derive an expression for the electrostatic potential energy of a system of point charge
Answers
I got the answer for system of 3 point charges.
The electrostatic potential energy (U) of a system of point charges is the work required to assemble the charges from infinity to their final positions. The expression for the electrostatic potential energy of a system of point charges is given by:
U = (1/4πε₀) ∑i<j (qi qj / r_ij)
where ε₀ is the permittivity of free space, qi and qj are the magnitudes of the charges, and r_ij is the distance between the ith and jth charges.
The sum ∑i<j indicates that we sum over all pairs of charges only once, since the contribution of the pair of charges (i, j) is equal to the contribution of the pair (j, i).
The factor (1/4πε₀) is a constant of proportionality that depends on the units of charge and distance being used. It is often written as k = 1/(4πε₀), giving the expression:
U = k ∑i<j (qi qj / r_ij)
The expression for the electrostatic potential energy of a system of point charges can be understood as follows. When two charges are brought closer together, they experience a force of attraction or repulsion that depends on their magnitudes and the distance between them. This force can do work as the charges move towards or away from each other. The work done is stored as potential energy in the system. The total potential energy of the system is the sum of the potential energies of all the pairs of charges.
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