Книга: Scalar Potential: Scalar Potential, Scalar Curvature, Riemannian Geometry, Curvature, Riemannian Manifold, Real Number, Gaussian Curvature, Volume, Curvature of Riemannian Manifolds

High Quality Content by WIKIPEDIA articles! The physical meaning of the scalar potential depends on the type of the field. For a velocity field of a fluid or gas flow, the definition of the scalar potential implies that the direction of the flow at any point coincides with the direction of the steepest decrease of the potential at that point, and for a force field the same is true of the acceleration at a point. The scalar potential of a force field is closely related to the field's potential energy. Not every vector field has a scalar potential those which do are called conservative, corresponding to the notion of conservative force in physics. Among velocity fields, any lamellar field has a scalar potential, whereas a solenoidal field only has a scalar potential in the special case when it is a Laplacian field.