Compression of Magnetic Field Between Two Semi-Infinite Slabs of Constant Conductivity

Abstract

A uniform magnetic field is compressed in a circuit containing two semi‐infinite slabs of constant conductivity σ. The separation l of the slabs decreases uniformly according to l=l₀−vt. An equation involving the magnetic Reynolds number R_m=σμ₀l₀v is derived for the magnetic field in the gap. Expressions are given for the magnetic and electric fields everywhere up to the instant of collision. These expressions are evaluated for several values of R_m and it is found that the ratio of Joule energy density to magnetic energy density at the surfaces of the slabs is fairly close to unity throughout the motion. For R_m»1 it is shown that the maximum magnification of the initial field is approximately R_m/8.