Potential energy

Potential energy
In physics, the potential energy of an object is the energy it has because of its position or orientation relative to a force field. In the case of a system, the potential energy may depend on the arrangement of its component elements. Potential energy can also be seen as the ability of an object (or system) to transform its energy into another form of energy, such as kinetic energy. The term “potential energy” was coined by Rankine in 1853. In the international system, it is measured in joules (J).
An object can store energy as the result of its position relative to other objects, stresses within itself, its electric charge, or other factors. Potential energy is associated with forces that act on a body in a way that the total work done by these forces depends only on the initial and final positions of the body in space. These forces, which are called conservative forces, can be represented at every point in space by vectors expressed as gradients of a certain scalar function called potential.
It is a scalar function of the coordinates of the object in the reference system used. Given a conservative vector field, the potential energy is its capacity to do work: the work relative to a force acting on an object is the line integral of the second kind of force evaluated on the path taken by the object, and if it is conservative the value of this integral does not depend on the type of path followed. When dealing with conservative forces we can define a scalar potential defined in all the space, usually the potential is defined as the potential energy over the variable which is responsible for the force. In particular, from the mathematical point of view this potential exists only if the force is conservative, and it is assumed that for all conservative forces we can always physically define a potential energy.
Potential energy can also be defined for the magnetic field, which is not conservative, in regions where there is no electric current. In such a case, in fact, the rotor of the field is zero. The magnetic potential energy of a magnet in a magnetic field is defined as the work of the magnetic force (the mechanical moment) in realigning the magnetic dipole moment.
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