The mutual electrostatic potential energy between two point charges of 12 and 5 microcoulombs, placed 10 cm apart in air, is:

Options

A. 5.4 J
B. 2.8 J
C. 3.6 J
D. 4.8 J

Explanation

To find the mutual electrostatic potential energy between two point charges, we can use the formula:

\[ U = \frac{k \cdot q_1 \cdot q_2}{r} \]

where:
- \( U \) is the electrostatic potential energy,
- \( k \) 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 two charges,
- \( r \) is the distance between the charges.

### Step-by-Step Solution:

1. **Identify the values:**
- \( q_1 = 12 \, \mu C = 12 \times 10^{-6} \, C \)
- \( q_2 = 5 \, \mu C = 5 \times 10^{-6} \, C \)
- \( r = 10 \, cm = 0.1 \, m \)

2. **Substitute the values into the formula:**
\[ U = \frac{9 \times 10^9 \cdot (12 \times 10^{-6}) \cdot (5 \times 10^{-6})}{0.1} \]

3. **Calculate the numerator:**
- First, calculate \( 12 \times 5 = 60 \).
- Then, \( 60 \times 10^{-6} \times 10^{-6} = 60 \times 10^{-12} \).
- Now multiply by \( 9 \times 10^9 \):
\[ 9 \times 60 \times 10^{-12} = 540 \times 10^{-12} = 5.4 \times 10^{-10} \]

4. **Now divide by \( 0.1 \):**
\[ U = \frac{5.4 \times 10^{-10}}{0.1} = 5.4 \times 10^{-9} \, J \]

5. **Convert to joules:**
- Since \( 5.4 \times 10^{-9} \, J \) is already in joules, we can conclude that the potential energy is:
\[ U = 5.4 \, J \]

### Final Answer:
The mutual electrostatic potential energy between the two point charges is **5.4 joules**.