When physicists cannot write a law in its pure form, using only measured parameters and constants, they introduce coefficients into it. And this is normal practice. But is it possible to do without coefficients that do not carry any physical meaning? Let's try to rewrite two well-known laws using coefficientless expressions.

To do this, recall some electron parameters:

• classic radius:   \(r_ {e} = 2.82 \cdot 10 ^ {- 15} \) (m);
• charge:   \(e = 1.6 \cdot 10 ^ {- 19} \) (C);
• own capacity:   \(C_ {e} = 3.14 \cdot 10 ^ {- 25} \) (F);
• self-inductance:   \(L_ {e} = 2.82 \cdot 10 ^ {- 22} \) (H).

Based on these data, we can deduce the laws of Coulomb and Ampere in a non-coefficient form.

This law determines the strength of the interaction \(F \) between two charges. In private form, this law has been known to us since school and is written in this form: \[F = k {q_1 \, q_2 \over r ^ 2} \qquad (1) \] where \(q_1, q_2 \) is the magnitude of the charges, \(r \) is the distance between them, \(k \) - proportionality coefficient, which is found like this: \(k = 1 / (4 \pi \varepsilon) \). In turn, \(\varepsilon \) is an electrical constant [1]. A more general form of this law can be found here [2].

From the point of view of the previously obtained parameters of the electron, we can take a fresh look at this law: \[F = {r_e \over C_e} {q_1 \, q_2 \over r ^ 2} \qquad (2) \] From a new point of view, it turns out that the interaction between charges is provided by the capacity of the electron and its size, and, if other charged particles are found in the future, then the force of interaction between them will be proportional to their radius and inversely proportional to their own capacity.

In a more general vector form, Coulomb's law can now be written as follows: \[\vec F_ {12} = {r_e \over C_e} {q_1 \, q_2 \over r ^ 2_ {12}} {\vec r_ {12} \over r_ {12}} \qquad (3) \] Here: \(\vec F_ {12} \) is the force with which charge 1 acts on charge 2, \(\vec r_ {12} \) - radius vector directed from charge 1 to charge 2, and equal in absolute value to the distance between charges: \(| \vec r_ {12} | = r_ { 12}\).

This law determines the force of interaction \(F \) between two conductors with current. In its form of notation, it is very similar to the previous one: \[F = {\mu \over 4 \pi} {I_1 \, I_2 \over r} 2 \ell \qquad (4) \] where \(\mu \) is the magnetic constant [4], \(I_1 \, I_2 \) are the currents passing through the conductors, \(r \) is the distance between them, \(\ell \) - the length of the conductors. A more general form of this law can be found here [3].

Applying a new approach, Ampere's law can now be written like this: \[F = {L_e \over r_e} {I_1 \, I_2 \over r} 2 \ell \qquad (5) \] A new point of view on this law assumes that the interaction between conductors with current occurs due to the inductance of the elementary charges that form this current, and the size of the electron itself. The force of interaction between conductors with current is directly proportional to the electron's own inductance and inversely proportional to its radius.

It seems to the authors that this form of recording these laws is more relevant, since each term of the formulas describing them carries a physical meaning.