Why do we need to square the separation in Coulomb's experiment?

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Coulomb's experiment demonstrates that the electrical force between two charges is inversely proportional to the square of the distance separating them, represented mathematically as 1/r². This relationship arises from the nature of how forces diminish with distance in three-dimensional space. Additionally, the force is directly proportional to the product of the magnitudes of the charges involved, represented as Q1Q2, which reflects the fundamental interaction between charged particles. Understanding these principles is essential for grasping the behavior of electric forces in physics. The discussion emphasizes the need for these mathematical relationships to accurately describe physical reality.
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Coulomb experiment torsion balance.

I know that electrical force is inversely to the square of the separation r ...My question is why we take r square? why we need square? And another question, why Q1Q2(multiplication of charges) is proportional to electrical force? (why we need to multiply them?) I know it sounds like silly question..but I really want to know (my teacher didn't tell me anything .he told me "just remember the formula" )

Thank you in advance! :D
 
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The answer is because if we measure the force as a function of distance it is proportional to 1/r^2. Similarly if we measure the force as a function of charge it is proportional to q. Since we want the equations to match reality, that's what they look like.
 

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