Force field (physics)
Region of space in which a force acts
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Examples
- 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 Earth's gravity.
- An electric field exerts a force on a point charge q, given by .
- In a magnetic field , a point charge moving through it experiences a force perpendicular to its own velocity and to the direction of the field, following the relation: .
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Work
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.
Conservative force field
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. If these points are given by x = a and x = b, respectively: