Two charged particles are placed at a distance 1.0 cm apart. What is the minimum possible magnitude of the electric force acting o each charge?

Options

A. `2.3 xx 10^(-24) N`
B. `6.2 xx 10^(-34)N`
C. `1.02 xx 10^(-26)N`
D. `4.2 xx 10^(-27)N`

Answer

To find the minimum possible magnitude of the electric force acting on each charge when two charged particles are placed at a distance of 1.0 cm apart, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Problem**: We need to calculate the electric force between two charged particles that are 1.0 cm apart. The minimum possible magnitude of the electric force occurs when both charges are at their smallest possible value.

2. **Identifying the Charge**: According to the principle of quantization of charge, the smallest unit of charge is the elementary charge (e), which is approximately \(1.6 \times 10^{-19}\) coulombs. Therefore, we can assume both charges are equal to \(e\).

3. **Using Coulomb's Law**: The electric force \(F\) between two point charges can be calculated using Coulomb's law, which is given by the formula:
\[ F = k \frac{q_1 \cdot q_2}{r^2} \]
where:
- \(F\) is the electric force,
- \(k\) is Coulomb's constant (\(8.99 \times 10^9 \, \text{N m}^2/\text{C}^2\)),
- \(q_1\) and \(q_2\) are the magnitudes of the charges,
- \(r\) is the distance between the charges.

4. **Substituting Values**: In our case, both charges are \(q_1 = q_2 = e = 1.6 \times 10^{-19} \, \text{C}\) and the distance \(r = 1.0 \, \text{cm} = 0.01 \, \text{m}\). Thus, we can substitute these values into the formula:
\[ F = k \frac{(1.6 \times 10^{-19}) \cdot (1.6 \times 10^{-19})}{(0.01)^2} \]

5. **Calculating the Force**:
- First, calculate \( (1.6 \times 10^{-19})^2 \):
\[ (1.6 \times 10^{-19})^2 = 2.56 \times 10^{-38} \]
- Then, calculate \( (0.01)^2 \):
\[ (0.01)^2 = 1.0 \times 10^{-4} \]
- Now, substitute these values into the force equation:
\[ F = (8.99 \times 10^9) \frac{2.56 \times 10^{-38}}{1.0 \times 10^{-4}} \]
- Simplifying this gives:
\[ F = (8.99 \times 10^9) \cdot (2.56 \times 10^{-34}) = 2.30 \times 10^{-24} \, \text{N} \]

6. **Final Result**: The minimum possible magnitude of the electric force acting on each charge is approximately:
\[ F \approx 2.30 \times 10^{-24} \, \text{N} \]