Electric Charges and Fields

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consider a system of three charges q₁, q₂ and q₃, as shown in given figure.The force on one charge, say q₁, due to two other charges q₂, q₃ can, therefore, be obtained by
performing a vector addition of the forces due to each one of these charges. Thus, if the force on q₁ due to q₂ is denoted by F₁₂, F₁₂ is given by,

In the same way, the force on q₁ due to q₃, denoted by F₁₃, is given by

which again is the Coulomb force on q₁ due to q₃, even though other charge q₂ is present.

The principle of superposition says that in a system of charges q₁, q₂, ..., qn, the force on q₁ due to q₂ is the same as given by Coulomb’s law, i.e., it is unaffected by the presence of the other charges q₃, q₄, ..., qn. The total force F1 on the charge q₁, due to all other charges, is then given by the vector sum of the forces F₁₂, F₁₃, ..., F_1n: