Potential gradient

In physics, chemistry and biology, a potential gradient is the local rate of change of the potential with respect to displacement, i.e. spatial derivative, or gradient. This quantity frequently occurs in equations of physical processes because it leads to some form of flux. In physics, chemistry and biology, a potential gradient is the local rate of change of the potential with respect to displacement, i.e. spatial derivative, or gradient. This quantity frequently occurs in equations of physical processes because it leads to some form of flux. The simplest definition for a potential gradient F in one dimension is the following: where ϕ(x) is some type of scalar potential and x is displacement (not distance) in the x direction, the subscripts label two different positions x1, x2, and potentials at those points, ϕ1 = ϕ(x1), ϕ2 = ϕ(x2). In the limit of infinitesimal displacements, the ratio of differences becomes a ratio of differentials: