The force of attractions between two charges `8muC` and `-4muC` is 0.2 N. Find the distance of separation.

Options

A. 1.2 m
B. 12 m
C. 120 m
D. 0.12 m

Explanation

To solve the problem of finding the distance of separation between two charges using Coulomb's Law, we can follow these steps:

### Step-by-Step Solution:

1. **Understand Coulomb's Law**:
Coulomb's Law states that the force \( F \) between two point charges \( q_1 \) and \( q_2 \) separated by a distance \( r \) is given by:
\[ F = k \frac{|q_1 \cdot q_2|}{r^2} \]
where \( k \) is Coulomb's constant, approximately \( 9 \times 10^9 \, \text{N m}^2/\text{C}^2 \).

2. **Identify the Given Values**:
- \( q_1 = 8 \, \mu C = 8 \times 10^{-6} \, C \)
- \( q_2 = -4 \, \mu C = -4 \times 10^{-6} \, C \)
- \( F = 0.2 \, N \)

3. **Substitute the Values into Coulomb's Law**:
Substitute the known values into the equation:
\[ 0.2 = 9 \times 10^9 \cdot \frac{|8 \times 10^{-6} \cdot (-4) \times 10^{-6}|}{r^2} \]
Since we are interested in the magnitude, we can ignore the negative sign for the purpose of calculating force:
\[ 0.2 = 9 \times 10^9 \cdot \frac{32 \times 10^{-12}}{r^2} \]

4. **Rearranging the Equation**:
Rearranging the equation to solve for \( r^2 \):
\[ r^2 = 9 \times 10^9 \cdot \frac{32 \times 10^{-12}}{0.2} \]

5. **Calculating the Right Side**:
Calculate \( 9 \times 10^9 \cdot 32 \times 10^{-12} \):
\[ 9 \times 32 = 288 \]
So,
\[ 9 \times 10^9 \cdot 32 \times 10^{-12} = 288 \times 10^{-3} = 0.288 \]
Now divide by \( 0.2 \):
\[ r^2 = \frac{0.288}{0.2} = 1.44 \]

6. **Finding \( r \)**:
Taking the square root to find \( r \):
\[ r = \sqrt{1.44} = 1.2 \, \text{m} \]

7. **Convert to Centimeters**:
Convert meters to centimeters:
\[ r = 1.2 \, \text{m} = 120 \, \text{cm} \]

### Final Answer:
The distance of separation between the charges is \( 120 \, \text{cm} \).