Two charges each equal to `2mu C` are o.5 m apart. If both of them exist inside vacuum, then the force between them is

Options

A. 1.89 N
B. 2.44 N
C. 0.144 N
D. 3.144 N

Answer

To find the force between two charges using Coulomb's law, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Charge \( Q_1 = 2 \, \mu C = 2 \times 10^{-6} \, C \)
- Charge \( Q_2 = 2 \, \mu C = 2 \times 10^{-6} \, C \)
- Distance \( r = 0.5 \, m \)

2. **Coulomb's Law Formula:**
The formula for the electrostatic force \( F \) between two charges is given by:
\[ F = k \frac{Q_1 Q_2}{r^2} \]
where \( k \) is Coulomb's constant, approximately \( 9 \times 10^9 \, N \, m^2/C^2 \).

3. **Substitute the Values:**
Substitute the values of \( Q_1 \), \( Q_2 \), \( r \), and \( k \) into the formula:
\[ F = 9 \times 10^9 \frac{(2 \times 10^{-6})(2 \times 10^{-6})}{(0.5)^2} \]

4. **Calculate \( r^2 \):**
Calculate \( (0.5)^2 \):
\[ (0.5)^2 = 0.25 \, m^2 \]

5. **Calculate the Numerator:**
Calculate \( (2 \times 10^{-6})(2 \times 10^{-6}) \):
\[ (2 \times 10^{-6})^2 = 4 \times 10^{-12} \, C^2 \]

6. **Combine the Values:**
Now substitute back into the formula:
\[ F = 9 \times 10^9 \frac{4 \times 10^{-12}}{0.25} \]

7. **Simplify the Fraction:**
Calculate \( \frac{4 \times 10^{-12}}{0.25} \):
\[ \frac{4 \times 10^{-12}}{0.25} = 16 \times 10^{-12} \, C^2/m^2 \]

8. **Calculate the Force:**
Now multiply:
\[ F = 9 \times 10^9 \times 16 \times 10^{-12} \]
\[ F = 144 \times 10^{-3} \, N \]

9. **Convert to Standard Form:**
Convert \( 144 \times 10^{-3} \, N \) to standard form:
\[ F = 0.144 \, N \]

### Final Answer:
The force between the two charges is \( 0.144 \, N \).

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