# Dictionary:Laplace’s equation

(la plas’) A differential equation that describes field behavior in free space. The **Laplacian** of a potential function *U* vanishes in space that contains neither sources nor sinks. ( is the operator ‘‘del’’.) In rectangular coordinates,

Gravity, magnetic, electrical, electromagnetic fields obey Laplace's equation in free space (where there are no sources). See Figure C-14 for the Laplacian in cylindrical and spherical coordinates. Compare *Poisson’s equation*. Named for Pierre Simon Laplace (1749–1827), French mathematician.