In coulomb's law, on what factors does the value of electrostatic force constant K depend ?

Options

A. nature of medium
B. system of units
C. intensity of charge
D. both (a) and (b)

Explanation

To determine the factors on which the value of the electrostatic force constant \( K \) depends in Coulomb's law, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Coulomb's Law**:
Coulomb's law states that the electrostatic force \( F \) between two point charges \( Q_1 \) and \( Q_2 \) is given by the formula:
\[ F = K \frac{Q_1 Q_2}{R^2} \]
where \( R \) is the distance between the charges and \( K \) is the electrostatic force constant.

2. **Expression for \( K \)**:
The electrostatic force constant \( K \) can be expressed as:
\[ K = \frac{1}{4 \pi \epsilon_0} \]
where \( \epsilon_0 \) is the permittivity of free space.

3. **Understanding Permittivity**:
- The value of \( \epsilon_0 \) is a constant that characterizes the ability of a vacuum (free space) to permit electric field lines.
- The value of \( K \) is specifically \( 9 \times 10^9 \, \text{N m}^2/\text{C}^2 \) in free space.

4. **Effect of Medium**:
- When charges are placed in a medium other than vacuum, the permittivity changes. The permittivity of a medium is denoted as \( \epsilon \) and is related to \( \epsilon_0 \) by:
\[ \epsilon = \epsilon_r \epsilon_0 \]
where \( \epsilon_r \) is the relative permittivity (dielectric constant) of the medium.

5. **Conclusion**:
- Therefore, the value of the electrostatic force constant \( K \) depends on the nature of the medium in which the charges are placed. In free space, it has a specific value, but in other media, it changes according to the permittivity of that medium.

### Final Answer:
The value of the electrostatic force constant \( K \) depends on the **nature of the medium** in which the charges are located.