(a) An electric field E exerts (in SI units) a pressure ∈_oE²/2 orthogonal to itself and a tension of this same magnitude along itself. Similarly, a magnetic field B exerts a pressure B²/2_μo = ∈_oc²B²/2 orthogonal to itself and a tension of this same magnitude along itself. Verify that the following stress tensor embodies these stresses:

(b) Consider an electromagnetic field interacting with a material that has a charge density ρ_e and a current density j. Compute the divergence of the electromagnetic stress tensor (1.38) and evaluate the derivatives using Maxwell’s equations. Show that the result is the negative of the force density that the electromagnetic field exerts on the material. Use momentum conservation to explain why this has to be so.

Transcribed Image Text:

T= €/ [(E² + c²B²³) g = 2(E ® E + c²B ® B)]. (1.38)