If point charges `Q_(1) = 2xx 10^(-7)`C and `Q_(2) = 3 xx 10^(-7)`C are at 30 cm separation, then find electrostatic force between them

Options

A. `2 xx 10^(-3)`N
B. `6 xx 10^(-3)`N
C. `5 xx 10^(-3)`N
D. `1 xx 10^(-3)`N

Explanation

To find the electrostatic force between two point charges \( Q_1 \) and \( Q_2 \) separated by a distance \( R \), 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 electrostatic force,
- \( k \) is Coulomb's constant (\( 9 \times 10^9 \, \text{N m}^2/\text{C}^2 \)),
- \( Q_1 \) and \( Q_2 \) are the magnitudes of the charges,
- \( R \) is the distance between the charges.

### Step-by-Step Solution:

1. **Identify the values:**
- \( Q_1 = 2 \times 10^{-7} \, \text{C} \)
- \( Q_2 = 3 \times 10^{-7} \, \text{C} \)
- Distance \( R = 30 \, \text{cm} = 0.30 \, \text{m} \) (convert cm to m)

2. **Substitute values into the formula:**
\[ F = \frac{9 \times 10^9 \cdot |2 \times 10^{-7} \cdot 3 \times 10^{-7}|}{(0.30)^2} \]

3. **Calculate \( |Q_1 \cdot Q_2| \):**
\[ |Q_1 \cdot Q_2| = 2 \times 10^{-7} \cdot 3 \times 10^{-7} = 6 \times 10^{-14} \, \text{C}^2 \]

4. **Calculate \( R^2 \):**
\[ R^2 = (0.30)^2 = 0.09 \, \text{m}^2 \]

5. **Substitute \( |Q_1 \cdot Q_2| \) and \( R^2 \) back into the formula:**
\[ F = \frac{9 \times 10^9 \cdot 6 \times 10^{-14}}{0.09} \]

6. **Perform the multiplication in the numerator:**
\[ 9 \times 10^9 \cdot 6 \times 10^{-14} = 54 \times 10^{-5} = 5.4 \times 10^{-4} \, \text{N m}^2 \]

7. **Finally, divide by \( 0.09 \):**
\[ F = \frac{5.4 \times 10^{-4}}{0.09} = 6 \times 10^{-3} \, \text{N} \]

### Conclusion:
The electrostatic force between the two point charges is:
\[ F = 6 \times 10^{-3} \, \text{N} \]