Potential energy of a system of charges

Potential energy of a 

system of charges 

 

1) Potential energy of a system of two point charges:

1) Suppose there is a charge q₁ with position vector 

2) Now a new charge q₂ is bring closour to a position with position vector 

3) Now is the distance between the point charges  q₁ and q₂.

4) then electrostatic potential at q₂ due to charge q₁ is

5) the potential energy on charge q₂ is

Potential energy  = potential × charge

Or

This the potential energy of the system of two charges.

 

2) Potential energy of a system of three point charges:

1) Suppose there are three point charges q_1, q_2, & q₃, and their position vectors

r_1, r_2, & r₃ respectively.

2) Then potential energy of the system is

 3) Potential energy of a system of four point charges:

1) Suppose there have four charges q_1, q_2, q₃ & q₄ with their position vectors

r_1, r_2, r₃ & r₄.

2) then the potential energy of the system is