Final answer:
The question involves deriving the fluid velocity component perpendicular to the magnetic field B in a perfectly conducting fluid, using equations from plasma physics, specifically the equation of motion and generalized Ohm's Law.
Step-by-step explanation:
The student's question pertains to deriving a specific equation for fluid velocity in a perfectly conducting fluid under steady-state conditions, using the equation of motion and generalized Ohm's Law from Bittencourt's Fundamentals of Plasma Physics. Because the full derivation depends on the details provided in the textbook's specific equations (6.6 and 6.10), which are not provided in the question, a general approach includes considering the forces acting on the fluid (like pressure gradients and electromagnetic forces), and how charge and current densities relate to the magnetic field in the context of a plasma. The generalized Ohm's Law for a perfectly conducting fluid will suggest that the electric field and fluid velocity components perpendicular to the magnetic field B should be related to maintain a steady state.
To derive the relationship, one would typically set the electric field in the frame of the moving conductor to zero, as for a perfect conductor E + v x B = 0, where E is the electric field, v is the fluid velocity, and B is the magnetic field. This relation would be used in conjunction with the equation of motion, which balances inertial forces with electromagnetic and pressure gradient forces. The derivation would yield an expression for v, the fluid velocity component perpendicular to the magnetic field B.