By Adolf Schwab
"Field thought ideas" is a brand new method of the educating and realizing of box idea. Exploiting formal analo- gies of electrical, magnetic, and conduction fields and introducing accepted ideas ends up in a transparently based electomagnetic box concept. hugely illustrative phrases alloweasyaccess to the thoughts of curl and div which typically are conceptually difficult. Emphasis is put on the static, quasistatic and dynamic nature of fields. finally, numerical box calculation algorithms, e.g. Finite point strategy and Monte Carlo strategy, are provided in a concise but illustrative manner.
Read or Download Field Theory Concepts: Electromagnetic Fields Maxwell’s Equations grad, curl, div. etc. Finite-Element Method Finite-Difference Method Charge Simulation Method Monte Carlo Method PDF
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Additional resources for Field Theory Concepts: Electromagnetic Fields Maxwell’s Equations grad, curl, div. etc. Finite-Element Method Finite-Difference Method Charge Simulation Method Monte Carlo Method
E. dp/dt. In order to obtain this form we transpose the displacement component to the equation's right side and put the differentiation with respect to time in front of the differential operator diy, div J c = - div J d = - div ~~ = - :t div D (3-59) With div D = P we finally obtain div J c ap = - at (3-60) This is the differential form of the law oj conservation oj charge. It relates the source density of the conduction current density to the variation of the charge density at a particular field point.
We always have s , Xv(r) • dS = O. 3 Law or Continuity in Integral Form 37 Differential Form of Maxwell's Equations Maxwell's equations in integral form make an integral or global statement about the properties of a field region which depends on the field as well as on the integration path chosen. The vortex strength of a contour C may yield a higher value the wider the contour chosen, if more vortices (of same orientation) are enclosed. In much the same way, a source strength will yield a higher value the greater the volume of the closed surface (as long as more charges of the same polarity are enclosed).
If we further imagine the closed surface to exist in a dielectric, for example in the vicinity of an antenna where the conduction current can always be neglected over the displacement current (IJel « IJdl), we find (3-20) This is the special law of continuity for problems involving exclusively displacement currents (displacement fields Jd (r)). e. dQv / dt. In order to obtain this form we transpose the displacement component to the equation-s right side and put the differentiation with respect to time in front of the integral; thus we get With S pD.