In the computer design of electric and magnetic devices, when the fields can be derived from a scalar potential satisfying the Laplace equation, integral equation methods are powerful tools, particularly in 3-d problems. A certain Fredholm integral equation of the first kind, used first to obtain the potential, may be utilized a second time with a different right-hand side to obtain directly the rate of change in potential due to a change in the position of an electrode or magnet pole-piece. The new righthand side of the integral equation is formulated in simple terms. Knowledge. of this rate of change suggests itself to two types of applications: Alignment sensitivity study and improved numerical optimization of electromagnetic devices. Copyright © 1985 by The Institute of Electrical and Electronics Engineers, Inc.