Electric potential energy

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. An object may have electric potential energy by virtue of two key elements: its own electric charge and its relative position to other electrically charged objects. U E ( r ) = − W r r e f → r = − ∫ r r e f r q E ( r ′ ) ⋅ d r ′ {displaystyle U_{mathrm {E} }(mathbf {r} )=-W_{r_{ m {ref}} ightarrow r}=-int _{{mathbf {r} }_{ m {ref}}}^{mathbf {r} }qmathbf {E} (mathbf {r'} )cdot mathrm {d} mathbf {r'} } , U E ( r ) = q Φ ( r ) {displaystyle U_{mathrm {E} }(mathbf {r} )=qPhi (mathbf {r} )} , U E ( r ) = k e q Q r {displaystyle U_{E}(r)=k_{e}{frac {qQ}{r}}} ,The electrostatic force F acting on a charge q can be written in terms of the electric field E as U E ( r ) = k e q ∑ i = 1 n Q i r i {displaystyle U_{E}(r)=k_{e}qsum _{i=1}^{n}{frac {Q_{i}}{r_{i}}}} , U E = 1 2 ∑ i = 1 N q i Φ ( r i ) = 1 2 k e ∑ i = 1 N q i ∑ j = 1 N ( j ≠ i ) q j r i j {displaystyle U_{mathrm {E} }={frac {1}{2}}sum _{i=1}^{N}q_{i}Phi (mathbf {r} _{i})={frac {1}{2}}k_{e}sum _{i=1}^{N}q_{i}sum _{j=1}^{N(j eq i)}{frac {q_{j}}{r_{ij}}}} ,    (1)The electrostatic potential energy UE stored in a system of two charges is equal to the electrostatic potential energy of a charge in the electrostatic potential generated by the other. That is to say, if charge q1 generates an electrostatic potential Φ1, which is a function of position r, thenUsing the formula given in (1), the electrostatic potential energy of the system of the three charges will then be:One may take the equation for the electrostatic potential energy of a continuous charge distribution and put it in terms of the electrostatic field.One may assemble charges to a capacitor in infinitesimal increments, d q → 0 {displaystyle dq o 0} , such that the amount of work done to assemble each increment to its final location may be expressed as 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. An object may have electric potential energy by virtue of two key elements: its own electric charge and its relative position to other electrically charged objects. The term 'electric potential energy' is used to describe the potential energy in systems with time-variant electric fields, while the term 'electrostatic potential energy' is used to describe the potential energy in systems with time-invariant electric fields.