(a) Verify that −∇ · T_M = j × B, where T_M is the magnetic stress tensor (19.11).

(b) Take the scalar product of the fluid velocity v with the equation of motion (19.10) and combine with mass conservation to obtain the energy conservation equation (19.16).

(c) Combine energy conservation (19.16) with the first law of thermodynamics and mass conservation to obtain Eq. (19.17) for the evolution of the entropy.

dv P. =pg - VP+jx B=pg - VP + dt (V x B) x B (19.10)