he system shown in Fig. 6P.8 consists of a coaxial line of inner radius a and outer radius b, with an annular conductor that makes perfect electrical contact with the inner and outer conductors. The annular conductor is constrained to move to the right with constant velocity v. All conductors can be assumed to have infinite conductivity. A battery V, supplies a current I to the system through a resistance R. This excitation is physically arranged to
maintain cylindrical symmetry about the center line. Fringing fields at the left end can be neglected. A voltmeter is connected between the inner and outer conductors at the extreme right end as shown.
(a) In terms of the current I, find the fields E and H throughout the length of the line between the conductors.
(b) Using the constraints imposed by the battery and resistance, find E, H, and the terminal variables I and V in terms of V0 and the other constants of the system.
(c) What does the voltmeter read? Why can this be different from the terminal voltage V?
(d) Compute the rate of change of stored magnetic energy and the power VI into the line. If there is a discrepancy between these values, explain where the power goes (or comes from).
(e) Treat the problem as a lumped inductor with a mechanical variable. Find L(X) and the force.fe acting on the sliding short. Use this to explain your answer to part (d).
