The electrical force that one electric charge exerts on anot

The electrical force that one electric charge exerts on another is proportional to the product of their charges—that is,
F1 on 2 proportional q1q2. How would Columb\'s observations be different if the force were proportional to the sum of their charges (q1+q2)?

Solution

according to Columb\'s law, we ahve

                 F₁₂ = q₁q₂/r²

from the above relation, the force is directly proportional to product of the charges q₁ and q₂.

if the force is directly proportional to sum of the charges q₁ and q₂, the Columb\'s law becomes as follows:

        F₁₂ = [q₁+q₂]² / r²