Electric potential energy, or electrostatic potential energy, is a potential energy (measured in joules) that results from conservative Coulomb forces and is associated with the configuration of a particular set of point charges within a defined system. Not to be confused with the term electric potential (measured in volts), the term "electric potential energy" is used to describe the potential energy in systems with electric fields that change with time (time variant), while the term "electrostatic potential energy" is used to describe the potential energy in systems with electric fields that do not change with time (time invariant).
Contents
[hide] 1 Definition 1.1 One point charge
1.2 Many point charges
2 Electrostatic potential energy stored in a configuration of discrete point charges 2.1 One point charge
2.2 Two point charges
2.3 Three or more point charges
3 Energy stored in an electrostatic field distribution
4 Energy in electronic elements
5 References
[edit] Definition
The reference zero is usually taken to be a state in which the individual point (test) charges are very well separated ("are at infinite separation") and are at rest.[1]:§25-1
[edit] One point charge
For one point charge q in the presence of an electric field E due to another point charge Q, the electric potential energy is defined as the negative of the work done to bring it from the reference position rref to some position r: mathematically this is a line integral.[2] The field is conservative, and, for one point charge, radial, so it is path independent and equal to the difference in potential between the two endpoints the charge has moved. Mathematically:
where:
r = position in 3d space, using cartesian coordinates r = (x, y, z), r = |r| is the magnitudes of the position vector,
is the work done to bring the charge from the reference position rref to r,
F = force exerted on charge q by Q,
E = electric field due to Q.
Usually UE is set to zero when rref is infinity:
so
Since E and therefore F, and r, are all radially directed from Q, F and dr must be antiparallel and so
using Coulomb's law:
allows the integral to easily be evaluated:
Sometimes the factor ke called Coulomb's constant is used in these expressions. In SI units, the Coulomb constant is given by
,
in turn is the electric constant.
[edit] Many point charges
The electric potential energy of a system, UE, relative to the chosen zero of potential (position where potential is zero), is defined equal to the total work W that must be done by a hypothetical external agent to bring the charges slowly, one by one, from infinite separation, to the stated system configuration.
In this process the external agent provides or absorbs any relevant work, and the point charge being slowly moved gains no kinetic energy. Sometimes reference is made to the potential energy of a charge in an electrostatic field. This actually refers to the potential energy of the system containing the charge and the other charges that created the electrostatic field.[1]:§25-1
Electrical energy is energy newly derived from electrical potential energy. When loosely used to describe energy absorbed or delivered by an electrical circuit (for example, one provided by an electric power utility) "electrical energy" refers to energy which has been converted from electrical potential energy. This energy is supplied by the combination of electric current and electrical potential that is delivered by the circuit. At the point that this electrical potential energy has been converted to another type of energy, it ceases to be electrical potential energy. Thus, all electrical energy is potential energy before it is delivered to the end-use. Once converted from potential energy, electrical energy can always be described as another type of energy (heat, light, motion, etc.).
To calculate the work required to bring a point charge into the vicinity of other (stationary) point charges, it is sufficient to know only (a) the total field generated by the other charges and (b) the charge of the point charge being moved. The field due to the charge being moved and the values of the other charges are not required. Nonetheless, in many circumstances it is mathematicall
الرئيسية 
