In the intricate dance of particles that populate our universe, two fundamental forces reign supreme: the electric force and the gravitational force. These forces dictate the interactions between charged particles and massive bodies, respectively, shaping the very fabric of our reality. But what happens when we compare the strength of these forces between two electrons, those tiny yet enigmatic particles? Join us as we delve into the realm of particle physics to explore the ratio of electric force to gravitational force between two electrons placed at the same distance.

### Understanding the Forces:

Before we dive into the calculations, let’s first understand the nature of the electric and gravitational forces:

**Electric Force (Fe):**This force arises from the interaction between electrically charged particles. Like charges repel each other, while opposite charges attract. The magnitude of the electric force between two point charges is governed by Coulomb’s Law.**Gravitational Force (Fg):**This force arises from the gravitational attraction between masses. Every mass in the universe attracts every other mass, with the magnitude of the gravitational force between two point masses determined by Newton’s Law of Universal Gravitation.

### Calculating the Ratio:

Now, let’s consider two electrons placed at the same distance apart. We’ll calculate the ratio of the electric force to the gravitational force between them.

**Electric Force (Fe):**The electric force between two electrons can be calculated using Coulomb’s Law:

[ Fe = k_e \cdot \frac{{|q_1 \cdot q_2|}}{{r^2}} ]

Where ( k_e ) is Coulomb’s constant (( 8.9875 \times 10^9 \, \text{N m}^2/\text{C}^2 )), ( q_1 ) and ( q_2 ) are the charges of the electrons (which are equal since they’re both electrons), and ( r ) is the distance between them.

**Gravitational Force (Fg):**The gravitational force between two electrons can be calculated using Newton’s Law of Universal Gravitation:

[ Fg = G \cdot \frac{{m_1 \cdot m_2}}{{r^2}} ]

Where ( G ) is the gravitational constant (( 6.674 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 )), ( m_1 ) and ( m_2 ) are the masses of the electrons (which are the same for all electrons), and ( r ) is the distance between them.

### The Ratio:

Now, let’s calculate the ratio of electric force to gravitational force:

[ \text{Ratio} = \frac{{Fe}}{{Fg}} = \frac{{k_e \cdot |q|^2}}{{G \cdot m^2}} ]

Where ( |q| ) is the magnitude of the charge of an electron, and ( m ) is the mass of an electron.

it comes nearly about 10 power 42.

plz try your self for your practice.

### Conclusion:

In conclusion, the ratio of electric force to gravitational force between two electrons placed at the same distance apart is governed by the relative magnitudes of the electric charge and the mass of the electrons. Due to the vastly different strengths of the electric and gravitational forces (with the electric force being much stronger), this ratio is typically extremely large. This disparity in strength underscores the dominance of the electric force at the atomic and subatomic scales, shaping the behavior of charged particles and driving the dynamics of matter in the universe.