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The total electric potential energy is .
Electric Potential Energy of a System of Charges :
The system's electric potential energy is equal to the amount of work necessary to create a system of charges by guiding them toward their designated locations from infinity against the electrostatic force without accelerating them. The symbol for it is U.U=W=qV. Electrostatic fields are conservative, therefore the work is independent of the path.
Assume three charges q₁ , q₂ and q₃ bring from infinity to point P.
To bring q₁ no work is done,
where, V = electric potential energy.
q = point charge.
r = distance between any point around the charge to the point charge.
k = Coulomb constant; k = 9.0 × 109 N.
Now bring q₂,
Work done by q₁ ;
Now bring q₃,
Work done on q₃ by q₁ and q₂
This work done is stored in the form of potential energy.
∴U=W= potential energy of three systems.
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