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The capacity for doing work that arises from position or configuration is called potential energy. 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. Moving an electric charge in a electric field requires or release energy. Such energy is called electric potential energy.
When a free positive charge q is accelerated by an electric field, such as shown in Figure it is given kinetic energy. The process is analogous to an object being accelerated by a gravitational field. It is as if the charge is going down an electrical hill where its electric potential energy is converted to kinetic energy. Let us explore the work done on a charge q by the electric field in this process, so that we may develop a definition of electric potential energy.
Potential Energy is the energy stored within an object which arises from its position relative to others, so electric potential energy is when there is a collection of charges with each exerting a force on another. For example, if an ion,is positively charged then another ion that is also positively charged that comes near it will experience repulsive force and that energy behind the force is called potential energy.
The electric potential energy stored by two charges q1 and q2 a distance r apart is given by Where U is the potential energy.
Electric potential energy can be defined in two ways i.e. by means of electric field and electric potential
The electrostatic potential energy, UE, of one point charge q at position r in the presence of an electric field E is defined as the negative of the work W done by the electrostatic force to bring it from the reference position r to that position r, where E is the electrostatic field and ds is the displacement vector in a curve from the reference position rref to the final position r.
The electric potential energy, UE, of one point charge q at position r in the presence of an electric potential is defined as the product of the charge and the electric potential’s where Φ is the electric potential generated by the charges, which is a function of position r.
Electric potentials are measured in Volts, V. 1V = 1Joule/Coulomb = 1J/C. If a charge Q is at a position where the electric potential is V, then the potential energy of that charge is QxV. (The symbol for electric potential is usually a V and the units are also V; so it can be confusing. I’ll use V for the symbol and V for the unit of Volt.) So 2C of charge at a place where the potential is 6V has a potential energy of 2x6J = 12J. A charge of -3C at a place where the potential is 1.5V has a potential energy of -4.5J.