1. Understand the Concepts
* Coulomb's Law: This law describes the electrostatic force between two charged objects. It states:
* The force is directly proportional to the product of the charges.
* The force is inversely proportional to the square of the distance between the charges.
* Charge of an Electron: The charge of an electron is -1.602 x 10^-19 Coulombs (C).
2. Set Up the Equation
Coulomb's Law is represented by the equation:
```
F = k * (q1 * q2) / r^2
```
Where:
* F is the force between the charges
* k is Coulomb's constant (approximately 8.98755 x 10^9 N⋅m^2/C^2)
* q1 and q2 are the magnitudes of the charges
* r is the distance between the charges
3. Convert Units
* The distance, 1 micrometer, needs to be converted to meters: 1 micrometer = 1 x 10^-6 meters
4. Plug in the Values
```
F = (8.98755 x 10^9 N⋅m^2/C^2) * ( -1.602 x 10^-19 C) * (-1.602 x 10^-19 C) / (1 x 10^-6 m)^2
```
5. Calculate
```
F ≈ 2.30 x 10^-17 N
```
Conclusion
The force between two electrons separated by 1 micrometer is approximately 2.30 x 10^-17 Newtons. This force is repulsive because both electrons have the same negative charge.
