The unit of permittivity in free space `epsilon_(0)` is:

Options

A. `"coulomb"/"newton-metre"`
B. `"newton-metre"^(2)/"coulomb"^(2)`
C. `"coulomb"^(2)/"newton-metre"^(2)`
D. `"coulomb"^(2)/("newton-metre")^(2)`

Explanation

To determine the unit of permittivity in free space, denoted as \( \epsilon_0 \), we can derive it from the formula for the electrostatic force between two point charges. Let's break down the steps:

### Step-by-Step Solution

1. **Start with Coulomb's Law**:
The electrostatic force \( F \) between two point charges \( q_1 \) and \( q_2 \) separated by a distance \( r \) is given by:
\[ F = \frac{1}{4 \pi \epsilon_0} \frac{q_1 q_2}{r^2} \]

2. **Rearrange the Formula**:
To find \( \epsilon_0 \), we can rearrange the formula to isolate it:
\[ \epsilon_0 = \frac{q_1 q_2}{F \cdot r^2} \cdot \frac{1}{4 \pi} \]
For simplicity, we can ignore the \( \frac{1}{4 \pi} \) factor for unit analysis, focusing on the main components.

3. **Identify the Units**:
- The unit of charge \( q \) is Coulombs (C).
- The unit of force \( F \) is Newtons (N).
- The unit of distance \( r \) is meters (m).

4. **Substituting the Units**:
Substitute the units into the rearranged formula:
\[ \epsilon_0 = \frac{(C)(C)}{(N)(m^2)} = \frac{C^2}{N \cdot m^2} \]

5. **Final Unit of Permittivity**:
Therefore, the unit of permittivity in free space \( \epsilon_0 \) is:
\[ \epsilon_0 = \frac{C^2}{N \cdot m^2} \]

### Conclusion
The unit of permittivity in free space \( \epsilon_0 \) is \( \frac{C^2}{N \cdot m^2} \).