Find the value of force for the charges `2xx 10^(-7)`C placed 2m apart?

Options

A. `9 xx 10^(-5)N`
B. `5 xx 10^(-28)N`
C. `2.22 xx 10^(-28)`N
D. `3.5 xx 10^(-28)N`

Explanation

To find the value of the force between two charges, we can use Coulomb's Law, which is given by the formula:

\[ F = \frac{k \cdot |q_1 \cdot q_2|}{r^2} \]

where:
- \( F \) is the force between the charges,
- \( k \) is Coulomb's constant (\( k \approx 9 \times 10^9 \, \text{N m}^2/\text{C}^2 \)),
- \( q_1 \) and \( q_2 \) are the magnitudes of the charges,
- \( r \) is the distance between the charges.

### Step-by-step Solution:

1. **Identify the values**:
- Given \( q_1 = 2 \times 10^{-7} \, \text{C} \)
- Given \( q_2 = 2 \times 10^{-7} \, \text{C} \) (since both charges are the same)
- Given \( r = 2 \, \text{m} \)

2. **Substitute the values into the formula**:
\[ F = \frac{9 \times 10^9 \cdot (2 \times 10^{-7}) \cdot (2 \times 10^{-7})}{(2)^2} \]

3. **Calculate \( (2)^2 \)**:
\[ (2)^2 = 4 \]

4. **Calculate the numerator**:
\[ 9 \times 10^9 \cdot (2 \times 10^{-7}) \cdot (2 \times 10^{-7}) = 9 \times 10^9 \cdot 4 \times 10^{-14} = 36 \times 10^{-5} = 3.6 \times 10^{-4} \]

5. **Now substitute back into the formula**:
\[ F = \frac{3.6 \times 10^{-4}}{4} \]

6. **Calculate the force**:
\[ F = 0.9 \times 10^{-4} = 9 \times 10^{-5} \, \text{N} \]

### Final Answer:
The value of the force is:
\[ F = 9 \times 10^{-5} \, \text{N} \]