Why in coulomb's law for charges force is inversely proportional to square of distance between charges?

Answer 1

Imagine a light bulb in the center of a sphere. It emits a fixed quantity of light. That's how much light will reach the sphere. The concentration of light per unit of area, on the sphere, will depend upon how large the sphere is. And the area of a sphere is proportional to the square of the radius of the sphere. So the intensity of the light will be inversely proportional to the square of the distance which it has to travel. It is effectively illuminating a larger sphere (even if there is no actual sphere, the principle remains the same).

Answer 2

The inverse square law in Coulomb's law results from the spread of electrical field lines in three-dimensional space. As the distance between charges increases, the field lines originating from one charge become distributed over the surface area of an expanding sphere. This results in the density of field lines decreasing as the square of the distance, leading to the force between charges decreasing proportionally.