Unizor - Physics4Teens - Electromagnetism - Electrical Field - Coulomb's Law
Channel: Zor Shekhtman on UNIZOR Education
Date: 2020-01-07

Unizor - Physics through a Looking Glass of Mathematician

Just as a thought experiment, imagine two point objects A and B with one excess electron in each e1A and e1B. The object A will repel object B with some strength F. If the number of excess electrons in object A is increased to two (e1A and e2A), the forces of repelling B must be added: one part from e1A to e1B and another from e2A to e1B. So, the repelling force acting on B will be doubled.

Similar arguments used M times for M excess electrons in object A will lead to multiplication of the initial force by M. If we increase the number of excess electrons in object B to N, we will have to multiply our force by N.
As a result, the total force will be proportional to a product M·N.

We know that the unit of electric charge coulomb is proportional to a charge of one electron. More precisely, the charge of 1 electron is 1.602176634·10−19C.
Therefore, if objects A and B have electric charge qA and qB in coulombs, the force of attraction or repelling between them is proportional to qA·qB.

The next variable that should be taken into consideration when examining the force of electric field is the distance between objects. The logic we will use to analyze the dependency of the force on distance is similar to the one we used in case of gravitational field.

Consider a set of tiny springs attached to each electron of the charged object A. Each such spring represents a force developed by one electron.
Obviously, the greater the distance between a probe object B and object A - the smaller is the density of springs in the space. It is intuitively obvious that the force of attraction or repelling acting on object B is proportional to a density of springs in the area where B is located, the less springs are observed where B is - the smaller the force will be and vice versa.

In turn, the density of springs is inversely proportional to a square of a distance from object A because the area of a sphere equals to 4πR2, where R is a radius.

Therefore, the force of an electrical field at a distance R from its source (a charged object) is inversely proportional to a square of R.

Summarizing all the above, we suspect that the force of attraction or repelling between two charged objects with charges qA and qB at a distance R from each other should be proportional to
qA·qB / R²