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Inverse-square laws are fundamental in physics, describing how certain physical quantities diminish in intensity as the distance from the source increases. Coulomb's law and Newton's law of gravitation are quintessential examples of inverse-square laws, both asserting that the force between two bodies weakens as the square of the distance between them grows. To visualize this, imagine the surface of a sphere: as the radius of the sphere doubles, its surface area quadruples, hence the same amount of force or flux disperses over a larger area, reducing its intensity on any given point of the sphere by a factor of four.

In the context of these laws, this relationship can be mathematically expressed by the formulas: \( F = k \frac{q_1 q_2}{r^2} \) for Coulomb's law, where \( F \) is the electric force, \( k \) is Coulomb's constant, \( q_1 \) and \( q_2 \) are the charges, and \( r \) is the distance between them; and by \( F = G \frac{m_1 m_2}{r^2} \) for Newton's law of gravitation, where \( F \) is the gravitational force, \( G \) is the gravitational constant, and \( m_1 \) and \( m_2 \) are the masses. Understanding this concept aids in grasping why the force decreases so drastically with increased distance, which is why satellites can orbit Earth without being pulled down by gravity immediately.

Electric force is a fundamental aspect of Coulomb's law, governing the interactions between particles with electric charge. Charged particles exert force on one another, and this force can be attractive or repulsive depending on the nature of the charges involved: like charges repel, while opposite charges attract. The magnitude of the electric force depends not only on the amount of charge but also on the distance between the charges, following the inverse-square law.

The force remains consistent with the formula \( F = k \frac{q_1 q_2}{r^2} \), where each symbol has a specific meaning integral to understanding electric force. 'F' stands for force, 'k' is a proportionality constant known as Coulomb's constant (approximately \( 8.987 \times 10^9 N m^2/C^2 \)), 'q_1' and 'q_2' represent the charges of the interacting particles, and 'r' is the distance between the charges. Learners often find it helpful to consider imaginary scenarios, such as two electrons placed at a certain distance from each other, and predict they would repel due to their like charges, exemplifying electric force at work.

In contrast to the electric force, the gravitational force is always attractive and it is what keeps our feet firmly on the ground as well as the planets in orbit. Described by Newton's law of gravitation, this force acts between any two masses in the universe, regardless of their size. It may seem less apparent to us than electrical forces because of its relative weakness; however, at the scale of planets and stars, it's the dominant force.

Newton's law is encapsulated by the equation \( F = G \frac{m_1 m_2}{r^2} \), where 'F' indicates the gravitational force, 'G' represents the gravitational constant (\( 6.674 \times 10^{-11} N m^2/kg^2 \)), 'm_1' and 'm_2' are the masses of the two objects, and 'r' is the distance between their centers. The universality of gravity offers an excellent foundation for understanding celestial motions and phenomena such as tides on Earth. It's also critical to realize that although the force is weak compared to electric force, it acts over much larger distances and is always additive due to the exclusively positive nature of mass.