The elementary charge sets the strength of electric interactions between charged particles. Changing it opens up a wide range of possible simulations that explore how electricity, chemistry and atomic structure would behave in different universes.

The elementary charge e has a value of ≈ 1.602×10⁻¹⁹ coulombs. All electrical charges of stable objects are integer multiples (...−1e, 0e, 1e...) of the elementary charge. Quarks have charges that are multiples of 1/3 e but they can only appear as groups with a total charge that is indeed an integer multiple of e. As a result, we define the elementary charge as e, and objects as stable things with a charge of an integer multiple of the elementary charge.

Coulomb’s force describes the force between two electrically charged stationary objects. It can be either attractive (different charges) or repulsive (same charges). In scalar form the force is given by

where r₀ is the distance between the charges and q₁ and q₂ are the magnitudes of the charges. q₁q₂ can be either positive (F is repulsive) or negative (F is attractive).

The electron has a charge of negative one elementary charge and the proton has a charge of positive one elementary charge. The magnitude of the Coulomb force between an electron and a proton is

where qₑ is the elementary charge. The Coulomb force between two charged objects is proportional to the square of the elementary charge. In a situation where the objects in question have a larger charge, the same proportionality applies. For example the Coulomb force between two objects that have the charges of 10qₑ and −6qₑ would be

Changing the elementary charge to be k·qₑ where k >0, the Coulomb force changes in proportion to k².

Electric fields form around charged objects exerting a force on other charged objects. An electric field is defined as the force per the charge that is in the field

where q is the charge in the field. The field depends only on the source charge. The magnitude of the electric field of an elementary charge (proton) is

The magnitude of the field is directly proportional to the elementary charge.

The Bohr radius is inversely proportional to the square of the elementary charge:

As the charge increases the force between the nucleus and the electron increases as well, pulling the electron closer. In the opposite situation the elementary charge gets smaller and the electron obtains a further Bohr radius.

The energy levels of the hydrogen atom are expressed as

where n is the number of the energy level, m is the mass of the electron and qₑ is the elementary charge. The energy levels are proportional to the fourth power of the elementary charge. If the elementary charge increased it would take a lot more energy to for example ionise the hydrogen atom.

Would changing the elementary charge change our everyday life in any way?  Would turning on electricity in our houses produce unexpected results?

Let’s look at a circuit of a standard light bulb plugged into a regular socket. There is a certain voltage over the light bulb determined by external factors, and the circuit as well as the light bulb have some resistance. The current that goes through the light bulb (more specifically the cross section of the light bulb’s filament) is

where Q is the electric charge that goes through in the time interval. According to Ohm’s law, the relation between voltage, current and resistance is

where U is the voltage across the conductor in volts (V), R is the resistance of the conductor in ohms (Ω) and I is the current going through the conductor, in amperes (A).

 Changing the value of the elementary charge only slightly will not affect the household scale of electricity usage. Assuming that the electric potential available will not change, i.e. the electric potential difference from the socket remains the same, the current will also remain at its initial value if the resistance is not altered.

However, changing the elementary charge would set a new limit for the lowest non-zero current possible. For example, if the elementary charge became three times its initial value, those 3·qₑ chunks would be the smallest non-zero electrical charges to go through the cross section of the conductor at a time. Increasing the elementary charge a lot would lead to a situation where one would need a large electric potential difference to create current.