(a) From Eqs. (2.75) and (2.45) compute the components of the electromagnetic stress-energy tensor in an inertial reference frame (in Gaussian units). Your answer should be the expressions given in electrodynamics textbooks:

(b) Show that the divergence of the stress-energy tensor (2.75) is given by

(c) Combine this with Maxwell’s equations (2.48) to show that

(d) The matter that carries the electric charge and current can exchange energy and momentum with the electromagnetic field. Explain why Eq. (2.81b) is the rate per unit volume at which that matter feeds 4-momentum into the electromagnetic field, and conversely, +F^αμJ_μ is the rate per unit volume at which the electromagnetic field feeds 4-momentuminto the matter. Show, further, that (as viewed in any reference frame) the time and space components of this quantity are

where ρ_e is charge density, and j is current density. The first of these equations describes ohmic heating of the matter by the electric field, and the second gives the Lorentz force per unit volume on the matter.

Transcribed Image Text:

Taß = - 4π Fаμ FB μl 1 4 Fuv). gaß Fuv F gaß (2.75)