Potentialfelder

Potentialfelder, or potential fields, denote scalar fields from which a vector field can be derived as F = -∇φ. The scalar function φ is the potential, and the vector field F represents the magnitude and direction of the physical quantity in space. In many contexts, F is conservative, meaning the work done moving along a path depends only on endpoints.

In physics, classical examples include gravitational and electrostatic fields. For gravity, φ = -GM/r and F = -∇φ points toward the mass. For electrostatics, φ = kq/r and F = -∇φ is the electric field, pointing away from a positive charge. Static conservative fields satisfy ∇×F = 0 and are related to a potential by F = -∇φ. The potential energy U is related by U = qφ for a test charge q, and Poisson or Laplace equations relate φ to charge or mass density via ∇^2 φ = -ρ/ε0 or ∇^2 φ = 4πGρ.

In other disciplines, potential fields describe magnetic fields in current-free regions, or chemical potential landscapes around molecules. In geophysics, gravitational or magnetic potential fields are used to model subsurface structures; in chemistry, electrostatic potential maps help predict reaction sites.

In robotics and computer vision, artificial potential-field methods use φ to guide motion: an attractive potential draws a robot toward a goal, while repulsive potentials push it away from obstacles. While conceptually simple, these methods can suffer from local minima and require additional strategies or global planners.