Points to Ponder

Why protons stay together in the nucleus despite repelling each other is explained by the strong nuclear force, a third fundamental force. Its effective range is extremely short, about $10^{-14}$ m — the size of a nucleus. Additionally, quantum mechanics prevents electrons from occupying the nucleus, which gives atoms their stable structure.

Both Coulomb force and gravitational force obey the inverse-square law ($\propto 1/r^2$). However, gravity is always attractive, while electric forces can be attractive or repulsive. This allows electric forces to cancel out, making gravity — though much weaker — the dominant force over large scales.

In Coulomb’s law, the constant $k$ could be chosen arbitrarily if charge were defined by it. But in SI units, the ampere (unit of current) is defined via magnetic effects, and the coulomb is derived as $1\ \text{C} = 1\ \text{A} \cdot \text{s}$. Hence $k$ is fixed at approximately $9 \times 10^9\ \text{N m}^2 \text{C}^{-2}$.

The large value of $k$ (and the large size of 1 C) arises because the coulomb is defined from the ampere, which is based on magnetic forces — typically much weaker than electric forces. So 1 A is a reasonable unit for magnetic effects, but 1 C is huge for electric effects.

Additivity of charge is not automatically obvious. It holds because charge is a scalar — it has no direction — so charges simply add algebraically.

Charge is invariant under both rotation and change of reference frame (relative motion). This is not true for all scalars; for example, kinetic energy is a scalar under rotation but changes with reference frame.

Conservation of charge is independent of its scalar nature. Conservation means total charge in an isolated system remains constant over time in a given frame. A scalar may not be conserved (e.g., kinetic energy in an inelastic collision), while a vector can be conserved (e.g., angular momentum).

Quantisation of charge is a fundamental, unexplained law of nature. Interestingly, there is no analogous quantisation of mass.

The superposition principle is not just vector addition. It asserts two things: (a) the force between two charges is unaffected by other charges, and (b) there are no extra three-body or four-body forces that appear only when more than two charges are present. …