(a) From Maxwell equations, where E and H denote the electric and magnetic fields in a plasma,...
Question:
(a) From Maxwell equations,
where E and H denote the electric and magnetic fields in a plasma, p denotes the electric charge density nq, and J the electric current density nqu, show that
where ∈0μ0 (E x H) is the electromagnetic momentum density, and T is the electromagnetic stress dyad whose components are given by
where δij is the Kronecker delta.
(b) From this equation, which expresses conservation of the electromagnetic momentum density, and the continuity equation
show that the momentum transport equation
can be written in the form
where G denotes the total momentum density
and Π is the total momentum flux dyad (rate of transport of momentum through unit area)
(c) Using Maxwell curl equations, show that the energy transport equation
can be written in the form [note that u · (u x B) = 0]
where W denotes the total energy density
and S is the total energy flux (power per unit area)
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