In physics, a force field is a vector field corresponding with a non-contact force acting on a particle at various positions in space. Specifically, a force field is a vector field , where is the force that a particle would feel if it were at the point .
Gravity is the force of attraction between two objects. A gravitational force field models this influence that a massive body (or more generally, any quantity of energy) extends into the space around itself. In Newtonian gravity, a particle of mass M creates a gravitational field , where the radial unit vector points away from the particle. The gravitational force experienced by a particle of light mass m, close to the surface of Earth is given by , where g is the standard gravity.
An electric field is a vector field. It exerts a force on a point charge q given by .
A magnetic field is a vector field. A point charge moving through one experiences a force perpendicular to its own velocity and to the direction of the field, following the relation: .
Work is dependent on the displacement as well as the force acting on an object. As a particle moves through a force field along a path C, the work done by the force is a line integral:
This value is independent of the velocity/momentum that the particle travels along the path.
For a conservative force field, it is also independent of the path itself, depending only on the starting and ending points. Therefore, the work for an object travelling in a closed path is zero, since its starting and ending points are the same:
If the field is conservative, the work done can be more easily evaluated by realizing that a conservative vector field can be written as the gradient of some scalar potential function:
The work done is then simply the difference in the value of this potential in the starting and end points of the path.
This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.
Related concepts (12)
In physics, a force field is a vector field corresponding with a non-contact force acting on a particle at various positions in space. Specifically, a force field is a vector field , where is the force that a particle would feel if it were at the point . Gravity is the force of attraction between two objects. A gravitational force field models this influence that a massive body (or more generally, any quantity of energy) extends into the space around itself.
The gradient theorem, also known as the fundamental theorem of calculus for line integrals, says that a line integral through a gradient field can be evaluated by evaluating the original scalar field at the endpoints of the curve. The theorem is a generalization of the second fundamental theorem of calculus to any curve in a plane or space (generally n-dimensional) rather than just the real line. For φ : U ⊆ Rn → R as a differentiable function and γ as any continuous curve in U which starts at a point p and ends at a point q, then where ∇φ denotes the gradient vector field of φ.
Telekinesis () is a hypothetical psychic ability allowing a person to influence a physical system without physical interaction. Experiments to prove the existence of telekinesis have historically been criticized for lack of proper controls and repeatability. There is no reliable evidence that telekinesis is a real phenomenon, and the topic is generally regarded as pseudoscience. There is a broad scientific consensus that telekinetic research has not produced a reliable demonstration of the phenomenon.
The course gives (1) a review of different types of numerical models of control of locomotion and movement in animals, (2) a presentation of different techniques for designing models, and (3) an analy
Aborder, formuler et résoudre des problèmes de physique en utilisant des méthodes numériques simples. Comprendre les avantages et les limites de ces méthodes (stabilité, convergence). Illustrer différ
Students have the opportunity to apply their knowledge in a project contributing to specialize them in a physics field. The project can take place in a laboratory at EPFL, in an external laboratory or