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.

Electric Potential energy definition

Electric potential energy can be defined in two ways i.e. by means of electric field and electric potential

Electric potential energy in terms of electric field

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 r to the final position r.


Electric potential energy in terms of electric potential

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 potential energy in terms of electric potential

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.

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