Symmetric energymomentum tensor in maxwell, yangmills. Multiple part video deriving the maxwell stress tensor. Mit opencourseware for any use or distribution of this. Pdf electromagnetic force and the maxwell stress tensor. We find it useful to define the maxwell stress tensor as a function of the field quantities from which the force density can be obtained by space differentiation. Chapter 6 maxwells equations in tensor form we now have learned the transformation properties of th electric and magnetic elds and together they form an antysymmetric tensor f f under poincare transformation. Electromagnetic force and the maxwell stress tensor in condensed systems.
Maxwell stress tensor and electromagnetic waves 2 thus there is no momentum. Di erential geometric formulation of maxwells equations maris ozols january 16, 2012 abstract maxwell s equations in the di erential geometric formulation are as follows. The goal of these notes is to introduce the necessary notation and to derive these equations from the standard di erential formulation. Can we write maxwells equations in tensor form to show that they are in accord with special. Advanced texts often present the maxwell stress tensor as a mathematical abstraction without explaining why is is useful. This derivation requires to know vector calculus, linear algebra, and electrodynamics. Differential geometric formulation of maxwells equations. Calculation of the maxwell stress tensor and the poisson. But theres another place in physics where the speed of light plays a promi. The method is seldom discussed in introductory texts on electromagnetism. Since the average of cos2 xover a single cycle is 1 2, the average momentum.
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