1. Coulomb's Law
The force between two point charges is described by Coulomb's Law:
* F = k * (q₁ * q₂) / r²
Where:
* F is the force (in Newtons)
* k is Coulomb's constant (approximately 8.98755 × 10⁹ N⋅m²/C²)
* q₁ and q₂ are the magnitudes of the charges (in Coulombs)
* r is the distance between the charges (in meters)
2. Charge of an Electron
The charge of an electron is approximately -1.602 × 10⁻¹⁹ Coulombs. Since we're dealing with repulsion, the magnitudes of the charges are positive.
3. Solving for Distance
We need to rearrange Coulomb's Law to solve for 'r':
* r² = k * (q₁ * q₂) / F
* r = √(k * (q₁ * q₂) / F)
4. Calculation
Plug in the values:
* r = √((8.98755 × 10⁹ N⋅m²/C²) * (1.602 × 10⁻¹⁹ C)² / 12 N)
* r ≈ 1.04 × 10⁻¹⁰ meters
Therefore, the two electrons are approximately 1.04 × 10⁻¹⁰ meters (or 0.104 nanometers) apart.
Important Note: This calculation assumes the electrons are treated as point charges, which is a simplification. In reality, the distribution of charge within an electron is more complex.
