Effect of a conducting shield on the inductance of an air-core solenoid

A magnetostatic integral equation for the current induced by a solenoidal inductor in the conducting wall of a closed, perfectly conducting cylindrical shield was solved by the method of moments and point matching. The induced current was then used to determine the self-inductance of the solenoid. A chart of the ratio of the shielded inductance to that in free space was produced to aid in the design of practical air-core inductors. In addition, Wheeler's well-known formula for the free-space inductance of a single-layer solenoid was shown to be sufficiently accurate to serve as a basis for the design of practical coils if the effect of the shield, available from the chart, is included.