Potentialfeld

Potentialfeld, in physics and engineering, refers to a scalar field that encodes the potential energy per unit charge or per unit mass at every point in space. It is central to describing conservative force fields, since a force F is obtained as the negative gradient of the potential: F = -∇φ. Common instances include the electric potential in electrostatics and the gravitational potential in Newtonian gravity. In fluids and other contexts, potential fields can describe irrotational velocity fields or energy landscapes.

As a property, a potentialfeld is conservative: the line integral of the force along any path depends only on the endpoints and not on the path taken. Equipotential surfaces, where φ is constant, are orthogonal to field lines. In charge-free or source-free regions, the potential satisfies Laplace’s equation ∇^2φ = 0; in the presence of sources, it satisfies Poisson’s equation ∇^2φ = -ρ/ε0. Boundary conditions on a domain determine a unique solution under appropriate constraints, which is the core of potential theory and boundary value problems.

Calculation and analysis often involve numerical methods such as finite difference, finite element, or boundary element methods to solve Poisson or Laplace equations. Visualization uses maps of φ and its gradient to depict potential landscapes and field directions.

Applications span physics and geophysics (electric and gravitational field mapping), engineering (electrostatic design, energy landscapes), and robotics (artificial potential field methods for path planning and obstacle avoidance). The concept underpins broader mathematical study of harmonic and subharmonic functions and their properties.