potenciál

Potenciál is a term used in physics and mathematics to denote a scalar field from which forces can be derived. The word derives from Latin potens meaning "power" or "able." In physics, the most common usages are potential energy and electric potential.

In mechanical systems, a potential function V assigns a scalar value to every point in space so that the force at that point is F = -∇V. Many forces are conservative and can be described this way; the total energy is the sum of kinetic and potential energy. This framework simplifies the analysis of motion and energy transfer in systems ranging from gravitation to springs.

Electric potential is the work required per unit charge to move a test charge from a reference point to a given point in an electric field. The electric field is related to the potential by E = -∇V. The potential difference between two points satisfies V(B) - V(A) = -∫_A^B E · dl, and the electric potential energy of a charge q is U = qV. The concept is essential for understanding circuits, capacitors, and electrostatic interactions.

Beyond electricity, potential appears in fluid dynamics (velocity potential), magnetism (magnetic scalar potential in current-free regions), and mathematical potential theory, where Laplace’s equation ∇²V = 0 describes V in charge- or mass-free regions. In quantum mechanics, the potential energy function is a central element of the Schrödinger equation, shaping particle behavior through the potential landscape.

Potenciál serves as a foundational concept for modeling conservative systems, energy storage and transfer, and field configurations, providing a unifying framework for calculating forces, energies, and related quantities.

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