# Irodov Solutions : Problem 3.1

Calculate the ratio of the electrostatic to gravitational interaction forces between two electrons, and between two protons. At what value of specific charge q/m of a particle would these forces become equal (in magnitude) in the case of interaction of identical particles?

Let's consider two charged particles having charges q₁ and q₂ and masses m₁ and m₂ respectively kept fixed at a distance r from each other as shown below in the drawing. The expressions for the mutual electrostatic and gravitational interactions can be written by using the Coulomb's Law and the Newton's Law of Gravitation respectively.

### Remarks

⌲ The ratio of electrostatic to gravitational force for two charged particles is independent of the separation r between them.

⌲ The electrostatic force of repulsion between two electrons is nearly 4 × 10⁴² times stronger in magnitude than the gravitational force of attraction between them.

⌲ The electrostatic force of repulsion between two protons is nearly 1 × 10³⁶ times stronger in magnitude than the gravitational force of attraction between them.

⌲ Gravitational force is of zero importance as far as the interactions of elementary particles are concerned. In general, the electrostatic force is stronger than the gravitational force.
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