What is the smallest electric force between two charges placed at a distance of `1.0m`?

Options

A. `2.304xx10^-25N`
B. `4.4xx10^-28N`
C. `2.304xx10^-28N`
D. `4.4xx10^-25N`

Explanation

To find the smallest electric force between two charges placed at a distance of 1.0 m, we can use Coulomb's Law, which states that the electric force \( F \) between two point charges \( Q_1 \) and \( Q_2 \) separated by a distance \( r \) is given by the formula:

\[ F = \frac{1}{4 \pi \epsilon_0} \cdot \frac{Q_1 \cdot Q_2}{r^2} \]

Where:
- \( F \) is the electric force,
- \( Q_1 \) and \( Q_2 \) are the magnitudes of the charges,
- \( r \) is the distance between the charges,
- \( \epsilon_0 \) is the permittivity of free space, approximately \( 8.85 \times 10^{-12} \, \text{C}^2/\text{N m}^2 \).

### Step 1: Identify the smallest charge
The smallest charge known is the elementary charge, which is approximately \( 1.6 \times 10^{-19} \, \text{C} \). Therefore, we can set both charges \( Q_1 \) and \( Q_2 \) to this value for the smallest force calculation.

### Step 2: Substitute values into Coulomb's Law
We will substitute \( Q_1 = 1.6 \times 10^{-19} \, \text{C} \), \( Q_2 = 1.6 \times 10^{-19} \, \text{C} \), and \( r = 1.0 \, \text{m} \) into the formula.

\[ F = \frac{1}{4 \pi \epsilon_0} \cdot \frac{(1.6 \times 10^{-19}) \cdot (1.6 \times 10^{-19})}{(1.0)^2} \]

### Step 3: Calculate the constant
The value of \( \frac{1}{4 \pi \epsilon_0} \) is approximately \( 9 \times 10^9 \, \text{N m}^2/\text{C}^2 \).

### Step 4: Calculate the force
Now, substituting this constant into the equation:

\[ F = 9 \times 10^9 \cdot \frac{(1.6 \times 10^{-19})^2}{1} \]

Calculating \( (1.6 \times 10^{-19})^2 \):

\[ (1.6 \times 10^{-19})^2 = 2.56 \times 10^{-38} \]

Now substituting back into the force equation:

\[ F = 9 \times 10^9 \cdot 2.56 \times 10^{-38} \]

### Step 5: Final calculation
Calculating the final value:

\[ F = 2.304 \times 10^{-28} \, \text{N} \]

Thus, the smallest electric force between two charges placed at a distance of 1.0 m is:

\[ \boxed{2.304 \times 10^{-28} \, \text{N}} \]