl (J )d = + l S t S B E dl d = − l S t d = 0 S B S q S = D dS The integral form t = + D H J t = − B E B = 0 D = The differential form
aDV.B=0VxH=JataBVxE:V.D=patThe time-varying electric field is both divergent and curly, and thetime-varying magnetic field is solenoidal and curly.Nevertheless, thetime-varying electric field and the time-varying magnetic field cannotbe separated, and the time-varying electromagnetic field is divergentand curlyIn a source-free region, the time-varying electromagnetic field issolenoidal.The electric field lines and the magnetic field lines are linked witheach other, forming closed loops, and resultingin an electromagneticwaveinspaceThe time-varying electric field and the time-varying magnetic fieldareperpendicularto each other7
The time-varying electric field is both divergent and curly, and the time-varying magnetic field is solenoidal and curly. Nevertheless, the time-varying electric field and the time-varying magnetic field cannot be separated, and the time-varying electromagnetic field is divergent and curly. In a source-free region, the time-varying electromagnetic field is solenoidal. The electric field lines and the magnetic field lines are linked with each other, forming closed loops, and resulting in an electromagnetic wave in space. The time-varying electric field and the time-varying magnetic field are perpendicularto each other. t = + D H J t = − B E B = 0 D =
In order to describe more completely the behavior of time-varyingelectromagnetic fields, Maxwell's eguations need to be supplementedby the charge conservation equation and the constitutiverelationsapV.JD=εEB=uHJ=oE+Jatwhere J' stands for the impressed source producing the time-varyingelectromagneticfieldThe four Maxwell's equations are not independent.Equations 4 and3 can be derived from Equation 1 and 2, respectively,and viseversa.Forstaticfields,wehaveaEaDaHaB=0atatatatMaxwell's eguationsbecometheformerequationsforelectrostaticfield and steady magnetic field. Furthermore, the electric field and themagneticfieldareindependenteachother
In order to describe more completely the behavior of time-varying electromagnetic fields, Maxwell’s equations need to be supplemented by the charge conservation equationand the constitutive relations: t = − J D = E B = H J = E + J The four Maxwell’s equations are not independent. Equations 4 and 3 can be derived from Equation 1 and 2, respectively, and vise versa. For static fields, we have = 0 = = = t t t t E D H B Maxwell’s equations become the former equationsfor electrostatic field and steady magnetic field. Furthermore, the electric field and the magnetic field are independent each other. where stands for the impressed source producing the time-varying electromagnetic field. J
As the founder of relativity, Albert Einstein (1879-1955), pointed outin his book“TheEvolutionofPhysics"thatThe formulation of these equations is the most important event inphysics since Newton's time, and they are the quantitative mathematicaldescription of the laws of the field. Their content is much richer than wehave been able to indicate, and the simple form conceals a depthrevealedonlybycareful study""These equations are the laws representing the structure of the field.They do not, as in Newton's laws, connect two widely separated events:they do not connect the happenings here with the conditions there"The field here and now depends on the field in the immediateneighborhood at a time just past. The equations allow us to predictwhat will happen a little further in space and a little later in time, if weknowwhathappens hereandnow
“These equations are the laws representing the structure of the field. They do not, as in Newton’s laws, connect two widely separated events; they do not connect the happenings here with the conditionsthere”. As the founder of relativity, Albert Einstein (1879-1955), pointed out in his book “The Evolutionof Physics” that “The field here and now depends on the field in the immediate neighborhood at a time just past. The equations allow us to predict what will happen a little further in space and a little later in time, if we know what happens here and now” “The formulation of these equations is the most important event in physics since Newton’s time, and they are the quantitative mathematical description of the laws of the field. Their content is much richer than we have been able to indicate, and the simple form conceals a depth revealed only by carefulstudy
Maxwell's eguationshave madeimportantimpact onthehistoryof mankind, besidestheadvancementof scienceandtechnology.As American physicist,RichardP.Feynman,saidin his bookThe Feynman Lectures on Physics",that"From alongview of thehistory of mankind--seen from say, ten thousand years from now-there can be littledoubt that the most significantevent of the19.th centurywill be judged as Maxwell's discoveryof the laws ofelectrodynamics. The American civil war will pale into provincialinsignificance in comparison with this important scientific event ofthe samedecade
Maxwell’s equations have made important impact on the history of mankind, besides the advancement of science and technology. As American physicist, Richard P. Feynman, said in his book “The Feynman Lectures on Physics”, that “From along view of the history of mankind──seen from say, ten thousand years from now ──there can be little doubt that the most significant event of the 19- th century will be judged as Maxwell’s discovery of the laws of electrodynamics. The American civil war will pale into provincial insignificance in comparison with this important scientific event of the same decade