The significance of coulomb's law goes for beyond the description of the force acting b/w charged spheres. This law when incorporated into the structure of quantum physics, correctly described as.
1) The electrical forces that bin the electrons of an atom to its nucleus.
2) The forces that bind atoms together to form molecules.
3) The forces that bind atoms and molecules together to form solids or liquids.
Thus most of the forces of our daily experience that are not gravitational in nature are electrical. Coulomb's law is an exact result for stationary charges and not an approximation for some higher law. It holds not only for ordinary objects but also for the most fundamental " point "particles such as electrons and quarks. Coulomb's law remains valid in the quantum limit ( e.g in calculating the electrostatic forces b/w the proton and the electron in an atom of hydrogen). When charged particles moves at speed close to the speed of light, such as a in a high-energy accelerator. coulomb's law does not give a complete description of their electromagnetic interaction , instead, a more complete analysis based on Maxwell's equations must be done.
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