Recently, in continuum mechanics, special attention has been paid to the determination of path-independent integrals. The interest in these integrals is not only of a theoretical nature, but also of practical importance considering their application, for example in fracture and crack problems. For these reasons, this paper provides an extension of the application of Neter's theorem to the linear theory of an elastic dielectric in the field of an elastic potential. Appropriate families of transformations and their corresponding conservation laws or path-independent integrals are derived. In the general case, four conversion laws are obtained, one of which is new.