Two parallel rectangular superconducting plates of length l, width be and separation a (l >> b >> a) are joined at each end to form a one-turn coil of negligible resistance. What is the its self-inductance? How much energy is stored in the magnetic field when a steady current I flows? The separation a increases by a small amount δa. Calculate the various energy changes
(a) When the coil includes in its circuit a lossless battery which maintains a constant current I, and
(b) When the circuit consists of the coil alone. Deduce the magnitude and direction of the force per unit area between the tow plates.