- #1
Vrbic
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Homework Statement
An electric field E exerts (in Gaussian cgs units) a pressure E2/8π orthogonal to itself and a tension of this same magnitude along itself. Similarly, a magnetic field B exerts a pressure B2/8π orthogonal to itself and a tension of this same magnitude along itself. Verify that the following stress tensor embodies these stresses:
T = 1/ 8π ((E2 + B2 )g − 2(E ⊗ E + B ⊗ B))
Homework Equations
##T_{ii}=P##
The Attempt at a Solution
##T_{xx}=P=1/ 8π(\textbf{E}^2 + \textbf{B}^2-2(E_x^2 + B_x^2))=1/ 8π(-E_x^2- B_x^2 + E_y^2+ B_y^2+ E_z^2 + B_z^2)##
##T_{xy}=2/ 8π(-E_xE_y- B_xB_y )##
Why I didn't get a right result? I probably don't understand "a pressure orthogonal to itself". In particular, it means that if E=(Ex,0,0) so in which direction is pressure? I would say in same but there is written orthogonal.
Please advise.